CN118074671B - A geometric quantization digital filtering method and digital filter - Google Patents
A geometric quantization digital filtering method and digital filter Download PDFInfo
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Abstract
The embodiment of the invention discloses a geometric series quantization digital filtering method and a digital filter, wherein the digital filtering method comprises the steps of quantizing a digital filter impulse response coefficient based on a preset quantization bit number m to obtain a digital filter impulse response quantized result q (k), wherein the quantized result q (k) comprises a real part coefficient q r (k) and an imaginary part coefficient q i (k), the real part coefficient q r (k) and the imaginary part coefficient q i (k) both comprise values after an exponential operation based on 2, calculating an input signal based on the quantized digital filter impulse response to obtain a shift calculation result s (k, l) of the input signal, and adding and calculating the shift calculation result to obtain a filtering output result. According to the embodiment of the invention, the convolution calculation of the existing digital filter is realized through displacement calculation and replacement by converting the quantized result of the impulse response function of the digital filter, so that the hardware resources and the calculation complexity required by the digital filter are greatly reduced.
Description
Technical Field
The present invention relates to the field of wireless communication and signal processing technologies, and in particular, to a geometric progression quantization digital filtering method and a digital filter.
Background
Filtering is a basic and important technology in signal processing, is mainly used for filtering, detecting and predicting signals, and has wide application in various fields such as computer networks, big data analysis, instruments, military, industrial control, communication, aerospace and the like. The digital filter is an algorithm or device composed of a digital multiplier, an adder and a delay unit, has the outstanding advantages of high stability, high precision, flexible design, convenient implementation and the like, and avoids the problems of voltage drift, temperature drift, noise and the like which cannot be overcome by the analog filter. Due to the development of electronic computer technology and large-scale integrated circuits, digital filters have been implemented in computer software, and also in large-scale integrated digital hardware in real time.
For a finite impulse response (Finite Impulse Response, FIR) filter, the output y (k) of the operation is the convolution of the input signal x (k) with the impulse response h (k), i.e., the input signal x (k) at each instant is multiplied by the corresponding attenuation or amplification of the finite impulse response h (k), and then added together to be output as an output signal,. The computational complexity of the FIR filter is determined by the order N of its impulse response. The larger N is, the larger the memory space occupied by the filter is, and the more multipliers, adders and delay units are needed, which causes great challenges to the real-time calculation of the large-scale integrated digital circuit.
Disclosure of Invention
The embodiment of the invention provides a geometric progression quantization digital filtering method and a digital filter, which can greatly reduce hardware resources and computational complexity required by the digital filter. The specific technical scheme is as follows:
In a first aspect of the present invention, a geometric progression quantization digital filtering method is provided, where the digital filtering method includes quantizing the digital filter impulse response coefficient based on a preset quantization bit number m, and obtaining the digital filter impulse response quantization result The quantization resultComprising real part coefficientAnd the imaginary coefficientThe real part coefficientAnd the imaginary coefficientAll include values after an exponential operation with a base of 2,
Calculating an input signal based on the quantized digital filter impulse response to obtain a shift calculation result of the input signal,
And adding and calculating the shift calculation result to obtain a filtering output result.
In one possible implementation manner, based on a preset quantization bit number m, the digital filter impulse response coefficient is quantized to obtain the digital filter impulse response quantization resultSpecifically, the method comprises the following steps of,
Calculating the maximum quantized amplitude M of the impulse response function h (k) of the digital filter, wherein the maximum quantized amplitude M is the absolute value of the maximum value in the real part and the imaginary part of all impulse responses,
Based on the preset quantization bit number M and the maximum quantization amplitude M, a minimum quantization interval delta is calculated,
Using the minimum quantization interval delta, at least by division of the real part and the imaginary part of the impulse response h (k) and rounding calculation, respectively obtaining a real part operation parameter r k and an imaginary part operation parameter i k,
Based on the real part operation parameter r k and the imaginary part operation parameter i k, obtaining quantized impulse response quantization results of the digital filter through 2-based exponential operation under preset conditionsAnd。
In one possible implementation manner, the calculating the minimum quantization interval delta based on the preset quantization bit number and the maximum quantization amplitude M specifically includes calculating the minimum quantization interval delta using the following formula,
。
In one possible implementation manner, the use of the minimum quantization interval Δ obtains the real part operation parameter r k and the imaginary part operation parameter i k through at least division and rounding calculation of the real part and the imaginary part absolute value of the impulse response h (k), and specifically includes calculating the real part operation parameter r k and the imaginary part operation parameter i through the following formula k
,
,
Wherein, The representation is rounded down and up,Representing an upward rounding.
