JP5774475B2 - Apparatus and method for SRC by extracting and synthesizing impulse response - Google Patents

Description

  The present invention relates to an apparatus and method for SRC (Sampling Rate Conversion) for obtaining new data having different specifications such as sampling frequency by conversion from discrete data.

  FIR configured with a finite number of taps for digital signal processing of audio and images as a sampling frequency rate conversion method in a broad sense that can be applied to audio (audio) sampling frequency rate conversion, image resolution conversion or frame rate conversion One using a filter (Finite Impulse Response Filter) is known (for example, see Patent Document 1).

  In some cases, after sampling frequency rate conversion, an output is generated by a plurality of FIR filters corresponding to a plurality of converted frequencies (see Patent Document 2).

JP 2005-217837 A JP 2008-109279 A

  However, in the above-mentioned Patent Document 1, the impulse response constituting the FIR filter is fixedly determined, and for example, linear interpolation is performed between two samples obtained by increasing the sampling frequency rate to an integral multiple. Depending on the frequency conversion rate, which is the ratio of conversion from one frequency to a new frequency, it may take time for conversion and it may be difficult to increase the speed, or the data quality after conversion may be reduced.

  Therefore, an object of the present invention is to provide a sampling frequency rate conversion (SRC) apparatus and method that enable high-speed and high-precision data conversion.

  In order to solve the above problems, an apparatus and method for sampling frequency rate conversion (SRC) based on extraction and synthesis of impulse responses according to the present invention have been developed. The sampling frequency rate conversion described below means a broad meaning unless otherwise specified, and includes various data conversion processes such as resolution conversion or frame rate conversion related to images, etc., in addition to narrow sampling frequency rate conversion. Shall be.

  The sampling frequency rate conversion apparatus according to the present invention provides (a) a conversion value at a time interpolation position corresponding to new data to be obtained by conversion from discrete original data, in accordance with the time interpolation position. Data for calculating a conversion value at the time interpolation position by convolution of the original data using the coefficient preparation means for preparing the filter coefficient based on the discrete impulse response function, and (b) the filter coefficient prepared in the coefficient preparation means. Calculating means. It should be noted that the preparation of the filter coefficient as described above by the coefficient preparation means not only incorporates a circuit or program capable of outputting or operating the filter coefficient but also simply holding the separately prepared filter coefficient in the memory. Is also included.

  In the sampling frequency rate conversion apparatus, the coefficient preparation unit prepares a filter coefficient based on a discrete impulse response function for giving a conversion value at a time interpolation position corresponding to new data, and the data calculation unit calculates the filter. Since the conversion value at the time interpolation position is directly calculated by the convolution operation of the original data using the coefficient, the original data is converted in a very high speed and high quality state, and the sampling frequency rate has different specifications. New data can be obtained.

  Further, in a specific aspect of the present invention, (a) the coefficient preparation unit prepares a coefficient table as a filter coefficient based on the discrete impulse response function, and (b) the data calculation unit includes each data of the coefficient table and the original A conversion value is calculated by a convolution operation with data. In this case, digital data processing using a coefficient table enables extremely high-speed and high-quality data conversion.

  In another aspect of the present invention, the coefficient preparation means converts the conversion values at a series of time interpolation positions set corresponding to the difference between the sampling period for the original data and the sampling period for the new data. The discrete impulse response function is determined so as to give In this case, the sampling frequency is changed from the original data set to a specific sampling frequency to new data set to another sampling frequency by a coefficient filter given based on a group of discrete impulse response functions determined for each time interpolation position. Rate conversion is possible.

  In another aspect of the present invention, an arbitrary wavenumber band is selected by setting a filter coefficient based on a discrete impulse response function. For example, the filter coefficient is set so that a high frequency band equal to or higher than a predetermined value can be cut off. In this case, generation of noise accompanying data conversion can be suppressed.

  In another aspect of the present invention, the coefficient preparation means uses a lower frequency as a reference for cutting off a high frequency band equal to or higher than a predetermined value among the sampling frequency of the original data and the sampling frequency of the new data. In this case, generation of noise due to aliasing or aliasing noise can be suppressed during frequency conversion.

  In another aspect of the present invention, the coefficient preparation means prepares a filter coefficient based on a discrete impulse response function according to a change in a predetermined parameter corresponding to a difference between a discrete point of original data and a time interpolation position. In this case, the filter coefficient based on the discrete impulse response function functions as a non-fixed filter that oscillates or fluctuates due to a change in a predetermined parameter.

  According to another aspect of the present invention, the coefficient preparation unit corrects the filter coefficient based on the discrete impulse response function and the window function. In this case, the discontinuity of the calculated value in the arithmetic processing in which the finite discrete points are extracted can be relaxed by the correction using the window function. The window function can be applied to the discrete impulse response function.

  In another aspect of the present invention, the coefficient preparation means further includes normalization means for normalizing filter coefficients based on the discrete impulse response function. In this case, by performing the normalization process, the information to be processed can be made more reproducible.

  In another aspect of the present invention, new data is generated based on a function that is restored from the original data. In this case, an arbitrary value (in theory, including an irrational number as well as a rational number) can be assigned to the restored function. For example, a time interpolation position corresponding to new data is assigned. Thus, it is possible to obtain new data close to the exact theoretical value.

やその近似式を用いて表現される。この場合、当該数式により、エイリアシングの発生を防止しつつ、元のデータによるアナログ信号の復元を利用することで理論的に厳密な関数に基づいた離散インパルス応答関数の決定が可能となる。In another aspect of the present invention, the function restored from the original data is a function Y (t) at time t, T is the sampling period of the original data, and Y (nT) is the original data and data, the f _s, and the sampling frequency of original data, the f _c, as the value of the smaller of the sampling frequency of the new data and the sampling frequency of original data, the following equation

And its approximate expression. In this case, it is possible to determine a discrete impulse response function based on a theoretically exact function by using the restoration of the analog signal based on the original data while preventing the occurrence of aliasing.

又はｎを有限値とする窓関数を用いた近似式を用いて表現される。この場合、当該所定パラメーターの変化又は変更によって振動又は変動する固定的でないフィルターにより新しいデータが生成される。In another aspect of the present invention, the new data has _Tb as the new data sampling period, Pr as a predetermined parameter corresponding to the difference between the discrete points of the original data and the time interpolation position, Assuming that Pr = n ₀ T−m ₀ T _b is expressed by n ₀ and m ₀ which are both integers,

Alternatively, it is expressed using an approximate expression using a window function with n as a finite value. In this case, new data is generated by a non-fixed filter that vibrates or fluctuates due to a change or change in the predetermined parameter.

  In order to solve the above problems, a sampling frequency rate conversion method according to the present invention provides (a) a conversion value at a time interpolation position corresponding to new data to be obtained by conversion from discrete original data. Therefore, a coefficient preparation step for preparing filter coefficients based on discrete impulse response functions set discretely, and (b) a time interpolation position by convolution calculation of the original data using the filter coefficients prepared in the coefficient preparation step And a data calculation step for calculating a conversion value at.

  In the sampling frequency rate conversion method, a filter coefficient based on a discrete impulse response function for providing a conversion value at a time interpolation position corresponding to new data is prepared in the coefficient preparation step, and the filter is calculated in the data calculation step. Using the coefficient, the conversion value at the time interpolation position is calculated by convolution of the original data, so the original data can be converted at a very high speed to obtain new data in a spectrally high quality state. It becomes possible.

