CN110807169B - Fast processing method for audio signal - Google Patents

Fast processing method for audio signal Download PDF

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CN110807169B
CN110807169B CN202010015986.5A CN202010015986A CN110807169B CN 110807169 B CN110807169 B CN 110807169B CN 202010015986 A CN202010015986 A CN 202010015986A CN 110807169 B CN110807169 B CN 110807169B
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左罡
胡晨光
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Yizhao Micro Electronics Hangzhou Co ltd
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Abstract

In order to save the computation of audio processing, the present invention provides a fast processing method for audio signals, which comprises the following steps: step 1, extracting FFT/IFFT according to frequency; step 2, extracting the change rule of the FFT butterfly operation data address according to the frequency domain: for the base-4 DIF FFT, each stage of calculation is N input data composed of a group of four data, and N output data are obtained by performing butterfly operation. Step 3, obtaining the change rule of the DIF rotation factor of the base 4: for the FFT algorithm extracted according to the frequency, except for the last stage, the calculation results of the butterfly units of other stages need to be multiplied by the twiddle factors, and the law of the DIF FFT/IFFT output data sorting of the base 4 is obtained. Step 4, executing mixed base DIF FFT/IFFT; step 5, the FFT operation scheme of the real sequence comprises the following steps: simultaneously calculating two N-point real sequence FFTs by using one N-FFT; an N-FFT is used to compute an FFT of a real sequence of 2N points.