In one possible embodiment, the method comprises, among other things,The quantized digital filter impulse response quantization result is obtained by exponential operation based on the real part operation parameter r k and the imaginary part operation parameter i k under the preset condition and based on 2AndSpecifically, the method comprises the following steps of,
Wherein, AndRespectively obtaining impulse responses of the digital filter after quantizationReal and imaginary parts of (a) are provided.
In one possible implementation manner, the quantized digital filter impulse response is calculated on the basis of an input signal, so as to obtain a shift calculation result of the input signalAnd specifically includes, in particular,
Based on the impulse response coefficient of the digital filterAndObtaining multiplication results of the input signal x (k) and the digital filter impulse response q (k) through shift operation of a shifter on the input signal x (k), wherein the shift calculation resultsThe calculation formula is as follows:
Wherein, N is the order of the digital filter.
In one possible implementation manner, the adding and calculating the shift calculation result to obtain a filtering output result specifically includes,
And summing the shift calculation results, multiplying the sum by the minimum quantization interval delta, and calculating to obtain a filtering output result.
In one possible implementation manner, the shift calculation result is summed and multiplied by the minimum quantization interval delta to obtain a filtered output result, which specifically includes calculating by the following formula
Wherein, The result is output for filtering.
In one possible implementation, the preset quantization bit number is a positive integer associated with the digital filter digital shifter bit number and the filtered signal precision.
A second aspect of the present invention provides a geometric progression quantization digital filter, comprising a shifter, an adder, a delay unit, and a data preprocessing unit,
The data preprocessing unit is configured to perform quantization on the digital filter impulse response coefficient based on a preset quantization bit number m, and obtain a quantized result of the digital filter impulse responseThe quantization resultComprising real part coefficientAnd the imaginary coefficientThe real part coefficientAnd the imaginary coefficientAll include values after an exponential operation with a base of 2,
The shifter is used for executing calculation based on quantized digital filter impulse response to input signals to obtain a shift calculation result of the input signals,
And the adder is used for executing addition calculation on the shift calculation result to obtain a filtering output result.
The method has the beneficial effects that the method quantizes the impulse response coefficient of the digital filter based on the preset quantization bit number, and converts the impulse response function into the real part coefficientAnd the imaginary coefficientAll the values comprise values subjected to exponent operation based on 2, a shift calculation result of the digital filter is obtained through further shift operation according to the input signals, and finally a filtering output result is obtained through addition calculation. The complex multiplication calculation of the digital filter is converted into the shift calculation of the shifter, the complexity of the structure and calculation of the digital filter is greatly reduced, and the signal processing efficiency and the processing timeliness are improved.
Drawings
FIG. 1 is a schematic flow chart of a geometric series quantization digital filtering method according to an embodiment of the present invention;
FIG. 2a is a schematic diagram of an 8-bit shift of a method for implementing a geometric progression quantized digital filter in accordance with an embodiment of the present invention;
FIG. 2b is a schematic diagram of a 16-bit shift of a method of implementing a geometric progression quantized digital filter in an embodiment of the invention;
FIG. 3 is a schematic diagram of a geometric progression quantization digital filter framework according to an embodiment of the present invention;
Fig. 4 is a schematic block diagram of a quantization digital filter with n=4 order geometric progression according to an embodiment of the present invention;
fig. 5a-5d are schematic diagrams illustrating simulation verification of a geometric progression quantization digital filtering method according to an embodiment of the present invention.
Detailed Description
The present invention will now be described in further detail with reference to the accompanying drawings, wherein the embodiments described are some, but not all embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
It should be noted that the terms "first," "second," and the like are used for descriptive purposes only and are not to be construed as indicating or implying a relative importance or implying a number of technical features being indicated. Thus, a feature defining "a first" or "a second" may explicitly or implicitly include at least one such feature. In the description of the present invention, the meaning of "plurality" means at least two, for example, two, three, etc., unless specifically defined otherwise.
