JP2001042033A - Peak frequency computing method in fft signal processing - Google Patents

Abstract

PROBLEM TO BE SOLVED: To perform FFT(fast Fourier transformation) signal processing accurately at a high speed. SOLUTION: A frequency f0 which is a maximum value in a power data distribution obtained by FFT signal processing is selected as an approximate frequency. Interpolation computation is performed between a low-frequency-side adjacent frequency f1 and a high-frequency-side adjacent frequency f2 in the front and rear of the approximate frequency f0 to compute a low-frequency-side peak frequency F1 and a high-frequency-side peak frequency F2. A peak frequency Fp is computed by the expression through the use of power p0, p1, and p2 at the proximate frequency f0, low-frequency-side adjacent frequency f1, and the high-frequency-side adjacent frequency f2 and the low-frequency-side peak frequency F1 and the high-frequency-side peak frequency F2.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

The present invention relates to an FFT signal processing for calculating various frequency characteristics and the like by signal processing using a fast Fourier transform (hereinafter sometimes abbreviated as "FFT") and obtaining a peak frequency. And a peak frequency calculation method.

[0002]

2. Description of the Related Art Conventionally, signal processing using FFT has been
It is widely used to convert time domain data to frequency domain data and calculate frequency characteristics and the like. For example, in the FM-CW radar, the distance and relative speed between the radar and the detection target are calculated based on the frequency of a beat signal obtained by mixing a transmission signal and a reception signal. Prior art regarding the FM-CW radar is disclosed in, for example, Japanese Patent Application Laid-Open Nos. 52-111395 and 7-1205.
49, JP-A-9-80148, JP-A-9-145824
And so on.

FIG. 4 shows a typical FM-CW radar device 1.
The schematic configuration of is shown. The FM-CW radar device 1 transmits a continuous wave frequency-modulated by a triangular wave from the transmitting antenna 3 in order to obtain the distance R to the target 2 and the relative speed V. When the transmission wave is reflected by the target 2, a part is received by the receiving antenna 4. From the time when the transmission wave is transmitted from the transmission antenna 3 to the time when the reception wave is received by the reception antenna 4, a time corresponding to the distance to the target 2 elapses and the transmission wave is frequency-modulated by the triangular wave. Based on this time difference, a frequency shift occurs between the transmission wave and the reception wave. Further, if there is a relative speed change with respect to the target 2, a frequency change based on the Doppler effect also occurs.

[0004] The FM-CW radar device 1 is mounted, for example, in front of a running direction of an automobile, and is used for detecting an obstacle and detecting an inter-vehicle distance to a preceding vehicle. In a vehicle-mounted radar device, the directional characteristics of the transmitting antenna 3 and the receiving antenna 4 are sharpened, and the scanning mechanism 5 controls the transmitting antenna 3.
In addition, the direction of the receiving antenna 4 is changed so that information on the detected two directions of the target can also be obtained. The received signal received by the receiving antenna 4 is subjected to signal processing by the target detection circuit 6 to obtain data based on the received wave that is a reflected wave from the target 2. The target recognition circuit 7 recognizes the number and direction of the targets 2 based on the data obtained by the target detection circuit 6.

FIG. 5 shows the principle of calculating the distance R to the target 2 and the relative speed V in the FM-CW radar apparatus 1 shown in FIG. A transmission wave 10 indicated by a solid line in FIG. 5A is transmitted from the transmission antenna 3 to the target 2. The transmission wave 10 is frequency-modulated by a triangular wave having a constant cycle, and the frequency continuously changes within a certain range. The reception wave 11 indicated by the broken line has a time delay corresponding to the distance to the target 2 and a difference in the frequency fd based on the Doppler effect. As shown in FIG. 5B, the beat signal between the transmission wave 10 and the reception wave 11 in FIG.
The upbeat signal 12 when the frequency of the transmission wave 10 increases and the downbeat signal 13 when the frequency of the transmission wave 10 decreases are obtained. The upbeat signal 12 has a long period in which the frequency is fub, and fub is the downbeat signal 1
3, the frequency becomes lower than the frequency fub having a longer period.