  In a specific aspect of the present invention, (a) in the coefficient preparation step, a coefficient table is prepared as a filter coefficient based on the discrete impulse response function, and (b) in the data calculation step, each data in the coefficient table and the original A conversion value is calculated by a convolution operation with data, and (c) in the coefficient preparation step, a series of time interpolation positions corresponding to the difference between the sampling period for the original data and the sampling period for the new data is calculated. A discrete impulse response function is determined so as to give a converted value.

又はｎを有限値とする窓関数を用いた近似式を用いて表現される。この場合、変換においてエイリアシングによるノイズの発生が抑制され、また、当該所定パラメーターの変化によって振動又は変動する固定的でないフィルターにより新しいデータが生成される。In another aspect of the present invention, the new data has T as the sampling period of the original data, T _b as the sampling period of the new data, Y (nT) as the original data, and f the _s, the sampling frequency of original data, the f _c, a smaller value of the sampling frequency of the new data and the sampling frequency of original data, the Pr, discrete points of the original data and the temporal interpolation position As a predetermined parameter corresponding to the difference between the two, both are integers n ₀ and m ₀ and are expressed as Pr = n ₀ T−m ₀ T _b ,

Alternatively, it is expressed using an approximate expression using a window function with n as a finite value. In this case, generation of noise due to aliasing is suppressed in the conversion, and new data is generated by a non-fixed filter that vibrates or fluctuates due to the change of the predetermined parameter.

It is a block diagram which shows typically the structure of the apparatus of the sampling frequency rate conversion which concerns on 1st Embodiment. (A)-(C) is a figure for demonstrating the production | generation of new data from the original data by the apparatus of sampling frequency rate conversion. It is a figure which shows notionally the signal preparation process by the apparatus of sampling frequency rate conversion. It is a flowchart for demonstrating the process of preparing the coefficient table of a discrete impulse response function based on an impulse response function. It is a flowchart for demonstrating the process of preparing the coefficient table of a discrete impulse response function based on an impulse response function. It is a flowchart for demonstrating the process of preparing the coefficient table of a discrete impulse response function based on an impulse response function. It is a flowchart for demonstrating the process of preparing the coefficient table of a discrete impulse response function based on an impulse response function. It is a flowchart for demonstrating the process of preparing the coefficient table of a discrete impulse response function based on an impulse response function. It is a flowchart for demonstrating the process of calculating a conversion value by the convolution operation using a coefficient table, and outputting new data. It is a flowchart for demonstrating the process of calculating a conversion value by the convolution operation using a coefficient table, and outputting new data. It is a conceptual diagram explaining the structure of the apparatus of the sampling frequency rate conversion which concerns on 2nd Embodiment.

[First Embodiment]
Hereinafter, the sampling frequency rate conversion apparatus according to the first embodiment of the present invention and the principle of data conversion by the sampling frequency rate conversion apparatus will be described with reference to FIGS.

  A signal processing device 10 shown in FIG. 1 is a sampling frequency rate conversion device that converts an original data sequence and outputs a new data sequence with different specifications with respect to the sampling rate. ROM 30 for storing various programs such as processing programs and other information, RAM 40 for temporarily storing and storing information such as sample data to be processed, and for receiving data input from the outside An input interface unit 51 and an output interface unit 52 for transmitting data to the outside are provided.

Here, the original data string Y (nT) input to the signal processing apparatus 10 is audio or other time-series digital data, the sampling frequency is f _s , and the sampling period is T (T = 1 / f _s). ). On the other hand, the output data string Y (mT _b ) is similar digital data, but the sampling frequency is f _b and the sampling period is T _b (T _b = 1 / f _b ). In other words, the signal processing apparatus 10 performs narrow sampling frequency rate conversion, and the original sampling frequency f _s and the new sampling frequency f _b are converted from the original data string Y (nT) by processing using the CPU 20 or the like. Based on the above, a new data string Y (mT _b ) subjected to sampling frequency rate conversion is created. In the above description, n and m are integers.

2A to 2C are diagrams schematically illustrating a state in which a new data string Y (mT _b ) is generated from the original data string Y (nT) in the signal processing device 10. That is, the frequency shown in FIG. 2C is converted from the original discrete data string Y (nT) schematically shown in FIG. 2A through the data processing step in FIG. A new discrete data string Y (mT _b ) is created. Here, as shown in FIGS. 2 (A) to 2 (C), the periods T and T _b (that is, frequencies f _s and f _b ) of both data strings Y (nT) and Y (mT _b ) are different from each other. ing. That is, the signal processing device 10 of FIG. 1, the period before and after the conversion _{T (= 1 / f s)} , corresponding to the difference between _{T b (= 1 / f b} ), the original period T (= 1 / _{f s} It performs processing rate conversion of the sampling period or sampling frequency for the data sequence Y (nT)) of, and create a new period _{T b (= 1 / f b} ) of the data sequence Y (mT _b).

となる。ここで、式（１）のうち、

の部分は、アナログ再生のためのインパルス応答関数である。つまり、復元される関数Ｙ（ｔ）は、連続的な時間ｔの関数であり、標本化入力信号であるデータ列Ｙ（ｎＴ）とインパルス応答関数η（ｔ，ｎ）との積和演算によって再現されている。この関数によるアナログ波再生の手法でサンプリングレート変換のための補間が可能である。本手法の応用による補間の場合には、元の周期Ｔと新たな周期Ｔ_ｂとは異なるため、図２（Ａ）〜２（Ｃ）に示すように、例えば元のデータ列Ｙ（ｎＴ）のｎ_０番目の値に対応する時間即ち離散点ｎ_０Ｔと、新たなデータ列Ｙ（ｍＴ_ｂ）のうち離散点ｎ_０Ｔを最寄りとするｍ_０番目の値に対応して設けられる時間補間位置ｍ_０Ｔ_ｂとには差があり、この差に相当する所定パラメーターである差分補間位置Ｐｒ（図２（Ｂ）参照）を考慮する必要がある。しかし、この再生式そのままの応用による補間であると、エイリアシング発生と折り返し雑音発生との問題があり、再生周波数帯の抑制のための式修正が必要である。このことについては、式（８）以下に説明する。Hereinafter, rate conversion processing of the sampling frequency in the signal processing apparatus 10 will be described. First, with respect to the discrete original data string Y (nT), if the sampling period is T and the sampling frequency, which is the original frequency, is f _s (ie, T = 1 / f _s ) as described above, sampling is performed. The function restored from the original data string Y (nT) that is the input signal is expressed by Shannon's sampling theorem.

It becomes. Here, in formula (1),

Is an impulse response function for analog reproduction. That is, the restored function Y (t) is a function of a continuous time t, and is obtained by multiply-accumulate the data string Y (nT) that is the sampling input signal and the impulse response function η (t, n). It has been reproduced. Interpolation for sampling rate conversion is possible by analog wave reproduction using this function. In the case of interpolation by application of this technique is different from the new period T _b and original period T, as shown in FIG. 2 (A) ~2 (C) , for example, the original data sequence Y (nT) n ₀ th time or discrete points n corresponding to the value _{0 T} and the time provided corresponding to m ₀ th value to the nearest discrete points n _{0 T} of the new data string Y (mT _b) of There is a difference from the interpolation position m ₀ T _b, and it is necessary to consider the difference interpolation position Pr (see FIG. 2B), which is a predetermined parameter corresponding to this difference. However, if interpolation is performed by applying the reproduction formula as it is, there is a problem of aliasing and aliasing, and it is necessary to correct the formula to suppress the reproduction frequency band. This will be described below in Equation (8).