In the above description, descriptions of the terms "one embodiment," "some embodiments," "examples," "specific examples," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, schematic representations of the above terms are not necessarily directed to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, the different embodiments or examples described in this specification and the features of the different embodiments or examples may be combined and combined by those skilled in the art without contradiction.
Embodiment one:
The current filter in signal processing and chip design is usually a software or hardware composed of a digital multiplier, an adder and a delay unit, has the advantages of high precision and stability, flexible design and the like, and along with the rapid development of integrated circuits, communication technologies and the Internet, more complex application scenes provide higher requirements on the integration level of the digital filter, but along with the better integration level of the digital filter, the filter occupies more space, the number of corresponding multipliers, excitation units and delay units is also increased, the calculation scale complexity is also increased, the design of miniaturization and stability is provided with higher challenges, and no implementation scheme of the digital filter which can be well combined with the miniaturization and stability in more complexity of a functional module is still available in the current industry.
In view of the above problems, an embodiment of the present invention provides a geometric-series quantization digital filtering method and a digital filter, as shown in fig. 1, which is a schematic flow chart of the geometric-series quantization digital filtering method in the embodiment of the present invention. The geometric progression quantization digital filtering method comprises,
Step S100, based on a preset quantization bit number m, quantizing the impulse response coefficient of the digital filter to obtain the impulse response quantized result of the digital filterThe quantization resultComprising real part coefficientAnd the imaginary coefficientThe real part coefficientAnd the imaginary coefficientAll include values after an exponential operation with a base of 2.
For a finite impulse response (Finite Impulse Response, FIR) filter, the output y (k) of the operation is the convolution of the input signal x (k) with the impulse response h (k), i.e., the input signal x (k) at each instant is multiplied by the corresponding attenuation or amplification of the finite impulse response h (k), and then added together to be output as an output signal,. The computational complexity of the FIR filter is determined by the order N of its impulse response.
In a preferred implementation manner of the embodiment of the present invention, the impulse response h (k) of the finite impulse response filter is a complex number, which includes a real part coefficient and an imaginary part coefficient, and the quantization step in the embodiment of the present invention includes quantizing the impulse response coefficient of the digital filter, specifically includes simultaneously quantizing the real part coefficient and the imaginary part coefficient of the impulse response h (k), to obtain the quantized result of the impulse response of the digital filterWherein the quantization resultComprising real part coefficientAnd the imaginary coefficientAnd transforming the original digital filter impulse response coefficient into real coefficient by quantizationAnd the imaginary coefficientAll include values after an exponential operation with a base of 2.
In the impulse response function of the FIR filter, for both the real part coefficient of the geometric series quantization digital filter and the imaginary part coefficient of the geometric series quantization digital filter, the real part and the imaginary part of the impulse response h (k) are replaced by geometric series {0, ± 2^0, ± 2^1, ± 2^2,.+ -. 2 μm } to generate a geometric series quantized filter coefficient q (k).
It should be noted that, in other embodiments of the present invention, when the impulse response h (k) coefficient is a single but real number, the imaginary coefficient may be understood as 0, or when the impulse response h (k) coefficient is a single but imaginary number, the real coefficient may be understood as 0.
The preset quantization bit number in the embodiment of the invention is a positive integer related to the digital shifter bit number of the digital filter and the accuracy of the filtered signal, the quantization bit number is preset by selecting according to a specific digital circuit hardware structure by a person skilled in the art, in one implementation manner, in the FPGA implementation, the preset quantization bit number is selected according to matching between the shift register bit number and the signal accuracy, for example, when a shift register with 16 bits is selected, the ADC digital-analog conversion occupies 10 bits, and the preset quantization bit number in the geometric progression quantization digital filtering method in the embodiment of the invention is selected as 6 bits by the person skilled in the art.