The FM-CW radar apparatus 1 calculates a distance R to the target 2 and a relative speed V of the target 2 based on the frequency of the beat signal. Data obtained by detecting the target 2 has a certain width in the frequency domain. In general, the width is obtained as a frequency corresponding to data having the maximum power among data having a certain width,
The accuracy of the obtained data depends on the accuracy calculated as the peak frequency. Prior art regarding a method of detecting a peak value from obtained data is disclosed in, for example, Japanese Patent Application Laid-Open No. 6-88841.

In the FM-CW radar apparatus 1 shown in FIG. 4, a beat signal is converted into frequency domain data by an FFT process in a target detection circuit 6. In the FFT signal processing, the beat signal is sampled at fixed time intervals, and the data converted into a digital signal by digital / analog conversion (hereinafter abbreviated as “D / A”) is subjected to FFT signal processing by digital arithmetic processing. As such, the data in the frequency domain is obtained corresponding to discrete frequencies. Therefore, it is not always possible to calculate a highly accurate frequency only within the range of data obtained by FFT signal processing. Therefore, in order to calculate a frequency with high accuracy, it is necessary to obtain a fine frequency from a discrete frequency obtained as a result of the FFT signal processing by an interpolation operation. As a method of accurately calculating a peak frequency in FFT, a peak extraction method using phase information by a complex interpolation method. A method of adding zero-point data to increase the number of FFT points, performing FFT processing, and extracting a peak point from the peak of power. and so on. In September 1983, Hara and Iguchi described the "fixed frequency using complex spectrum" in pages 19-29 of "Transactions of the Society of Instrument and Control Engineers" Vol. It has been announced. Also, JP-A-10-2
13613 describes a prior art about a frequency measuring device that accurately obtains a peak frequency by an interpolation operation between the largest data of the spectrum data obtained from the result of the FFT operation and the data before and after the larger data. It has been disclosed.

[0008]

Generally, a digital signal processor (hereinafter, referred to as a digital signal processor) is provided in the target detection circuit 6 shown in FIG.
"DSP") and a central processing unit (hereinafter referred to as "DSP").
The arithmetic processing is performed according to a preset program. DSP and CPU
Can perform a decimal point operation in a fixed-point system or a floating-point system. However,
Performing floating-point operations with software slows down the operation speed, so floating-point operations are performed when a dedicated floating-point operation unit is provided as hardware, and fixed when such a floating-point operation unit is not provided. FFT signal processing is performed by decimal point calculation. By performing the floating-point arithmetic, interpolation can be performed with high precision without any loss of digits at the time of digital signal processing. However, DSPs and CPUs having a floating operation function do not have a D
It is more expensive than SP or CPU. Furthermore, even with the floating-point arithmetic function, processing time is longer than that of fixed-point arithmetic, and signal processing cannot be performed quickly. For this reason, there is a demand for performing FFT signal processing with high precision in fixed-point arithmetic.

Particularly, in the peak extraction using the phase information by the complex interpolation method as described above, a fixed-point DSP
When a CPU or CPU is used, the precision of peak extraction may be reduced due to loss of digits or the like. The method of adding zero point data increases the number of points in the FFT signal processing, which leads to an increase in calculation time.

An object of the present invention is to provide a peak frequency calculating method in FFT signal processing, which can calculate a peak frequency quickly and accurately.

[0011]

According to the present invention, discretely sampled data is converted into frequency domain data by a fast Fourier transform process, and a peak frequency at which the data takes a peak value with respect to a change in frequency is obtained. A maximum value or a minimum value in data for which a peak frequency is to be calculated, a frequency corresponding to the maximum value or the minimum value in the data is calculated as an approximate frequency, and a low frequency The low-frequency side adjacent frequency and the high-frequency side adjacent frequency that are adjacent on the high-frequency side and the high-frequency side are calculated, and each frequency is calculated between the approximate frequency and the low-frequency side adjacent frequency and between the approximate frequency and the high-frequency side adjacent frequency. The low frequency side peak frequency and the high frequency side peak frequency are calculated by performing interpolation for the interpolation based on the data difference corresponding to the low frequency side peak frequency. By interpolation calculation to interpolate between the clock frequency and the high-frequency side peak frequency, the peak frequency calculation method in the FFT signal processing and calculates the peak frequency.