となる。また、ここで、新たなデータ列Ｙ（ｍＴ_ｂ）を算出するために、インパルス応答関数η（ｔ，ｎ）を基にして離散化した離散インパルス応答関数を定める。具体的には、式（２）においてｔ＝Ｐｒとすると、ｎ_０を中心としてｎが正負の方向に変化する離散インパルス応答関数η（Ｐｒ，ｎ）は、

で表される。また、式（３）においても、ｍ_０Ｔ_ｂ＝０とすることはｔ＝Ｐｒとすることであり、

となる。この場合、Ｙ（Ｐｒ）は、離散点ｎ_０Ｔとその前後の離散点ｎＴに対応するデータ列Ｙ（ｎＴ）から求められるものであり、時間補間位置ｍ_０Ｔ_ｂにおける変換値Ｙ（ｍ_０Ｔ_ｂ）を表現するものとなる。また、式（５）のうち、加算要素の式又は値

は、式（４）の離散インパルス応答関数η（Ｐｒ，ｎ）とこれに対応する各データ列Ｙ（ｎＴ）の値とを掛けたもの（以後、離散インパルス応答と呼ぶ）である。これは、図２（Ｂ）に例示されるインパルス応答の各曲線Ｌ１〜Ｌ５のｔ＝ｍ_０Ｔ_ｂ上における上記値即ち離散インパルス応答Ａ（ｎ_０＋δ，Ｐｒ）にそれぞれ相当する（δ＝０，±１，±２）。つまり、上記式（５）から与えられる変換値Ｙ（Ｐｒ）＝Ｙ（ｍ_０Ｔ_ｂ）は、図２（Ｂ）に例示した離散インパルス応答Ａ（ｎ_０＋δ，Ｐｒ）をδについて無限に足し合わせたものに相当する。但し、実際に数値化をするにあたっては、相関性の高い有限個の離散インパルス応答Ａ（ｎ_０＋δ，Ｐｒ）を足し合わせることで変換値Ｙ（Ｐｒ）＝Ｙ（ｍ_０Ｔ_ｂ）を構成している。つまり、例えば式（５）において、まず、データ列Ｙ（ｎＴ）のうちｎ_０番目のデータ列Ｙ（ｎ_０Ｔ）の値を中心とするために、変数をｎ−ｎ_０（＝δ）として、

とする。さらに、ｎ_０番目のデータ値Ｙ（ｎ_０Ｔ）の値を中心として略左右対称に有限となるように、式（６）において、例えば３０個程度の少ない個数について和を取ることで、変換値Ｙ（Ｐｒ）＝Ｙ（ｍ_０Ｔ_ｂ）を、インパルス応答をシフトさせる整数δ（＝ｎ−ｎ_０）を用いて

とすることで、変換値Ｙ（Ｐｒ）＝Ｙ（ｍ_０Ｔ_ｂ）の近似的な値が求められる。Hereinafter, the n ₀ th reference point (corresponding to the discrete points n _{0 T)} of the original data sequence Y (nT), illustrating the generation of the conversion data. Here, it is assumed that the conversion value Y (m ₀ T _b ) of the m ₀ th time interpolation position m ₀ T _b is generated from the new data string Y (mT _b ) with the discrete point n ₀ T as a reference. . First, in this case, as already described with reference to FIG. 2 (B), the difference interpolation position Pr is based on the discrete point n ₀ T which is the nearest point of the time interpolation position m ₀ T _b , Pr = represented by _{n 0 T-m 0 T b} . The value of the differential interpolation position Pr illustrated in FIG. 2B is a negative value for the portion shown in the figure. Here, the conversion value Y (m ₀ T _b ) can be easily obtained by the product-sum operation of the original data string Y (nT) and the impulse response function η (t, n) as already described. In this case, the impulse response function η (t, n) is added with the difference interpolation position Pr. That is, in Equation (1), for example, when t = Pr + m ₀ T _b is substituted with the discrete point n ₀ T as a reference,

It becomes. Here, in order to calculate a new data string Y (mT _b ), a discrete impulse response function discretized based on the impulse response function η (t, n) is determined. Specifically, when t = Pr in the equation (2), the discrete impulse response function η (Pr, n) in which n changes in the positive and negative directions around n ₀ is

It is represented by Also in the formula (3), setting m ₀ T _b = 0 means setting t = Pr.

It becomes. In this case, Y (Pr) is obtained from the data point Y (nT) corresponding to the discrete point n ₀ T and the discrete points nT before and after the discrete point n ₀ T, and the converted value Y (m at the time interpolation position m ₀ T _{b 0} T _b ). Also, among the expressions (5), the expression or value of the addition element

Is a product of the discrete impulse response function η (Pr, n) of the equation (4) and the value of each data string Y (nT) corresponding thereto (hereinafter referred to as a discrete impulse response). This corresponds to the above values on the t = m ₀ T _{b of the} impulse response curves L1 to L5 illustrated in FIG. _2B, that is, the discrete impulse response A (n ₀ + δ, Pr), respectively (δ = 0, ± 1, ± 2). That is, the conversion value Y (Pr) = Y (m ₀ T _b ) given from the above equation (5) is infinite with respect to δ for the discrete impulse response A (n ₀ + δ, Pr) illustrated in FIG. Equivalent to the sum of these. However, in the actual digitization, a converted value Y (Pr) = Y (m ₀ T _b ) is formed by adding together a finite number of discrete impulse responses A (n ₀ + δ, Pr) having high correlation. doing. That is, for example, Equation (5), the first data sequence Y values to the center of (nT) of the _{n 0} th data sequence Y _(n 0 T), the variable _n-n 0 (= [delta]) As

And Furthermore, as a finite substantially symmetrical about the value of n ₀ th data values Y (n 0 _T), in equation (6), by taking the sum for example 30 or so little number, conversion The value Y (Pr) = Y (m ₀ T _b ) is used with an integer δ (= n−n ₀ ) that shifts the impulse response.

Thus, an approximate value of the conversion value Y (Pr) = Y (m ₀ T _b ) is obtained.

As described above, as one converted value of each data string Y (mT _b ), first, reference data corresponding to the converted value is determined from the original data string Y (nT) (as described above). When the m _0th conversion value Y (Pr) = Y (m ₀ T _b ) is obtained, the nearest n _0th data value Y (n ₀ T) corresponds, and this should be defined as a reference. Next, as the differential interpolation position Pr is determined in accordance with this, the discrete impulse response function η (Pr, n) is given from the impulse response function η (t, n), and the original data sequence A conversion value Y (Pr) = Y (m ₀ T _b ) is obtained by convolving Y (nT) and the discrete impulse response function η (Pr, n). That is, the data sequence Y in order to obtain the single conversion value (mT _b) (e.g. _{Y (Pr) = Y (m} 0 T b)) are the conversion value (e.g., _{Y (Pr) = Y (m} 0 T _b )) corresponding to the time interpolation position (for example, m ₀ T _b ), the position of one reference data value (for example, Y (n ₀ T)) in the original data string Y (nT) is determined. And a discrete point that provides the determined data value (for example, Y (n ₀ T)) and a time interpolation position that provides a converted value (for example, Y (Pr) = Y (m ₀ T _b )) It is necessary to set the differential interpolation position Pr.