In a preferred implementation manner, step S100 in the embodiment of the present invention quantizes the digital filter impulse response coefficient based on a preset quantization bit number m to obtain the digital filter impulse response quantized resultSpecifically, the method comprises the following steps of,
Step S101, calculating the maximum quantized amplitude M of the impulse response function h (k) of the digital filter, wherein the maximum quantized amplitude M is the absolute value of the maximum value in the real part and the imaginary part of all impulse responses, namely the maximum quantized amplitude M is calculated by the following formula
Step S102, calculating a minimum quantization interval delta based on the preset quantization bit number M and the maximum quantization amplitude M, wherein the minimum quantization interval delta can be calculated by the following formula
。
The absolute value of the maximum value in the real part and the imaginary part of the impulse response is set as the maximum quantization amplitude, so that the quantization range required by the original digital filter in the quantization process can be determined, the minimum quantization interval is further accurately determined based on the maximum quantization amplitude and the preset quantization bit number, the actual states of specific impulse response coefficients of different digital filters can be combined, the accurate quantization interval is accurately set, and the accuracy between the convolution calculation completed by combining the shifter instead of the convolution calculation directly completed by the original unquantized impulse response function on the basis of the quantized impulse response function can be ensured to be within an acceptable range in practical application.
Step S103, obtaining a real part operation parameter r k and an imaginary part operation parameter i k by dividing the real part of impulse response h (k) by the absolute value of the imaginary part and performing rounding calculation by using the minimum quantization interval delta, wherein the real part operation parameter r k and the imaginary part operation parameter i k are calculated by the following formulas
,
,
Wherein, The representation is rounded down and up,Meaning rounded up, in a preferred embodiment, rounded up or down, may be performed in a neighborhood according to rounding principles.
Step S104, based on the real part operation parameter r k and the imaginary part operation parameter i k, obtaining quantized impulse response quantization result of the digital filter through 2-based exponential operation under preset conditionsAnd。
In the embodiment of the invention, the exponent operation based on 2 under the preset condition can determine the real part quantization coefficient based on the relation of r k and 0Determining imaginary quantized coefficients based on a relationship of i k and 0。
In particular, wherein said digital filter impulse response quantization resultsAndCalculated by the following formula
Wherein, AndRespectively obtaining impulse responses of the digital filter after quantizationReal and imaginary parts of (a) are provided.
In the embodiment of the invention, the real part coefficient is used forAnd the imaginary coefficientAll the digital filter comprises the numerical values after the exponent operation based on 2, on the basis of the calculation principle of the binary multiplier, the impulse response coefficient is converted into the numerical values after the exponent operation based on 2, and the complex multiplication calculation of the digital filter can be converted into the shift calculation of the shifter, so that the complexity of the structure and calculation of the digital filter is greatly reduced.
The embodiment of the invention also comprises a step S200 of calculating the input signal based on the quantized digital filter impulse response to obtain a shift calculation result of the input signal。
Based on the step S100 of quantifying the impulse response system of the digital filter to an integer power of 2, the multiplication in the subsequent convolution operation can be substantially converted into a shift calculation, which can effectively reduce the complexity and resource consumption of the calculation compared with the complex multiplication, and can improve the accuracy and stability of the calculation under the complex calculation amount.
In a preferred implementation manner, step S200 specifically includes,
Based on the impulse response coefficient of the digital filterAndObtaining multiplication results of the input signal x (k) and the digital filter impulse response q (k) through shift operation of a shifter on the input signal x (k), wherein the shift calculation resultsThe calculation formula is as follows:
Wherein, N is the order of the digital filter.
The embodiment of the invention further comprises a step S300 of adding and calculating the shift calculation result to obtain a filtering output result.
As convolution operations in digital signal processing generally include multiplication operations and addition operations, in a preferred embodiment of the present invention, step S200 completes the multiplication operation, and step 300 completes the corresponding addition operation.
In a preferred implementation manner of the embodiment of the present invention, the addition calculation includes, in addition to a calculation manner of directly adding up a plurality of addition terms, adding up after assigning a coefficient to each addition term, where the coefficients may be the same or different, and further includes, after assigning a coefficient to each addition term, adding up a sum total number, and then adding up a multiplication coefficient, and taking a result after the multiplication calculation as a final calculation result of the addition calculation.
In a preferred implementation manner of the embodiment of the present invention, step S300 specifically includes summing the shift calculation results, multiplying the sum by the minimum quantization interval Δ, and calculating to obtain a filtered output result. The filtering output result is recorded asThe method can be calculated by the following formula:
Wherein, The result is output for filtering.