Description

Fast processing method for audio signal
Technical Field
The invention mainly utilizes the mixed base FFT/IFFT principle to realize the rapid operation processing of the audio data signal.
Background
Currently, processing algorithms (e.g., noise reduction, echo cancellation, etc.) for audio data signals are generally implemented in the frequency domain. In the digital signal processing of audio data, the time-frequency conversion needs to perform FFT/IFFT operation. Since the audio processing algorithm is implemented by framing. Each frame of audio data corresponds to different sampling rates, and the number of sampling points is generally 64/128/256 points, so that the 64/128/256-point FFT/IFFT is usually implemented by a radix-2 method for audio signals.
The defects of the prior art are as follows: the FFT/IFFT operation amount of the base 2 is larger than that of the base 4 and the mixed base; the default input of the FFT/IFFT is complex, and the operation amount of the FFT/IFFT is simplified without utilizing the characteristic that the audio is a real number signal; the existing algorithms are generally floating-point, and the operation cost is larger than that of a fixed point.
Fast Fourier Transform (FFT)/inverse fourier transform (IFFT) principles: the time domain signal obtains a frequency domain signal through Fourier transform; and the frequency domain signal obtains a time domain signal by utilizing inverse Fourier transform. Data sequence of length Nx(n)Discrete fourier transform ofX(k)Can be expressed as:
Figure 719851DEST_PATH_IMAGE002
（1-1）
accordingly, by x (k) through Inverse Discrete Fourier Transform (IDFT) to x (n) can be expressed as:
Figure 554952DEST_PATH_IMAGE004
（1-2）
wherein the content of the first and second substances,
Figure 643125DEST_PATH_IMAGE006
is a twiddle factor. The basic idea of Fast Fourier Transform (FFT) is to decompose the original N-point sequence into a series of short sequences in turn. The characteristics of the twiddle factors in DFT are fully utilized: symmetry, periodicity and reducibility, and the DFTs of these short sequences are obtained and combined appropriately to achieve the purposes of eliminating repetitive calculations, reducing multiplication operations and simplifying the structure. It can be known that the IFFT calculation is performed by performing an FFT operation after conjugating the input, and then dividing the result by the number N of IFFT points.
Disclosure of Invention
In order to solve the above drawbacks, the present invention provides a fast processing method for audio signals, which comprises the following steps:
step 1, extracting FFT/IFFT according to frequency: setting an input audio signal sequencex(n)Has a length of N =4LL is an integer, by pair performing DFTX(k)The remainder of dividing k by 4 is decomposed, the base 4 operations are regular, each level of operations is composed of N/4 butterfly operations, and the basic iterative formula of each butterfly operation is shown as formula (1-1).
Figure 896383DEST_PATH_IMAGE008
Figure 28287DEST_PATH_IMAGE010
（2-1）
Figure 364065DEST_PATH_IMAGE012
Figure 239618DEST_PATH_IMAGE014
In the above formula (2-1), m represents the m-th orderButterfly operation, k is the number of lines of data, N is the number of points of data to be calculated,
Figure 347382DEST_PATH_IMAGE016
is a twiddle factor, order
Figure 197657DEST_PATH_IMAGE018
，
Figure 210613DEST_PATH_IMAGE020
，
Figure 702905DEST_PATH_IMAGE022
，
Figure 599930DEST_PATH_IMAGE024
The frequency-decimated butterflies of the available radix 4 are shown in FIG. 2.
As can be seen from equation (2-1), a radix-4 butterfly requires 3 complex multiplications and 4 complex additions/subtractions. In summary, the computation of N-point FFT from radix-4 by frequency decimation algorithm requires log4N = L stages of operation. Fig. 2 is a 16-point basis four FFT flow chart.
Step 2, extracting the change rule of the FFT butterfly operation data address according to the frequency domain: for the radix-4 DIF FFT, each stage of calculation is N input data consisting of a group of four data, and a butterfly operation is performed to obtain N output data. In fig. 2, the difference between adjacent data in the four data subjected to the butterfly operation at stage 1 is 4, the difference between adjacent data in the four data subjected to the butterfly operation at stage 2 is 1, the difference is D, and the number of stages in which the butterfly operation is performed is P, and then for N =4LPoint FFT, total log4N = L stages of operation, each stage of operation having N/4 butterfly units, and thus, the relationship of D and P is: d =4L-P；
Step 3, obtaining the change rule of the DIF rotation factor of the base 4: for the FFT algorithm extracted according to frequency, except for the last stage, the calculation results of all the butterfly units of the other stages need to be multiplied by twiddle factors. In FIG. 2, the 2 nd butterfly does not need to be multiplied by the twiddle factor, and the 1 st butterfly does need to be multiplied by the twiddle factorThe corresponding 4 sets of twiddle factors are multiplied. The corresponding group number of each stage is (N, N/4, N/16.. 1), and the indexes of the butterfly factors of each stage are respectively:
Figure 604795DEST_PATH_IMAGE026
/
Figure 652516DEST_PATH_IMAGE028
/
Figure 135450DEST_PATH_IMAGE030
/
Figure 155490DEST_PATH_IMAGE032
/1，
obtaining the sorting rule of the DIF FFT/IFFT output data of base 4: as shown in FIG. 2, the output order of radix-4 DIF FFT/IFFT is the reverse order of the input according to the 4-ary system, for example, 03 (4-ary system) corresponds to 30 (4-ary system). For all the radix-four FFT/IFFT, the output is obtained by the operation result of the last stage according to the reverse order of the 4-system number.
And 4, executing mixed base DIF FFT/IFFT: setting an input sequencex(n)Has a length of N =4L2, L is an integer. For this case, such as 32-point, 128-point FFT/IFFT, based on radix 4, the patent can implement adding radix 2 operation in the last stage. The difference value of the butterfly operation data address of the last stage of the radix-2 operation is 1. The operation formula is as follows:
Figure 613147DEST_PATH_IMAGE034
(3-1)
step 5, calculating FFT of the real sequence: the inputs to the aforementioned FFT algorithm are all complex, but for audio signals, the inputs are all real. The FFT operation scheme of the real sequence comprises the following steps: simultaneously calculating two N-point real sequence FFTs by using one N-FFT; an N-FFT is used to compute an FFT of a real sequence of 2N points.
Drawings
FIG. 1 is a flow diagram of a radix-4 DIF butterfly;