Here, in the above description, the impulse response function η (t, n) or the portion corresponding to the discrete impulse response function η (Pr, n) made discrete is not fixed as in the prior art, and the differential interpolation position is used. Although it oscillates or fluctuates corresponding to Pr, it is possible to perform digital data processing as in the conventional FIR filter for calculation. Hereinafter, such a method is referred to as a “variable FIR filter”. Further, the deviation amount of time position indicated by the difference interpolation position Pr, as described above, the discrete points nT in the original data as a reference for configuring it and time interpolation position mT _b new data of interest Generally, it is determined by the relationship of the ratio f _s : f _b = N: M between the frequency f _s of the original data and the frequency f _{b of the} new data. As described above, the fluctuating FIR filter is completely different from the existing adaptive filter adapted to the situation of the outside world.

As described above, in the present embodiment, when the discrete impulse response function η (Pr, n) is extracted from the impulse response function η (t, n), the above-described differential interpolation position Pr and the periods T, T _b, Considering the frequencies f _s and f _b and combining the data using such a discrete impulse response function η (Pr, n), it is possible to convert the sampling frequency rate with high speed and high accuracy.

である。この式（８）は、サンプリング周波数レート変換に関する上記式（５）等に適用することができると考えられる。ここでは、式（５）を上記式（８）に基づいて変形するとともに、周波数ｆ_ｃを、ｆ_ｓとｆ_ｂとのうち、小さい方とし、以下の式

からサンプリング周波数レート変換の演算処理を行うものとする。この場合、変動ＦＩＲフィルター用の離散インパルス応答関数η(Ｐｒ，ｎ)は、エイリアシング発生と折り返し雑音発生との防止を可能にする修正式又は値として、

で表され、補間計算式即ち修正された新たな変換値は、ｔ＝Ｐｒとして、

となる。以上から明らかなように、本実施形態の変動ＦＩＲフィルターでは、本来の変換値Ｙ（Ｐｒ）＝Ｙ（ｍ_０Ｔ_ｂ）の一部のｆ_ｓをｆ_ｃに置き換えたものを用いるだけで、アンチエイリアシングのためのローパスフィルターとしての機能も持たせることができ、データ処理の非常な高速化を達成することができる。なお、式（９）の関数Ｙ（ｔ）は、時間ｔについての連続関数であるから、時間ｔには、有理数のみならず無理数を含む任意の値を代入することができる。これは、現状のオーバーサンプリング理論を用いた補間では実現できない無理数による位置の補間が可能となることを意味する。このように、ｔの値として、新たなデータに対応する任意のサンプリングタイミング即ち時間補間位置を代入することにより、元のデータ列Ｙ（ｎＴ）と修正されたインパルス応答関数η（Ｐｒ，ｎ）との積和演算によって変換値Ｙ（ｍ_０Ｔ_ｂ）を理論上厳密に求めることができ、延いては周期Ｔ_ｂの新たなデータ列Ｙ（ｍＴ_ｂ）を理論上厳密に求めることができる。結果的に、本手法により、上記オーバーサンプリング理論を用いた補間に比較して、１００倍から数１０００倍程度の変換処理の高速化を達成することができる。Here, in an analog signal f (t) in a random band, an ideal analog low-pass filter having a cutoff frequency f _c / 2 is

It is. This equation (8) is considered to be applicable to the above equation (5) and the like relating to sampling frequency rate conversion. Here, the equation (5) is modified based on the above equation (8), and the frequency f _{c is set} to the smaller one of f _s and f _b, and the following equation:

The sampling frequency rate conversion processing is performed. In this case, the discrete impulse response function η (Pr, n) for the fluctuating FIR filter can be expressed as a modified equation or value that enables prevention of aliasing and aliasing:

And a new conversion value corrected by the interpolation calculation formula, that is, t = Pr,

It becomes. As is clear from the above, in the variable FIR filter of the present embodiment, only a part of f _s of the original converted value Y (Pr) = Y (m ₀ T _b ) is replaced with f _c . A function as a low-pass filter for anti-aliasing can also be provided, and extremely high speed of data processing can be achieved. Note that since the function Y (t) in the equation (9) is a continuous function for the time t, an arbitrary value including not only a rational number but also an irrational number can be substituted for the time t. This means that it is possible to interpolate positions using irrational numbers that cannot be realized by interpolation using the current oversampling theory. Thus, by substituting an arbitrary sampling timing corresponding to new data, that is, a time interpolation position, as the value of t, the original data string Y (nT) and the modified impulse response function η (Pr, n) The converted value Y (m ₀ T _b ) can be theoretically strictly determined by the product-sum operation with the above, and a new data string Y (mT _b ) having the period T _b can be theoretically strictly determined. . As a result, according to this method, it is possible to achieve a conversion process speed increase of about 100 to several thousand times compared to the interpolation using the oversampling theory.

ここで、Ｚ＝ｅｘｐ（ｊωＴ）、ω：角周波数である。Note that the transfer function H (Z, Pr) of the fluctuating FIR filter is as follows.

Here, Z = exp (jωT), ω: angular frequency.

として定められる。ここで、周波数の比率は、Ｎ：Ｍ＝３２０：４４１となるため（３２０と４４１とは互いに素）、差分補間位置Ｐｒは、４４１個の循環するパターンを有するものとなる。数値化して行うデジタル処理による実際の演算においては、式（７）に示すように、１つの変換値の算出には、有限個（例えば３０個程度）の要素からなる離散インパルス応答関数η（Ｐｒ，ｎ）の係数列が必要となるが、この場合、離散インパルス応答関数η（Ｐｒ，ｎ）の係数列の数は、差分補間位置Ｐｒのパターンの数に対応して４４１列分用意されることになる。Hereinafter, as an example, a case where the conversion by the signal processing device 10 is converted from 32 kHz to 44.1 kHz will be considered. In this case, the sampling frequency f _{c serving as} a reference for the cut-off frequency is the smaller one of f _s and f _b , that is, f _{s of} 32 kHz becomes f _c . That is, the restored analog function equation (9) is the same as the equation (5), and the discrete impulse response function η (Pr, n) is created based on this equation as described above. In this case, the difference interpolation position Pr is, for example,

It is determined as Here, since the frequency ratio is N: M = 320: 441 (320 and 441 are relatively prime), the differential interpolation position Pr has 441 circulating patterns. In the actual calculation by digital processing performed by digitization, as shown in the equation (7), in order to calculate one conversion value, a discrete impulse response function η (Pr) composed of a finite number (for example, about 30) elements is used. , N) coefficient sequences are required. In this case, the number of coefficient sequences of the discrete impulse response function η (Pr, n) is prepared for 441 columns corresponding to the number of patterns of the differential interpolation position Pr. It will be.

Here, the coefficient table 60 in FIG. 3 schematically shows a table in which filter coefficients configured based on the discrete impulse response function η (Pr, n) are arranged. The coefficient table 60 includes a finite number (for example, about 30) data elements (hereinafter referred to as filter coefficient values) necessary for calculating one conversion value (for example, conversion value Y (Pr) = Y (m ₀ T _b )). The coefficient sequence of the filter coefficients consisting of the filter coefficients is a unit, and this coefficient sequence is converted to a number necessary for obtaining all the values of the new data sequence Y (mT _b ) (for example, conversion from 32 kHz to 44.1 kHz) In the case of 441 columns).