The embodiment of the invention quantizes impulse response coefficients of a digital filter based on a preset quantization bit number, and converts the impulse response functions into real part coefficientsAnd the imaginary coefficientAll the values comprise values subjected to exponent operation based on 2, a shift calculation result of the digital filter is obtained through further shift operation according to the input signals, and finally a filtering output result is obtained through addition calculation. The complex multiplication calculation of the digital filter is converted into the shift calculation of the shifter, the complexity of the structure and calculation of the digital filter is greatly reduced, and the signal processing efficiency and the processing timeliness are improved.
In addition, the shifted signal is multiplied by the minimum quantization interval value after the addition operation, and the minimum quantization interval value is inversely proportional to the quantization bit number, so that the minimum quantization interval value corresponds to the maximum quantization bit number, the larger the quantization bit number is, the closer the quantization bit number is to an actual output filtering signal, so that the error of the filtering signal at the corresponding output moment is reduced, the precise corresponding degree between the shift operation after quantization and the addition operation and the actual convolution operation is ensured, and the feasibility of the geometric-series quantization digital filtering method in practice is realized.
It should be noted that, in the geometric progression quantization digital filtering method in the embodiment of the present invention, the digital filtering specifically refers to a filtering method implemented by convolution operation in the field, and may also include correlation computation including autocorrelation and cross correlation.
Fig. 2a is a schematic diagram of an 8-bit shift of a method for implementing a geometric-series quantization digital filter according to an embodiment of the present invention. Taking an 8-bit shifter as an example, b7 is a sign bit, LSB is a least significant bit, and MSB is a most significant bit. In the shift operation, if=1 OrAll bits except the sign bit b7 are shifted by 1 bit to the right. If it isOr (b)The sign bit remains unchanged and the blank bit of the shifted LSB is zero padded.
Fig. 2b is a schematic diagram of 16-bit shift of a method for implementing a geometric-series quantization digital filter according to an embodiment of the present invention, where a 16-bit shifter is taken as an example, and b15 is a sign bit. In the shift operation, if=8 OrAll bits except the sign bit b15 are shifted 3 bits to the right. If it isOr (b)The sign bit is flipped. The blank bit of the shifted LSB is zero-padded.
In the embodiment of the invention, a frame diagram of the geometric progression quantization digital filter is shown in fig. 3, and the geometric progression quantization digital filter 200 includes a shifter 201, an adder 202, a delay unit 203, and a data preprocessing unit 204.
The data preprocessing unit 204 is configured to perform quantization on the digital filter impulse response coefficient based on a preset quantization bit number m, and obtain the digital filter impulse response quantization resultThe quantization resultComprising real part coefficientAnd the imaginary coefficientThe real part coefficientAnd the imaginary coefficientAll include values after an exponential operation with a base of 2,
The shifter 201 is configured to perform computation on an input signal based on the quantized digital filter impulse response to obtain a shift computation result of the input signal。
In other preferred embodiments of the present invention, the specific quantization operation, shift operation, and addition operation of the geometric progression quantization digital filter are performed in the same manner as the geometric progression quantization digital filtering method described above, and will not be repeated here.
As shown in fig. 4, the implementation of the n=4-order geometric quantization filter can be described by using the schematic block diagram of the digital filter in fig. 4, and corresponds to fig. 4, when the input discrete complex signal x (k) is subjected to a successive delay z (-1), a shift operation is performed based on the calculated real part and imaginary part of the corresponding digital filter coefficient, and the calculated result is calculated by a convolution expansion through shift substitution:
S (k, 0), s (k, 1), s (k, 2) and s (k, 3) are obtained, then s (k, 0), s (k, 1), s (k, 2) and s (k, 3) are accumulated, and the sum of the accumulated sums is multiplied by delta to obtain y ' k ', so that y ' k is the result of filtering x (k).
In order to illustrate the error between the convolution operation and the direct convolution operation implemented by the quantization operation, the shift operation, and the addition operation in the embodiment of the present invention, further evaluate the performance of the geometric progression quantization digital filtering method and the geometric progression quantization digital filter in the embodiment of the present invention, fig. 5a to fig. 5d show the result analysis of simulation verification.