According to the present invention, discretely sampled data is converted into frequency domain data by fast Fourier transform processing, a maximum value or a minimum value is extracted, and a frequency corresponding to the maximum value or the minimum value is determined. It is calculated as an approximate frequency. The low frequency side and high frequency side adjacent frequencies are calculated on the low frequency side and high frequency side adjacent to the approximate frequency, respectively, and the interpolation frequency based on the difference between the approximate frequency and the data corresponding to each frequency is calculated. An insertion operation is performed to calculate a low-frequency peak frequency and a high-frequency peak frequency, respectively. Since the peak frequency is calculated by an interpolation operation that interpolates between the low-frequency peak frequency and the high-frequency peak frequency, the frequency at which data is obtained by fast Fourier transform processing is interpolated and the calculation result is directly obtained. The peak frequency can be accurately calculated up to a frequency smaller than the interval.

In the present invention, the maximum value or the minimum value at the approximate frequency is defined as p0, the data at the low frequency side adjacent frequency is defined as p1, the data at the high frequency side adjacent frequency is defined as p2, and the low value is defined as p2. When the frequency side peak frequency is F1 and the high frequency side peak frequency is F2, the peak frequency Fp is calculated by the following interpolation formula:

[0014]

(Equation 2)

The calculation is performed by using

According to the present invention, the peak value at the approximate frequency, the adjacent frequency on the low frequency side and the adjacent frequency on the high frequency side, and the interpolation calculation process using the approximate frequency on the low frequency side and the approximate frequency on the high frequency side are performed. The frequency can be easily calculated.

In the present invention, the data in the frequency domain is:
It is characterized by being power data calculated from a real part and an imaginary part of a complex frequency component obtained by the fast Fourier transform processing.

According to the present invention, since the peak frequency is calculated from the power data calculated from the real part and the imaginary part of the complex frequency domain, the peak frequency corresponding to the maximum value or the minimum value of the signal strength can be accurately and quickly determined. Can be calculated.

[0019]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS FIG. 1 shows a basic concept for calculating a peak frequency according to an embodiment of the present invention. Generally, in FFT signal processing, real-time data is converted to complex frequency data. Assuming that the real part of the complex frequency data is R and the imaginary part is i, the amplitude and the like of each frequency component can be calculated as power p shown in the following equation 1. p = √ (R ² + i ² ) / 2 (1)

FIG. 1 shows an example of the frequency distribution of the power p obtained by the FFT signal processing. FM-CW of FIG.
In the radar device 1 or the like, it is necessary to calculate a frequency that shows a peak in the distribution of the power p after the beat signal is subjected to the FFT signal processing. In the data of the power p shown by the solid line in FIG. 1, the power p has the maximum value p0 at the frequency f0.
However, in the result of the FFT signal processing shown in FIG. 4, the number of points indicating the data frequency is finite and the points are spaced from each other. Therefore, the true peak frequency is not necessarily the frequency f0 indicating the maximum value p0, but the data peak. Is likely to be an intermediate frequency between the points where For this reason, in the present embodiment, the frequency f0 at which the power p becomes the maximum value p0 is set as an approximate frequency, and the frequency f1 which is a low frequency side adjacent frequency of a point adjacent to the low frequency side is represented by:
The interpolation calculation is also performed using the data at the high frequency side adjacent frequency f2 of the point adjacent on the high frequency side.

Approximate frequency f0 and lower frequency side adjacent frequency f1
And the approximate frequency f0 and the high frequency side adjacent frequency f
Interpolation between the two is performed by peak extraction using phase information by a conventional complex interpolation method. In the complex interpolation method, phase characteristics of a complex spectrum obtained by Fourier-transforming real number data are used. In the complex spectrum, frequency identification is performed using the fact that the phase is inverted before and after the peak frequency and that the reciprocal of the complex spectrum is plotted on a straight line. Two adjacent components forming the peak of the complex spectrum are defined as Zm and Zm + 1. The two vectors should theoretically differ in orientation by exactly π, but in reality, they have other frequency components, noise,
The phase difference does not exactly become π due to the influence of the quantization error and the like. Therefore, a unit vector of u = (Zm + 1−Zm) / | Zm + 1−Zm | (2) shown in the following equation 2 is defined, and the frequency f is estimated from the following equation 3.