Here, the column obtained by arranging a finite number (for example, about 30) of filter coefficient values, which are units for obtaining one converted value Y (Pr) = Y (m ₀ T _b ) by convolution, It is assumed as a column 60a. That is, the coefficient table 60 is a table in which the necessary number of filter coefficient strings 60a are arranged according to the ratio of the frequencies before and after the conversion. As will be described in detail later, in the case of digital data processing using a fluctuating FIR filter, in the coefficient table 60, a filter coefficient sequence 60a in which each filter coefficient value is arranged as an element is handled as a group of units in calculation. It is made to function as a digitized discrete impulse response function η (Pr, n). In the case of the present embodiment, an element shown in Equation (7) or the like is obtained by a variable FIR filter using a filter coefficient sequence 60a composed of a finite number of filter coefficient values obtained based on the discrete impulse response function η (Pr, n). By performing the product-sum operation with the data Y (nT), a new data string Y (mT _b ) can be calculated by the same arithmetic processing as the conventional FIR filter.

  Note that when the variable FIR filter is operated, the window function corresponding to the impulse response function η (t, n) described above is further used to reduce the discontinuity of the calculated value in the calculation process, and the normalization of the coefficient By performing the digitization process, even if it is a finite number of discrete impulse response functions η (Pr, n), information to be processed can be made more reproducible.

  As the window function used for the impulse response function η (t, n), for example, a Hanning window, a Blackman window, a Kaiser window, or the like is appropriate. The Hanning window, Blackman window, Kaiser window, and the like are effective in preventing noise because they become 0 so as to contact the coordinate axis at both ends of the window. The correction method using the window function is the correction using the discrete window function corresponding to the differential interpolation position Pr as in the relationship between the impulse response function η (n, t) and the discrete impulse response function η (Pr, n). It is preferable that

FIG. 3 is a block diagram conceptually showing an operation in the case of performing conversion by digital signal processing in the signal processing apparatus 10 which is a sampling frequency conversion apparatus. Here, first, the discrete impulse response function η (Pr, n) (for example, the modified discrete impulse response shown in the equation (10)) created from the impulse response function η (t, n) by the concept of the variable FIR filter. A function η (Pr, n)) is constructed. Further, in the coefficient table 60 of the signal processing device 10, as described above, a finite number (for example, 30) of filter coefficient values are arranged as filter coefficients determined from the discrete impulse response function η (Pr, n)). One filter coefficient string 60a is configured, and such filter coefficient string 60a is prepared in an amount necessary for the convolution calculation process described later. The signal processing apparatus 10 secures an area for filter coefficients in the RAM 40 of FIG. Further, the signal processing apparatus 10 selects each necessary filter coefficient string 60a from the created coefficient table 60 and appropriately reads it, while extracting a corresponding range of the data string Y (nT) as input data, and this data Each data value (transformed value) of the data string Y (mT _b ) is calculated by performing a convolution operation on the corresponding range of the string Y (nT) and the filter coefficient string 60a. That is, in the signal processing device 10, first, one filter coefficient string 60 a is read from the coefficient table 60 to the extraction unit 61, and corresponding input data 70 a whose address position is specified from the input data buffer 70 is collated. The calculation result data 80 a is output as one of data stored in the output data buffer 80. The signal processing apparatus 10 sequentially outputs the output of the conversion value data 80a that is each data value (conversion value) of the new data string Y (mT _b ) in the order of the data to be output by the above operation, that is, in the time series of the new data. Do.

A specific data processing step for obtaining a new data string Y (mT _b ) with different specifications from the original data string Y (nT) by digital signal processing using a variable FIR filter in the signal processing apparatus 10 of FIG. The operation is explained.

As the first half of the above description of the operation, first, a coefficient preparation process for preparing the creation of the coefficient table 60 of FIG. 3 and the like with reference to the block diagrams of FIGS. 1 and 3 and the flowcharts of FIGS. Will be described. That is, in the following, in order to enable calculation of the new data sequence Y (mT _b), conversion values of the difference interpolation position _{Pr Y (Pr) = Y (} m 0 T b) providing a discrete impulse response function η The operation of a process corresponding to the preparation of (Pr, n) (Pr changes within the range of the number of data constituting the new data string Y (mT _b )) will be described.

  As shown in FIG. 4, the CPU 20 of the signal processing apparatus 10 shown in FIG. 1 determines the value of the tap number TAmax (for example, about 30) that determines the number of product-sum operations (step S1). In other words, this corresponds to determining the number of filter coefficient values constituting one filter coefficient string 60a. This tap number TAmax is temporarily stored in an appropriate area of the RAM 40.

Next, as an input the reference period is a digital value corresponding to the original sampling period T defines the input period value A (step S2), and as an output the reference period is a digital value corresponding to a new sampling period T _b after conversion An output cycle value B is determined (step S3). These period values A and B are temporarily stored in an appropriate area of the RAM 40. Here, as a premise for determining the period values A and B, a minimum unit of time for digitization of time is a system time unit. That is, the system time unit is the shortest unit of time necessary for processing digital signals, and is determined by, for example, the reciprocal of the least common multiple of sampling frequencies f _s and f _b before and after conversion. Thus, the period value A, B are both expressed as the number of system time units, the number is, each period T, corresponding to the length of T _b. Specifically, for example, in the case of conversion from 32 kHz to 44.1 kHz, N: M = 320: 441 (320 and 441 are relatively prime). In steps S2 and S3, A = 441, B = 320 Determined. That is, the system time unit in this case is 1 / (441 × 320) × 10 ⁻² seconds.

  Next, the CPU 20 calculates the number of output buffers based on the cycle values A and B. That is, the CPU 20 reads the cycle values A and B stored in the RAM 40, determines the value of the coefficient k corresponding to the greatest common divisor, for example, from these values, and sets k × A as the number of output buffers (step S4). Since N and M providing the frequency ratio are originally prime, the difference interpolation position Pr also circulates in 441 patterns as described above. Therefore, in step S4, for example, k = 1 is determined. The CPU 20 temporarily stores these data, that is, the coefficient k and the output buffer number k × A in an appropriate area of the RAM 40. In the case of conversion from 44.1 kHz to 48 kHz, since N: M = 441: 480 = 3 × 147: 3 × 160 = 147: 160, A = 160 and B = 147 are determined. In this case, Pr circulates in 160 patterns, for example, k = 3.

Then, CPU 20 performs the determination of the value of the decision that is, the reference frequency _{f c} of the cut-off frequency _f c / 2 value (step S5). The reference frequency _{f c} is temporarily stored in an appropriate area of the RAM 40. As described above, in the case of conversion from 32 kHz to 44.1 kHz, for example, the cutoff frequency f _c / 2 is ½ of the original sampling frequency f _s . Conversely, in the case of conversion from 44.1 kHz to 32 kHz, the cutoff frequency f _c / 2 is ½ of the converted sampling frequency f _b .

  Next, the CPU 20 uses a counter provided in the RAM 40 to check whether filter coefficient normalization processing in step S17 described later has been performed a prescribed number of times (step S6), and if not reached (step S6). : No) The normalized total value is initialized (step S7), and the process for setting the initial number of taps (the number of taps TA = 0) is performed (step S8). The normalized total value and the initial value of the number of taps are temporarily stored in an appropriate area of the RAM 40.