In this embodiment, in order to perform simulation verification on the proposed implementation method of the geometric progression quantization digital filter, the quantization bit numbers m=1, 2,3, and 4 are respectively taken to perform convolution calculation, and compared with a conventional convolution algorithm, and it can be seen according to experimental comparison results. The quantized bit number m and the corresponding mean absolute percentage error (Mean Absolute Percentage Error, MAPE) results are noted in the figure.
The MAPE measurement calculation method is used for calculating the error between the calculation results of the method and the calculation results of the traditional convolution method:
as can be seen from the figure, as the number of quantization bits m increases, the calculation result of the method is more and more similar to that of the conventional convolution method, and is consistent with a formula.
Therefore, by using the geometric progression quantization digital filter and the implementation method thereof provided by the invention, on the premise that the result is close to the output of the traditional filter, the operation efficiency is greatly improved, the hardware (including storage and calculation) resources are reduced, and the implementation complexity is reduced.
The apparatus embodiments described above are merely illustrative, wherein the elements illustrated as separate elements may or may not be physically separate, and the elements shown as elements may or may not be physical elements, may be located in one place, or may be distributed over a plurality of network elements. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of this embodiment. Those of ordinary skill in the art will understand and implement the present invention without undue burden.
From the above description of the embodiments, it will be apparent to those skilled in the art that the embodiments may be implemented by means of software plus necessary general hardware platforms, or of course may be implemented by means of hardware. Based on this understanding, the foregoing technical solution may be embodied essentially or in a part contributing to the prior art in the form of a software product, which may be stored in a computer readable storage medium, such as ROM/RAM, a magnetic disk, an optical disk, etc., including several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the method described in the respective embodiments or some parts of the embodiments.
It should be noted that the above-mentioned embodiments are merely for illustrating the technical solution of the present invention, and not for limiting the same, and although the present invention has been described in detail with reference to the above-mentioned embodiments, it should be understood by those skilled in the art that the technical solution described in the above-mentioned embodiments may be modified or some technical features may be equivalently replaced, and these modifications or substitutions do not deviate the essence of the corresponding technical solution from the scope of the technical solution of the embodiments of the present invention.
Claims (5)
1. A geometric quantitative digital filtering method is characterized in that the method comprises the following steps of,
Based on a preset quantization bit number m, quantizing the impulse response coefficient of the digital filter to obtain the impulse response quantization result of the digital filterThe quantization resultComprising real part coefficientAnd the imaginary coefficientThe real part coefficientAnd the imaginary coefficientAll the digital filter impulse response coefficients comprise values subjected to exponential operation based on 2, and the digital filter impulse response quantized results are obtained by quantizing the digital filter impulse response coefficients based on a preset quantization bit number mSpecifically, the method comprises the following steps of,
Calculating the maximum quantized amplitude M of the impulse response function h (k) of the digital filter, wherein the maximum quantized amplitude M is the absolute value of the maximum value in the real part and the imaginary part of all impulse responses,
Calculating a minimum quantization interval delta based on a preset quantization bit number M and the maximum quantization amplitude M, calculating the minimum quantization interval delta based on the preset quantization bit number M and the maximum quantization amplitude M, specifically, calculating the minimum quantization interval delta using the following formula,,
Using the minimum quantization interval delta, at least by division of the real part and the imaginary part of the impulse response h (k) and rounding calculation, respectively obtaining a real part operation parameter r k and an imaginary part operation parameter i k,
Based on the real part operation parameter r k and the imaginary part operation parameter i k, obtaining quantized impulse response quantization results of the digital filter through 2-based exponential operation under preset conditionsAndThe quantized digital filter impulse response quantization result is obtained by exponential operation based on the real part operation parameter r k and the imaginary part operation parameter i k under the preset condition and based on 2AndSpecifically, the method comprises the following formula calculation,
Wherein, AndRespectively obtaining impulse responses of the digital filter after quantizationIs used for the real and imaginary parts of (a),
Calculating an input signal based on the quantized digital filter impulse response to obtain a shift calculation result of the input signalThe quantized digital filter impulse response is calculated on the basis of the input signal, and a shift calculation result of the input signal is obtainedSpecifically, the method comprises the following steps of,
Based on quantized impulse response coefficients of the digital filterAndObtaining multiplication results of the input signal x (k) and the digital filter impulse response q (k) through shift operation of a shifter on the input signal x (k), wherein the shift calculation resultsThe calculation formula is as follows:
Wherein, N is the order of the digital filter,
Adding and calculating the shift calculation result to obtain a filter output result, wherein adding and calculating the shift calculation result to obtain a filter output result specifically comprises adding and multiplying the shift calculation result by the minimum quantization interval delta, calculating to obtain a filter output result, adding and multiplying the shift calculation result by the minimum quantization interval delta, calculating to obtain a filter output result specifically comprises calculating by the following formula
Wherein, The result is output for filtering.