[0022]

(Equation 3)

Here, m indicates the frequency at Zm.
(U, Zm) and the like indicate an inner product as a vector. Assuming that the peak frequencies obtained by the interpolation operation are a low-frequency side peak frequency F1 and a high-frequency side peak frequency F2, respectively, the peak frequencies are obtained as indicated by a chain line. Further, a peak frequency Fp indicated by a two-dot chain line is calculated by the interpolation operation of the following Expression 4.

[0024]

(Equation 4)

FIG. 2 shows a schematic configuration of an FFM-CW radar apparatus 21 to which the peak frequency calculation method in the FFT signal processing as shown in FIG. 1 is applied. The FFM-CW radar device 21 is mounted on, for example, an automobile, and is used to detect a distance and a relative speed to a target 22 such as a vehicle ahead or an obstacle. From the transmitting antenna 23, the FF
A millimeter wave band radio wave frequency-modulated by a triangular wave according to the M-CW method is transmitted, and a reception wave reflected by the target 22 is received by the reception antenna 24. Transmitting antenna 23
The receiving antenna 24 has a sharp directional characteristic, and the scanning mechanism 25 performs scanning for changing the directional direction within a certain angle range based on the signal direction of the vehicle.
2 is performed. The reception signal received by the reception antenna 24 is input to the target detection circuit 26, and the target is detected based on the beat signal between the transmission wave and the reception wave. The scanning mechanism 25 swings the transmitting antenna 23 and the receiving antenna 24 by a certain angle,
Since the transmission wave for the detection 2 is transmitted and the reception wave is received, the same target 22 is generally detected at a plurality of scanning angles. The target recognition circuit 27 recognizes the size and direction of the target 22 based on the detection result of the target detection circuit 26.

The target detection circuit 26 includes a transmission circuit 30, a reception circuit 31, an A / D circuit 32, and an FFT circuit 33. The transmission circuit 30 generates a high frequency signal of the FM-CW system, amplifies the power, and supplies the amplified signal to the transmission antenna 23. The receiving circuit 31 compares the received signal received by the receiving antenna 24 with a part of the output from the transmitting circuit 30 and outputs a beat signal as a difference. Receiving circuit 31
The beat signal output from is an analog signal,
It is sampled at regular intervals by the D circuit 32 and converted into digital signals. The digital signal converted by the A / D circuit 32 is data in the time domain,
The data is converted into frequency domain data by the T circuit 33.

The FFT circuit 33 includes a DSP 34, a read-only memory (hereinafter abbreviated as "ROM") 35, and a random access memory (hereinafter abbreviated as "RAM").
36 and the like. DSP34 is a fixed-point DSP
In accordance with a program stored in the ROM 35 in advance, an FFT operation process and a power operation process as shown in Expression 1 for the complex frequency data obtained by the FFT signal processing are performed. Further, a peak frequency as shown in Expression 2 is calculated for the result of the power calculation process. RAM 36 is
It is used for storing the result of arithmetic processing by the DSP 34 and the progress of the process.

FIG. 3 shows the procedure of the arithmetic processing by the DSP 34 of FIG. The arithmetic processing is started from step s1, and in step s2, F is applied to the input digital data.
FT operation processing is performed. In step s3, power operation processing as shown in Expression 1 is performed on the complex frequency data obtained by the FFT operation processing. In step s4, the frequency f0 having the maximum value is selected as the approximate frequency in the result of the power calculation processing, and a calculation is performed before and after that, that is, the low frequency side adjacent frequency f1 and the high frequency side adjacent frequency f2 are selected. Are calculated. In step s5, an interpolation calculation of a peak value using the phase information by the complex interpolation method is performed between the adjacent frequency f0 and the low frequency side adjacent frequency f1 and the high frequency side adjacent frequency f2, and the low frequency side peak is calculated. The frequency F1 and the high frequency side peak frequency F2 are calculated. In step s6, equation 2
The peak frequency Fp is calculated according to the following formula, and the calculation procedure ends in step s7.

In the embodiment described above, the peak extraction using the phase information is performed by the complex interpolation method to calculate the low frequency side peak frequency F1 and the high frequency side peak frequency F2, but other interpolation methods are used. For example, JP
An interpolation method such as 0-213613 can also be used. Although the interpolation formula of Equation 2 is used to calculate the peak frequency Fp in step s6, the peak frequency is obtained by a simpler calculation such as the average value of the low-frequency peak frequency F1 and the high-frequency peak frequency F2. Can also. Although the FFT circuit 33 performs the FFT operation using the DSP 34, the FFT circuit 33 can also perform the FFT operation using a CPU or dedicated hardware. Also in these cases, the simplification of the configuration and the speeding up of the arithmetic processing can be achieved by not using the floating point method.