Next, the CPU 20 confirms the number of taps TA stored in the RAM 40 (step S16). If the maximum number of taps TAmax has not been reached (step S16: No), the time of the impulse response function η (t, n) The interpolation position m ₀ T _b and the difference interpolation position Pr are determined (step S9). The difference interpolation position Pr is represented by Pr = n ₀ T−m ₀ T _b as already described. Here, one differential interpolation position Pr (in the case of conversion from 32 kHz to 44.1 kHz, one pattern of 441 patterns) is determined. At this time, the variable m ₀ giving the differential interpolation position Pr gradually increases from 0, with A-1 being the maximum. The difference interpolation position Pr is temporarily stored in an appropriate area of the RAM 40. Next, the CPU 20 centers the time interpolation position m ₀ T _b with respect to n of the discrete impulse response function η (Pr, n) determined based on the impulse response function η (t, n) with the determination of the differential interpolation position Pr. A basic coefficient for creating a filter coefficient is calculated by substituting a finite number (for example, 30) of values (step S10). Specifically, for example, in Equation (10), the basic coefficient is determined by performing numerical operations on the sin part and the part other than sin of the corresponding discrete impulse response function η (Pr, n). , Temporarily stored in an appropriate area of the RAM 40. Next, the CPU 20 calculates a window function that operates on the basic coefficient obtained from the discrete impulse response function η (Pr, n) (step S11), reads out the basic coefficient calculated in step S10 from the RAM 40, and performs step S11. The provisional coefficient of the variable FIR filter is calculated by multiplying the window function calculated in step 1 and the basic coefficient (step S12). The CPU 20 embeds the calculated temporary coefficient in a temporary coefficient table temporarily provided in the RAM 40 (step S13) and adds it to the normalized total value stored in the RAM 40 (step S14). Thereafter, the CPU 20 increments the tap number TA stored in the RAM 40 by one (step S15).

  Next, the CPU 20 refers to the storage in the RAM 40 to check whether the tap number TA has reached the maximum number of taps TAmax (for example, TAmax = 30) set by the advance in step S15 (step S16). If not reached (step S16: No), the process returns to step S9 again, and the operation of calculating the temporary coefficient corresponding to each tap is repeated (steps S9 to S15).

  If it is determined in step S16 that the number of taps TA has reached the maximum number of taps TAmax (step S16: Yes), the CPU 20 calculates the temporary coefficient table calculated in step S15 and temporarily stored in the RAM 40. One filter coefficient string 60a normalized from one temporary coefficient string is created by dividing the entire one temporary coefficient string constituting by the normalized total value which is the sum (steps S116 and S17). Specifically, the CPU 20 checks whether or not the number of taps TA has reached the maximum number of taps TAmax (step S116), and determines that it has not been achieved (step S116: No), the calculated 1 An operation is performed to divide and update each temporary coefficient constituting one temporary coefficient sequence by the normalized total value (step S17), and this update operation is performed until it is determined that all the temporary coefficients are divided by the normalized total value. repeat. By this operation, the CPU 20 stores the finally obtained result, that is, one temporary coefficient string as one filter coefficient string 60a in the corresponding position of the table coefficient 60 prepared as a storage area in the RAM 40. .

  If the CPU 20 counts the number of taps in step S116 and determines that all the temporary coefficients have been processed for one temporary coefficient table (step S116: Yes), the filter coefficient string 60a is stored in the RAM 40 with reference to the storage in the RAM 40. It is confirmed whether or not the necessary amount has been formed (step S6). That is, the CPU 20 confirms whether the creation processing of the filter coefficient sequence 60a constituting the temporary coefficient table in steps S116 and S17 has been performed A times. If the filter coefficient sequence 60a is not formed for the minimum necessary units (A) (step S6: No), the CPU 20 sets a filter coefficient based on a new discrete impulse response function η (Pr, n), that is, a filter. The process (steps S7 to S17) for creating the coefficient sequence 60a is repeated.

If the CPU 20 determines that the filter coefficient string 60a has been created A times, that is, the filter coefficient string 60a for A times has been prepared in the table coefficient 60 (step S6: Yes), it is determined that the minimum necessary data has been prepared. Then, a process for creating a time interpolation position table associated with the coefficient table 60 is performed (steps S18 to S20). Specifically, first, the CPU 20 confirms whether or not the information in the time interpolation position table is necessary (step S18). Here, the time interpolation position table has a function as an index attached to the table coefficient 60 and is stored in a storage area of the RAM 40. If the necessary amount of information in the time interpolation position table is not prepared (step S18: No), the CPU 20 first performs a preparation process for determining the position of input data, that is, an address position table creation process (step S19). That is, the position of the original data serving as a reference is determined in order to create each newly generated data. For this purpose, the CPU 20 determines the address position of the specific input data 70a in the input data buffer 70 of FIG. 3, and associates the input position of a group of original data with one new data after conversion in the address position table. Is temporarily stored in an appropriate area of the RAM 40. Next, the CPU 20 prepares a differential interpolation position table corresponding to the differential interpolation position Pr that determines the amount of positional deviation between one new data and the original data (step S20). That is, the CPU 20 determines the address position of the specific filter coefficient string 60a in the coefficient table 60 corresponding to the specific difference interpolation position Pr. The address position of the prepared filter coefficient sequence 60a is temporarily stored in an appropriate area of the RAM 40 as a differential interpolation position table. When the above operation is repeated as many times as necessary for creating the time interpolation position table (step S18: Yes), the operation of the coefficient preparation process is terminated. In the above, step S19 corresponds to the reference of the original data string Y (nT) corresponding to the time interpolation position m ₀ T _b of one conversion value Y (Pr) = Y (m ₀ T _b ). This corresponds to preparing address data necessary for determining the position of one data value Y (n ₀ T). In step S20, a product-sum operation or convolution in a data calculation step to be described later is applied to a data value Y included by the number of taps TAmax before and after the reference data value Y (n ₀ T), and a specific differential interpolation position Pr is obtained. To prepare and store the address data necessary for designating the filter coefficient string 60a enabling calculation of the conversion value Y (Pr) = Y (m ₀ T _b ) in association with the address position obtained in step S19. Equivalent to.

Next, a data calculation process and the like performed based on the coefficient table 60 obtained in the coefficient preparation process will be described with reference to the block diagrams of FIGS. 1 and 3 and the flowcharts of FIGS. 9 and 10. That is, in the following, a new data sequence Y from the original data sequence Y (nT) by a convolution operation using a coefficient table 60 as a filter coefficient based on the discrete impulse response function η (Pr, n) prepared in the coefficient preparation step. The operation of the step of calculating (mT _b ) will be described.

First, as shown in FIG. 9, the CPU 20 in FIG. 1 adjusts the number of input buffers k × B (step S51). In other words, adjustment is made so that signals are sent in accordance with the number of input buffers k × B, and at the beginning and end of conversion, for example, the data (information α) for the shortage is adjusted. For example, the last part of the data acquired at the time immediately before the conversion process is taken out and used at the beginning of the conversion to compensate for the insufficient data. When there is no previous data at the beginning of conversion or when data is insufficient at the end of conversion, the information α is adjusted by a zero signal or a dummy signal. Note that the conversion value Y (Pr) = Y (m ₀ T _b ) corresponding to such initial and final signals can be deleted as unnecessary. Next, the CPU 20 refers to the storage in the RAM 40 to check whether or not the processing of the number of times that information can be output (number of output buffers k × A) has been performed (step S52). If not, a reference position address calculation process for reading the reference position of the lower data is performed (step S53). That is, the CPU 20 reads the address position for the original data string Y (nT) determined in step S19 from the RAM 40, and selects the part of the original data string Y (nT) required for the corresponding calculation. Perform the process. Next, the CPU 20 performs a difference interpolation position address preparation process (step S54). That is, the CPU 20 reads the address position for the differential interpolation position Pr determined in step S20 from the RAM 40. When preparation is made as described above, first, the CPU 20 checks whether the maximum number of taps TAmax (for example, TAmax = 30) has been operated with reference to the storage in the RAM 40, and if not, is prepared as described above. Each variation coefficient such as each filter system numerical value is loaded (step S56), and a convolution calculation process using the original data string portion and a filter coefficient including information on the difference interpolation position Pr is performed according to a program stored in the ROM 30. (Steps S56a and S56b) When the operation is processed for the number of taps TAmax, one converted value Y (Pr) = Y (m ₀ T _b ) of new data is created (Steps S57 and S58). ).