2. The geometric-series quantization digital filtering method of claim 1, wherein the dividing and rounding the absolute value of the real part and the imaginary part of the impulse response h (k) to obtain the real part operation parameter r k and the imaginary part operation parameter i k respectively by using the minimum quantization interval delta comprises calculating the real part operation parameter r k and the imaginary part operation parameter i k by the following formula,
Wherein, The representation is rounded down and up,Representing an upward rounding.
3. The geometric quantization digital filtering method of claim 1, wherein,。
4. The geometric progression quantization digital filtering method of claim 1, wherein the predetermined number of quantization bits is a positive integer associated with the number of digital filter digital shifter bits and the accuracy of the filtered signal.
5. A geometric quantitative digital filter is characterized by comprising a shifter, an adder, a delay unit and a data preprocessing unit,
The data preprocessing unit is used for executing, quantizing the impulse response coefficient of the digital filter based on a preset quantization bit number m, and obtaining the quantized result of the impulse response of the digital filterThe quantization resultComprising real part coefficientAnd the imaginary coefficientThe real part coefficientAnd the imaginary coefficientAll the digital filter impulse response coefficients comprise values subjected to exponential operation based on 2, and the digital filter impulse response quantized results are obtained by quantizing the digital filter impulse response coefficients based on a preset quantization bit number mSpecifically, the method comprises the following steps of,
Calculating the maximum quantized amplitude M of the impulse response function h (k) of the digital filter, wherein the maximum quantized amplitude M is the absolute value of the maximum value in the real part and the imaginary part of all impulse responses,
Calculating a minimum quantization interval delta based on a preset quantization bit number M and the maximum quantization amplitude M, calculating the minimum quantization interval delta based on the preset quantization bit number M and the maximum quantization amplitude M, specifically, calculating the minimum quantization interval delta using the following formula,,
Using the minimum quantization interval delta, at least by division of the real part and the imaginary part of the impulse response h (k) and rounding calculation, respectively obtaining a real part operation parameter r k and an imaginary part operation parameter i k,
Based on the real part operation parameter r k and the imaginary part operation parameter i k, obtaining quantized impulse response quantization results of the digital filter through 2-based exponential operation under preset conditionsAndThe quantized digital filter impulse response quantization result is obtained by exponential operation based on the real part operation parameter r k and the imaginary part operation parameter i k under the preset condition and based on 2AndSpecifically, the method comprises the following formula calculation,
Wherein, AndRespectively obtaining impulse responses of the digital filter after quantizationIs used for the real and imaginary parts of (a),
The shifter is used for executing calculation based on quantized digital filter impulse response to input signals to obtain a shift calculation result of the input signalsThe quantized digital filter impulse response is calculated on the basis of the input signal, and a shift calculation result of the input signal is obtainedSpecifically, the method comprises the following steps of,
Based on quantized impulse response coefficients of the digital filterAndObtaining multiplication results of the input signal x (k) and the digital filter impulse response q (k) through shift operation of a shifter on the input signal x (k), wherein the shift calculation resultsThe calculation formula is as follows:
Wherein, N is the order of the digital filter,
The adder is configured to perform addition calculation on the shift calculation result to obtain a filtered output result, where the addition calculation on the shift calculation result to obtain a filtered output result includes summing the shift calculation result, multiplying the summed shift calculation result by the minimum quantization interval delta, calculating to obtain a filtered output result, and calculating to obtain a filtered output result, where the filtered output result includes a step of calculating by the following formula
Wherein, The result is output for filtering.
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