CN110807169A - Fast processing method for audio signal - Google Patents

Fast processing method for audio signal Download PDF

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CN110807169A
CN110807169A CN202010015986.5A CN202010015986A CN110807169A CN 110807169 A CN110807169 A CN 110807169A CN 202010015986 A CN202010015986 A CN 202010015986A CN 110807169 A CN110807169 A CN 110807169A
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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 336193DEST_PATH_IMAGE001
（1-1）
accordingly, by x (k) through Inverse Discrete Fourier Transform (IDFT) to x (n) can be expressed as:
Figure 315651DEST_PATH_IMAGE002
（1-2）
wherein,
Figure 423284DEST_PATH_IMAGE003
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 input audio informationNumber 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 have a certain rule, each level of operations consists of N/4 butterfly operations, and the basic iterative formula of each butterfly operation is shown as a formula (1-1);
Figure 21755DEST_PATH_IMAGE004
（2-1）
Figure 720907DEST_PATH_IMAGE006
Figure 315836DEST_PATH_IMAGE007
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 108212DEST_PATH_IMAGE008
is a twiddle factor, order
Figure 245932DEST_PATH_IMAGE009
，
Figure 973717DEST_PATH_IMAGE010
，
Figure 321522DEST_PATH_IMAGE011
，
Figure 527375DEST_PATH_IMAGE012
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 conclusion, the radical4 log is needed for computing N-point FFT by frequency decimation algorithm4N = 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 909815DEST_PATH_IMAGE013
/
Figure 808501DEST_PATH_IMAGE014
//
Figure 387567DEST_PATH_IMAGE016
/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:
(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 all regular, each stage of operations is composed of N/4 butterfly operations, the basic iterative formula of each butterfly operation is shown as the following formula (2-1),
Figure 428521DEST_PATH_IMAGE018
Figure 756777DEST_PATH_IMAGE019
Figure 304433DEST_PATH_IMAGE020
Figure 536831DEST_PATH_IMAGE022
（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,is a twiddle factor, order，
Figure 797414DEST_PATH_IMAGE025
，
Figure 618740DEST_PATH_IMAGE026
，
Figure 154763DEST_PATH_IMAGE027
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 61539DEST_PATH_IMAGE028
/
Figure 75632DEST_PATH_IMAGE029
/
Figure 17043DEST_PATH_IMAGE030
//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 383619DEST_PATH_IMAGE032
(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 201403DEST_PATH_IMAGE033
/
Figure 731741DEST_PATH_IMAGE034
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 N-point real sequences are simultaneously calculated by using an N-FFT, and FFT operation is simultaneously carried out on left and right sound channel signals: assume that there are two N-point real signals:
Figure 750513DEST_PATH_IMAGE035
(ii) a The corresponding frequency domain signal after FFT is
Figure 756515DEST_PATH_IMAGE036
0≤k≤N-1。
Order:
Figure 112410DEST_PATH_IMAGE037
wherein
Figure 762834DEST_PATH_IMAGE038
Are all complex sequences. Therefore, the following steps are carried out:
Figure 686928DEST_PATH_IMAGE039
correspondingly:
Figure 180226DEST_PATH_IMAGE040
(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 215178DEST_PATH_IMAGE041
order:
Figure 110322DEST_PATH_IMAGE042
correspondingly:
,
Figure 185911DEST_PATH_IMAGE044
Figure 24554DEST_PATH_IMAGE045
（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 425411DEST_PATH_IMAGE001
Figure 578437DEST_PATH_IMAGE002
（2-1）
Figure 650518DEST_PATH_IMAGE003
Figure 281613DEST_PATH_IMAGE004
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,is a twiddle factor, order
Figure 869512DEST_PATH_IMAGE006
，
Figure 835414DEST_PATH_IMAGE007
，
Figure 801358DEST_PATH_IMAGE008
，
Figure 317176DEST_PATH_IMAGE009
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 radix4 log is needed for computing N-point FFT by frequency decimation algorithm4N = 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, the calculation results of all the butterfly units of the other stages except the last stage need to be multiplied by twiddle factors, in fig. 2, 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 sets of twiddle factors, the number of the corresponding sets of each stage is (N, N/4, N/16.. 1) the exponents of the butterfly factors of each stage are respectively:
Figure 952950DEST_PATH_IMAGE010
/
Figure 202884DEST_PATH_IMAGE011
/
Figure 910203DEST_PATH_IMAGE012
/
Figure 538980DEST_PATH_IMAGE013
/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 input orderColumn(s) ofx(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 402113DEST_PATH_IMAGE014
(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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Publication number Priority date Publication date Assignee Title
CN117037834A (en) * 2023-10-08 2023-11-10 广州市艾索技术有限公司 Conference voice data intelligent acquisition method and system

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101154215A (en) * 2006-09-27 2008-04-02 上海杰得微电子有限公司 Fast Fourier transform method and hardware structure based on three cubed 2 frequency domain sampling
CN107180636A (en) * 2017-05-19 2017-09-19 深圳市芯中芯科技有限公司 A kind of voice data acquisition methods based on Android system Fourier transform
US20190199604A1 (en) * 2014-12-30 2019-06-27 Research Electronics International, Llc System and Method for Detecting Constant-Datagram-Rate Network Traffic

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101154215A (en) * 2006-09-27 2008-04-02 上海杰得微电子有限公司 Fast Fourier transform method and hardware structure based on three cubed 2 frequency domain sampling
US20190199604A1 (en) * 2014-12-30 2019-06-27 Research Electronics International, Llc System and Method for Detecting Constant-Datagram-Rate Network Traffic
CN107180636A (en) * 2017-05-19 2017-09-19 深圳市芯中芯科技有限公司 A kind of voice data acquisition methods based on Android system Fourier transform

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117037834A (en) * 2023-10-08 2023-11-10 广州市艾索技术有限公司 Conference voice data intelligent acquisition method and system
CN117037834B (en) * 2023-10-08 2023-12-19 广州市艾索技术有限公司 Conference voice data intelligent acquisition method and system

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