Thereafter, the above operation is repeated k × A times for the number of output buffers (step S52). When data for the number of output buffers k × A is accumulated, a group of new data strings Y (mT _b ) from the output data buffer 80 of FIG. (Step S59). That is, a new data string Y (mT _b ) is output to the outside of the signal processing apparatus 10 via the output interface unit 52 of FIG. When data is output in step S59, it is determined whether there is new input data via the input interface unit 51 (step S60). If there is input data (step S60: Yes), the data is again displayed. Is repeated (step S51 to step S60), and if there is no input data (step S60: No), the operation of the data calculation process is terminated.

[Second Embodiment]
Hereinafter, a signal processing device according to a second embodiment of the present invention will be described with reference to FIG. Note that the signal processing apparatus of the present embodiment is configured to have a circuit structure, but is a modification of the first embodiment, and has the same name as the element of the signal processing apparatus 10 shown in FIG. Unless otherwise specified, the same function is assumed.

  11 includes a data creation unit 120, a controller 130, a coefficient table 140, a time interpolation position table 150, an extraction unit 160, an input data transmission unit 170, a convolution operation unit 180, An output data unit 190 and an output buffer unit 191 are provided. The time interpolation position table 150 includes an address position table 150a and a difference interpolation position table 150b.

The data creation unit 120 performs a coefficient preparation step for preparing for creation of a filter coefficient corresponding to the discrete impulse response function η (Pr, n). The controller 130 performs a data calculation step of calculating a conversion value conversion value Y (m ₀ T _b ) = Y (Pr) for new data by a convolution operation based on the filter coefficient.

  Hereinafter, the operation of the data processing step by the data creation unit 120 and the controller 130 will be described. First, when preparing the creation of filter coefficients corresponding to the discrete impulse response function η (Pr, n), the data creation unit 120 outputs information such as the created filter coefficient sequence 60a in the coefficient table 140. Also, information on the position of the original data used for creating a newly generated data string is output to the address position table 150a of the time interpolation position table 150 (corresponding to the process of step S19 in FIG. 8), and differential interpolation is performed. Information on the position Pr is output to the differential interpolation position table 150b of the time interpolation position table 150 (corresponding to the process of step S20 in FIG. 8). Thus, the coefficient preparation process is completed. Next, the controller 130 performs the operation of the data calculation process. Specifically, first, the controller 130 reads, from the coefficient table 140 and the time interpolation position table 150, one filter coefficient sequence 60a corresponding to a filter coefficient based on the discrete impulse response function η (Pr, n) to the extraction unit 160. . On the other hand, the original data string portion corresponding to the filter coefficient string 60 a is extracted from the original digital data string Y (nT) and arranged in the input data sending unit 170. Further, the controller 130 performs convolution operation processing on the input data 70 a extracted by the input data transmission unit 170 and the filter coefficient sequence 60 a read by the extraction unit 160 by the convolution operation unit 180. The calculation result in the convolution calculation unit 180 is output to the output data unit 190, and the output data 80a of the output data unit 190 is output to the outside by the output buffer unit 191. As described above, the operation of the data calculation process for calculating the conversion value for new data is performed under the control of the controller 130. In this case, as shown in the figure, the controller 130, the coefficient table 140 controlled thereby, the time interpolation position table 150, the extraction unit 160, the input data transmission unit 170, the convolution operation unit 180, the output data unit 190, and the output buffer The unit 191 functions as the variable FIR filter 200.

  Note that the present invention is not limited to the above. For example, the function Y (t) in the expression (1) can extract an arbitrary point with respect to the time t, and the output data has periodicity. It is also possible to configure by sampling from an arbitrary point on the function Y (t). The input data is also periodic, but not all data is necessarily periodic. For example, the present invention can be applied to a mode in which only the header portion of data is read. .

  In each of the above embodiments, the original data string Y (nT) is audio or other time-series digital data and the sampling frequency rate conversion in a narrow sense is described. However, the present invention is not limited to this, For example, the present invention can also be applied to sampling frequency rate conversion in a broad sense such as various data conversion processes such as frame rate conversion in the display of three-dimensional graphics and moving image reproduction, and resolution conversion such as enlargement and reduction of images.

  In the first embodiment, the window function is multiplied by the basic coefficient. However, the window function may be used in other ways. Also, various types of window functions can be adopted as described above.

  In the first embodiment, the normalization process is performed on the temporary coefficient calculated by multiplying the window function and the basic coefficient. However, the coefficient normalization process is not limited to this, and the program normalization process is not limited thereto. It is also possible to carry out in various states depending on the design or the like.

In the first embodiment, the variable FIR filter also serves as a low-pass filter for preventing aliasing by taking into account the cutoff frequency f _c / 2, but in addition to this, other functions Can also be given. For example, a low-pass filter that limits components below the desired frequency, a high-pass filter that limits components above the desired frequency, a band-pass filter that limits components within the desired frequency range, a band elimination filter that removes specific frequency bands, etc. It can be set as the structure which also served as.

ここで、式（１４）において、ｆ´_ｃ／２は、強制的遮断周波数である。なお、ｆ´_ｃ＜ｆ_ｃとなっている。この場合、式（１４）を適用することで、補間計算式即ち変換値は、

と表される。現実には、窓関数を含む近似式が用いられ、ｎを有限の積和演算タップ数とする。As a configuration having an arbitrarily settable low-pass filter function, for example, the following equation can be applied instead of the discrete impulse response function η (Pr, n) of equation (10).

Here, in Expression (14), f ′ _c / 2 is a forced cutoff frequency. It should be _noted, has become a _{f'c <f} c. In this case, by applying Expression (14), the interpolation calculation formula, that is, the converted value is

It is expressed. In reality, an approximate expression including a window function is used, and n is a finite number of product-sum operation taps.

ここで、式（１５）において、ｆ_ｃ／２は、エイリアシング防止のための遮断周波数であり、ｆ_ｄ／２は、ハイパス周波数である。なお、ｆ_ｄ＜ｆ_ｃとなっている。この場合、式（１５）を適用することで、補間計算式即ち変換値は、

と表される。As a configuration having a function of a high-pass filter that can be arbitrarily set, for example, the following formula can be applied instead of the discrete impulse response function η (Pr, n) of formula (10).

Here, in Expression (15), f _c / 2 is a cutoff frequency for preventing aliasing, and f _d / 2 is a high-pass frequency. It should be _noted, has become a _f d <f _c. In this case, by applying the equation (15), the interpolation calculation formula, that is, the converted value is

It is expressed.