FIG. 2 is a flow chart of a 16-point radix 4 DIF FFT operation;
fig. 3 is a schematic block diagram of an FFT/IFFT implementation fix-point scheme.
Detailed Description
The invention will be better embodied on the basis of the description with the attached drawings, and the method of the invention comprises the following steps:
step 1, extracting FFT/IFFT according to frequency: setting an input audio signal sequencex(n)Has a length of N =4LL is an integer, by pair performing DFTX(k)The remainder of dividing k by 4 is decomposed, the base 4 operations are regular, each stage of operations is composed of N/4 butterfly operations, and the basic iterative formula of each butterfly operation is shown in the following formula (2-1).
Figure DEST_PATH_IMAGE035
Figure 156954DEST_PATH_IMAGE036
Figure DEST_PATH_IMAGE037
Figure 53366DEST_PATH_IMAGE038
（2-1）
In the above equation (2-1), m represents the mth stage butterfly operation, k is the number of rows where the data is located, N is the number of points of the data to be calculated,
Figure DEST_PATH_IMAGE039
is a twiddle factor, order
Figure 786967DEST_PATH_IMAGE040
，
Figure DEST_PATH_IMAGE041
，
Figure 477842DEST_PATH_IMAGE042
，
Figure DEST_PATH_IMAGE043
The frequency-decimated butterflies of the available radix 4 are shown in FIG. 2.
As can be seen from equation (2-1), a radix-4 butterfly requires 3 complex multiplications and 4 complex additions/subtractions. In summary, the computation of N-point FFT from radix-4 by frequency decimation algorithm requires log4N = L stages of operation. Fig. 2 is a 16-point basis four FFT flow chart.
Step 2, extracting the change rule of the FFT butterfly operation data address according to the frequency domain: for the radix-4 DIF FFT, each stage of calculation is N input data consisting of a group of four data, and a butterfly operation is performed to obtain N output data. In fig. 2, the difference between adjacent data in the four data subjected to the butterfly operation at stage 1 is 4, the difference between adjacent data in the four data subjected to the butterfly operation at stage 2 is 1, the difference is D, and the number of stages in which the butterfly operation is performed is P, and then for N =4LPoint FFT, total log4N = L stages of operation, each stage of operation having N/4 butterfly units, and thus, the relationship of D and P is: d =4L-P；
Step 3, obtaining the change rule of the DIF rotation factor of the base 4: for the FFT algorithm extracted according to frequency, except for the last stage, the calculation results of all the butterfly units of the other stages need to be multiplied by twiddle factors. In FIG. 2, the level 2 butterflies do not need to be multiplied by twiddle factors, and the level 1 butterflies need to be multiplied by the corresponding 4 sets of twiddle factors. The corresponding group number of each stage is (N, N/4, N/16.. 1), and the indexes of the butterfly factors of each stage are respectively:
Figure 497226DEST_PATH_IMAGE044
/
Figure DEST_PATH_IMAGE045
/
Figure 213640DEST_PATH_IMAGE046
/
Figure DEST_PATH_IMAGE047
/1，
obtaining the sorting rule of the DIF FFT/IFFT output data of base 4: as shown in FIG. 2, the output order of radix-4 DIF FFT/IFFT is the reverse order of the input according to the 4-ary system, for example, 03 (4-ary system) corresponds to 30 (4-ary system). For all the radix-four FFT/IFFT, the output sequence is obtained by reversing the data address of the last stage according to the 4-system number.
And 4, executing mixed base DIF FFT/IFFT: setting an input sequencex(n)Has a length of N =4L2, L is an integer. For this case, such as 32-point, 128-point FFT/IFFT, based on radix 4, the patent can implement adding radix 2 operation in the last stage. The difference value of the butterfly operation data address of the last stage of the radix-2 operation is 1. The operation formula is as follows:
Figure 801748DEST_PATH_IMAGE048
(3-1)
taking 32 points as an example, the FFT implementation of the mixed base is described below: 1) the 32-point mixed base FFT can be realized by three stages of 4X4X2, the first two stages of base 4 operation and the last stage of base 2 operation; 2) the difference value of adjacent data of each stage is as follows: 8/2/1, respectively; 3) the number of the corresponding groups of each stage is 8/2/1, and the butterfly operation units in each group use the same set of butterfly factors circularly. The indexes of each stage of butterfly factors are as follows:
Figure 67119DEST_PATH_IMAGE050
/
Figure 763680DEST_PATH_IMAGE052
1; 4) for the output data of the last stage. And converting the data address into a 2-system, reversing the first 4 bits according to the 4-system, and reversing the last 1 bit according to the 2-system to obtain the output sequence of the FFT/IFFT.
Step 5, calculating FFT of the real sequence: the inputs to the aforementioned FFT algorithm are all complex, but for audio signals, the inputs are all real. For a real sequence n, it can be generally regarded as n + j0, and then the FFT operation is performed. Two algorithms are mentioned below to reduce the complexity and the computation of FFT for real signals: 1) two real sequences of N points, left, are calculated simultaneously using an N-FFTAnd simultaneously carrying out FFT operation on the right channel signal: assume that there are two N-point real signals:
Figure 142840DEST_PATH_IMAGE054
(ii) a The corresponding frequency domain signal after FFT is
Figure DEST_PATH_IMAGE056
0≤k≤N-1。
Order:
Figure DEST_PATH_IMAGE058
wherein
Figure DEST_PATH_IMAGE059
Are all complex sequences. Therefore, the following steps are carried out:
Figure DEST_PATH_IMAGE061
correspondingly:
Figure DEST_PATH_IMAGE063
(4-1)
2) an N-FFT is used to compute an FFT of a real sequence of 2N points, assuming there is a real signal of 2N points:
Figure DEST_PATH_IMAGE065
order:
Figure DEST_PATH_IMAGE067
correspondingly:
Figure DEST_PATH_IMAGE069
,
Figure DEST_PATH_IMAGE071
Figure DEST_PATH_IMAGE073
（4-2）
FIG. 3 is a fixed-point scheme for a DIF-based 4 butterfly unit, where auto scaling refers to a dynamic overflow checking scheme, if the input and output of each stage butterfly are set to (16, 15), so that the input signal is large and overflow is likely. Therefore, after each stage of operation is calculated, all values are traversed, and if a variable A exceeding an overflow allowable input value is found, the whole array is shifted to the right by one bit; if a variable 2A is found that exceeds the overflow enable input value, the entire array is right shifted by two bits. This ensures that smaller values of the input are not overscaled and larger values of data are also able to pass through the FFT operation.