In the above embodiment, the FFT signal processing is
Although the present invention is used in the target detection circuit 26 of the M-CW radar device 21, the present invention can be effectively applied to a frequency device or the like which is a target of the prior art of Japanese Patent Application Laid-Open No. H10-213613. As the peak frequency, not only the maximum or maximum peak frequency but also the minimum or minimum frequency corresponding to the so-called dip can be calculated in the same manner. Furthermore, although the peak frequency is calculated for the power data corresponding to the absolute value of the real part and the imaginary part in the complex frequency data, the peak frequency corresponding to only the real part or only the imaginary part can be accurately calculated by the same interpolation calculation. It can be calculated well.

[0031]

As described above, according to the present invention, the data of the maximum value or the minimum value and the data of the low frequency side and the maximum value or the minimum value of the frequency domain data after the fast Fourier transform processing of the discretely sampled data are performed. The peak frequency can be calculated with high accuracy using data adjacent to the high frequency side. Since the interpolation operation for interpolation is performed using the low frequency side adjacent frequency and the high frequency side adjacent frequency of the approximate frequency corresponding to the data of the maximum value or the minimum value, even if the fixed point calculation processing is performed in the fast Fourier transform processing It is possible to perform quick and high-precision arithmetic processing by making it less susceptible to the loss of digits and the like.

Further, according to the present invention, the peak frequency can be accurately obtained by a simple interpolation operation.

Further, according to the present invention, the peak frequency at which the power data has the maximum value or the minimum value can be obtained quickly and accurately.

[Brief description of the drawings]

FIG. 1 is a graph showing a basic concept of an embodiment of the present invention.

FIG. 2 is a block diagram showing a schematic electrical configuration of an FM-CW radar device 21 that calculates a peak frequency by applying the concept of FIG.

FIG. 3 is a flowchart showing a calculation procedure of the DSP 34 of FIG. 2;

FIG. 4 is a block diagram showing a schematic electrical configuration of a conventional FM-CW radar device 1;

FIG. 5 is a graph showing the operation principle of the FM-CW radar device of FIG.

[Explanation of symbols]

 Reference Signs List 21 FM-CW radar device 22 Target 26 Target detection circuit 30 Transmission circuit 31 Receiving circuit 32 A / D circuit 33 FFT circuit 34 DSP 35 ROM 36 RAM

Claims (3)

[Claims] 1. A method of converting discretely sampled data into frequency domain data by a fast Fourier transform process, and calculating a peak frequency when the data takes a peak value with respect to a change in frequency. Extract the maximum or minimum value in the data for which the peak frequency should be calculated, calculate the frequency corresponding to the maximum or minimum value in the data as the approximate frequency, and adjoin the approximate frequency on the low frequency side and the high frequency side Calculate the low frequency side adjacent frequency and the high frequency side adjacent frequency, respectively, based on the difference between the data corresponding to each frequency between the approximate frequency and the low frequency side adjacent frequency, and between the approximate frequency and the high frequency side adjacent frequency. The low frequency peak frequency and the high frequency peak frequency are calculated by performing interpolation for interpolation, and the low frequency peak frequency and the high frequency peak frequency are calculated. By interpolation calculation to interpolate between the clock frequency, the peak frequency calculation method in the FFT signal processing and calculates the peak frequency. 2. The maximum value or the minimum value at the approximate frequency is p0, the data at the low frequency side adjacent frequency is p1, the data at the high frequency side adjacent frequency is p2, and the low frequency side peak is When the frequency is F1 and the peak frequency on the high frequency side is F2, the peak frequency Fp is calculated by the following interpolation formula: 2. The FF according to claim 1, wherein the FF is calculated.
A peak frequency calculation method in T signal processing. 3. The FFT signal according to claim 1, wherein the frequency domain data is power data calculated from a real part and an imaginary part of a complex frequency component obtained by a fast Fourier transform process. Peak frequency calculation method in processing.