ここで、式（１６）において、ｆ´_ｃ／２は、強制的遮断周波数であり、ｆ_ｄ／２は、ハイパス周波数である。なお、ｆ_ｄ＜ｆ´_ｃ＜ｆ_ｃとなっている。この場合、式（１６）を適用することで、補間計算式即ち変換値は、

と表される。Furthermore, as a configuration having a function of a bandpass filter that can be arbitrarily set, for example, the following equation can be applied instead of the discrete impulse response function η (Pr, n) of equation (10).

Here, in Expression (16), f ′ _c / 2 is a forced cutoff frequency, and f _d / 2 is a high-pass frequency. It should be _noted, has become a _{f d <f'c <f c} . In this case, by applying Expression (16), the interpolation calculation formula, that is, the converted value is

It is expressed.

ここで、式（１７）において、ｆ_ｊ／２は、帯域除去下端周波数であり、ｆ_ｋ／２は、帯域除去上端周波数である。なお、ｆ_ｊ＜ｆ_ｋ＜ｆ_ｃとなっている。この場合、式（１７）を適用することで、補間計算式即ち変換値は、

と表される。Further, as a configuration having a function of a band elimination filter capable of arbitrarily removing a frequency in a specific band, for example, the following formula is applied instead of the discrete impulse response function η (Pr, n) of formula (10): can do.

Here, in Expression (17), f _j / 2 is a band elimination lower limit frequency, and f _k / 2 is a band elimination upper limit frequency. It should be _noted, it has become a _{f j <f k <f c} . In this case, by applying Expression (17), the interpolation calculation formula, that is, the converted value is

It is expressed.

  In the first embodiment, for example, as shown in FIG. 1, various processes in the signal processing apparatus 10 are performed by the CPU 20, but instead of the CPU 20, a signal is used so that the product-sum operation can be processed at high speed. It is also possible to use a DSP (Digital Signal Processor) specialized for processing, an MPU (Micro Processor Unit) in which a CPU or the like is integrated on one semiconductor chip, or the like. Further, the DSP or MPU may perform various processes such as a convolution operation including functions corresponding to storage portions such as the ROM 30 and the RAM 40 of the signal processing apparatus 10.

10, 110 ... signal processing unit, 20 ... CPU, 30 ... ROM , 40 ... RAM, Y (nT), Y (mT b) ... data string, T, T b _{... period, f s, f b, f} c ... Frequency, differential interpolation position ... Pr, 60,140 ... coefficient table, 60a ... filter coefficient sequence, 61,160 ... extraction unit, 70 ... input data buffer, 80 ... output data buffer, 120 ... data creation unit, 130 ... controller, 150 ... time interpolation position table, 170 ... input data transmission unit, 180 ... convolution operation unit

Claims (5)

Coefficient preparation for preparing a filter coefficient based on a discrete impulse response function corresponding to the time interpolation position in order to give a conversion value at a time interpolation position corresponding to new data to be obtained by conversion from discrete original data Means,
A variable FIR filter that always operates at an output sampling frequency to process the original data, the filter coefficient prepared in the coefficient preparation means is taken in as a coefficient of the variable FIR filter, and the fluctuation or fluctuation of the variable FIR Data calculation means for calculating the new data at the time interpolation position by a convolution operation of the filter coefficient ,
It said coefficients preparation unit, by setting the filter coefficient based on the discrete impulse response function, selects a frequency band,
The new data Y (Pr) restored from the original data is
T is the sampling period of the original data, n is an integer, Y (nT) is the original data, f _s is the sampling frequency of the original data, and f _c is the original data. And the smaller of the sampling frequency of the new data and the sampling frequency of the new data,
_Tb is the sampling period of the new data, Pr is a predetermined parameter corresponding to the difference between the discrete point of the original data and the time interpolation position, and Pr is given by n ₀ and m ₀ which are both integers. = N ₀ T−m ₀ T _b
As before Symbol frequency band, high-pass frequency band, one of the band-pass frequency band, and the band rejection frequency is selected and
Wherein when selecting the high-pass frequency _band, the _f d / 2 and a high-pass _frequency, as f d _{<f c,} the following convolution equation

Or an approximate expression using a window function with a finite value of n,
When selecting the band-pass frequency band, and forcibly cutoff frequency _f'c / _2, the _f d / 2 and a high-pass _frequency, as _{f d <f'c <f c} , the following convolution equation

Or an approximate expression using a window function with a finite value of n,
When selecting the band rejection _frequency, the _f j / 2 as a band elimination lower _frequency, the _f k / 2 as a band elimination upper _frequency, as _{f j <f k <f c} , the following convolution equation

Or the apparatus of sampling frequency rate conversion expressed using the approximation formula using the window function which makes n a finite value. The coefficient preparation means prepares a coefficient table as the filter coefficient based on the discrete impulse response function, and prepares a time interpolation position table for control associated with the coefficient table,
The data calculation means is based on the filter coefficient that oscillates or fluctuates according to the time interpolation position table between each data of the coefficient table and the original data by the fluctuation FIR filter for calculating the conversion value. The sampling frequency rate conversion apparatus according to claim 1, wherein the conversion value is calculated by performing a convolution operation.   The sampling frequency rate conversion device according to any one of claims 1 and 2, wherein the coefficient preparation means further includes normalization means for normalizing the filter coefficient based on the discrete impulse response function. . Coefficient preparation for preparing a filter coefficient based on a discrete impulse response function corresponding to the time interpolation position in order to give a conversion value at a time interpolation position corresponding to new data to be obtained by conversion from discrete original data Process,
The filter coefficient prepared in the coefficient preparation step is fetched as a coefficient of a variable FIR filter that always operates at an output sampling frequency, and the new value at the time interpolation position is obtained by convolution of the variable FIR oscillation or the variable filter coefficient. A data calculation process for calculating various data ,
Wherein a factor preparation step, by setting the filter coefficient based on the discrete impulse response function, selects a frequency band,
The new data Y (Pr) restored from the original data is
T is the sampling period of the original data, n is an integer, Y (nT) is the original data, f _s is the sampling frequency of the original data, and f _c is the original data. And the smaller of the sampling frequency of the new data and the sampling frequency of the new data,
_Tb is the sampling period of the new data, Pr is a predetermined parameter corresponding to the difference between the discrete point of the original data and the time interpolation position, and Pr is given by n ₀ and m ₀ which are both integers. = N ₀ T−m ₀ T _b
As before Symbol frequency band, high-pass frequency band, one of the band-pass frequency band, and the band rejection frequency is selected and
Wherein when selecting the high-pass frequency _band, the _f d / 2 and a high-pass _frequency, as f d _{<f c,} the following convolution equation

Or an approximate expression using a window function with a finite value of n,
When selecting the band-pass frequency band, and forcibly cutoff frequency _f'c / _2, the _f d / 2 and a high-pass _frequency, as _{f d <f'c <f c} , the following convolution equation

Or an approximate expression using a window function with a finite value of n,
When selecting the band rejection _frequency, the _f j / 2 as a band elimination lower _frequency, the _f k / 2 as a band elimination upper _frequency, as _{f j <f k <f c} , the following convolution equation

Alternatively, a sampling frequency rate conversion method expressed using an approximate expression using a window function in which n is a finite value. In the coefficient preparation step, a coefficient table is prepared as the filter coefficient based on the discrete impulse response function, and a time interpolation position table for control associated with the coefficient table is prepared,
According to the filter coefficient that vibrates or fluctuates according to the time interpolation position table between each data of the coefficient table and the original data by the fluctuation FIR filter for calculating the conversion value in the data calculation step. The sampling frequency rate conversion method according to claim 4, wherein the conversion value is calculated by performing a convolution operation.

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