Claims (1)

1. A fast processing method for audio signals, comprising the steps of:
step 1, extracting FFT/IFFT according to frequency: setting an input audio signal sequencex(n)Has a length of N =4LL is an integer, by pair performing DFTX(k)The remainder of dividing k by 4 is decomposed, the base 4 operations are regular, each level of operations is composed of N/4 butterfly operations,
Figure 541928DEST_PATH_IMAGE002
Figure 646019DEST_PATH_IMAGE004
（2-1）
Figure 48925DEST_PATH_IMAGE006
Figure 132550DEST_PATH_IMAGE008
in the above equation (2-1), m represents the mth stage butterfly operation, k is the number of rows where the data is located, N is the number of points of the data to be calculated,
Figure 71556DEST_PATH_IMAGE010
is a twiddle factor, order
Figure 517187DEST_PATH_IMAGE012
，
Figure 908854DEST_PATH_IMAGE014
，
Figure 733853DEST_PATH_IMAGE016
，
Figure 527365DEST_PATH_IMAGE018
The frequency-decimated butterfly operation of radix-4 is obtained,
as can be seen from equation (2-1), a radix-4 butterfly requires 3 complex multiplications and 4 complex additions/subtractions, and in summary, the frequency decimation algorithm from radix-4 requires log in the computation of an N-point FFT4N = L level operation;
step 2, extracting the change rule of the FFT butterfly operation data address according to the frequency domain: for the radix-4 DIF FFT, each stage of calculation is N input data composed of four data as a group, and butterfly operation is performed to obtain N output data, the difference value between adjacent data in the four data for butterfly operation at stage 1 is 4, the difference value between adjacent data in the four data for butterfly operation at stage 2 is 1, the difference value is D, the stage number where the butterfly operation is located is P, and for N =4LPoint FFT, total log4N = L stages of operation, each stage of operation having N/4 butterfly units, and thus, the relationship of D and P is: d =4L-P；
Step 3, obtaining the change rule of the DIF rotation factor of the base 4: for the FFT algorithm extracted according to the frequency, except for the last stage, the calculation results of the butterfly units of the other stages need to be multiplied by twiddle factors, the butterfly operation of the 2 nd stage does not need to be multiplied by twiddle factors, the butterfly operation of the 1 st stage needs to be multiplied by 4 corresponding groups of twiddle factors, the corresponding groups of each stage are (N, N/4, N/16.. 1) the indexes of the butterfly factors of each stage are respectively:
Figure 167336DEST_PATH_IMAGE020
/
Figure 46299DEST_PATH_IMAGE022
/
Figure 845628DEST_PATH_IMAGE024
/
Figure 995111DEST_PATH_IMAGE026
/1，
obtaining the sorting rule of the DIF FFT/IFFT output data of base 4: the output sequence of the radix 4 DIF FFT/IFFT is the reverse sequence of the input according to the 4-system, and for all radix four FFT/IFFT, the output is obtained by the reverse sequence of the operation result of the last stage according to the 4-system number;
and 4, executing mixed base DIF FFT/IFFT: setting an input sequencex(n)Has a length of N =4L2, L is an integer, and the last level is added with radix 2 operation on the basis of radix 4, the difference value of the butterfly operation data address of the last level radix 2 operation is 1, and the operation formula is as follows:
Figure 549590DEST_PATH_IMAGE028
(3-1) ；
step 5, calculating FFT of the real sequence: the inputs to the aforementioned FFT algorithm are all complex, but for audio signals, the inputs are all real, real sequence FFT computation schemes include: simultaneously calculating two N-point real sequence FFTs by using one N-FFT; an N-FFT is used to compute an FFT of a real sequence of 2N points.
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