A Sub-band Complex Variational Mode Decomposition Denoising Method for Multiple Sound Sources

Abstract

The present invention discloses a sub-band complex variational mode decomposition denoising method applied to multiple sound sources. The entire spectrum of the received signal is divided based on a polyphase filter, and a low-pass filter is constructed according to the number of sub-bands and the sound source frequency; the received signal and the low-pass filter are subjected to polyphase decomposition to obtain a polyphase signal and multiple filter coefficients; the time domain signal of each sub-band is obtained according to the polyphase signal and the multiple filter coefficients; a variational model is constructed based on the complex variational mode decomposition and the time domain signal of each sub-band, and the noise of the output signal of each sound source sub-band is suppressed by the variational model. The present invention extends variational mode decomposition to the field of complex signals, and denoises each sound source in each sub-band by using CVMD. The present invention can effectively improve the signal-to-noise ratio (SNR) of each sound source, and has a small amount of calculation and is easy to implement.

Description

Technical Field

[0001] The present invention belongs to the technical field of signal processing, and in particular relates to a sub-band complex variational mode decomposition denoising method applied to multiple sound sources. Background Art

[0002] Speech signal denoising is a key step before speech signal analysis. Its purpose is to reduce the impact of noise on speech signals to highlight the characteristics of speech signals. It has been widely used in speech enhancement, speech recognition, speech coding and other fields.

[0003] Many scholars at home and abroad have studied the problem of speech noise reduction. Lim and Oppenheim proposed the Wiener filter method, which can process single-input and single-output stationary random signals, but requires a prior distribution of noise. Yafeng et al. proposed an adaptive filtering noise reduction algorithm based on least mean square (LMS), which can effectively suppress the noise of stationary random signals, but the convergence factor of the filter performance is difficult to control, which greatly affects the noise reduction effect. The empirical mode decomposition (EMD) proposed by Huang et al. can significantly improve the signal-to-noise ratio of nonlinear non-stationary signals, but it has serious mode aliasing and lacks a complete mathematical theoretical derivation. The adaptive complete set empirical mode decomposition of noise (CEEMDAN) proposed by Torres can effectively suppress the mode aliasing in EMD, but it still lacks mathematical theoretical support. In 2014, Dragomiretskiy et al. proposed variational mode decomposition (VMD). Unlike traditional methods based on mode decomposition, this method has a solid theoretical foundation and achieves high computational efficiency and good noise robustness. In recent years, some scholars have proposed applying various neural network models to denoising and have achieved good denoising effects. However, such methods require a large number of samples for model training and require a large amount of computation.

[0004] Although the above algorithm can achieve a certain noise reduction effect in specific scenarios, it is unable to extract a single sound source and reduce noise in a scene with complex multiple sound sources. However, in practical applications, for example, when using a microphone to locate a faulty transformer, the microphone receiving signal will contain multiple sound sources. The existing technology is not only difficult to reduce noise, but also difficult to extract a single sound source in an environment with complex sound sources, and the amplification calculation of noise reduction is very large. Summary of the invention

[0005] Purpose of the invention: The purpose of the present invention is to provide a sub-band complex variational mode decomposition denoising method for multiple sound sources with good denoising effect and small computational complexity.

[0006] Technical solution: The sub-band complex variational mode decomposition denoising method applied to multiple sound sources described in the present invention comprises the following steps:

[0007] Step 1: Divide the entire spectrum of the received signal based on a polyphase filter, and construct a low-pass filter according to the number of sub-bands and the sound source frequency;

[0008] Step 2, performing multi-phase decomposition on the received signal and the low-pass filter to obtain a multi-phase signal and multiple filter coefficients;

[0009] Step 3: Obtain the time domain signal of each subband according to the multi-phase signal and the multiple filter coefficients;

[0010] Step 4: construct a variational model based on the complex variational mode decomposition and the time domain signal of each subband, and perform noise suppression on the output signal of each sound source subband through the variational model.

[0011] The division of the entire spectrum of the received signal in step 1 includes dividing the entire spectrum of the received signal x into K non-overlapping sub-bands using a polyphase filter, and dividing the entire spectrum into K non-overlapping sub-bands according to the number of sub-bands K and the sampling frequency f s Design a prototype low-pass filter h with bandwidth B and order N 0 (n), the system function of the prototype low-pass filter is:

[0012]

[0013] Among them, f s is the sampling frequency, the passband cutoff frequency of H(z) is B / 2, and f s =BK.

[0014] Among them, the prototype low-pass filter h 0 (n) Each subband filter is obtained by translation, and the filter response of the kth subband is:

[0015]

[0016] Where k = 0, 1, ... K-1, w k is the center frequency of the kth subband, w k =-π+2πk / K.

[0017] Wherein, in step 2, based on the received signal x and the prototype low-pass filter h 0 (n) performing a multiphase decomposition comprising:

[0018] x k (m) = x(Km+k);

[0019] e k (l) = h 0 (Kl+k);

[0020] Where k = 0, 1, ... K-1, x k (m) is the k-th multiphase signal, ek (l) is the coefficient of the k-th polyphase filter.

[0021] The relationship between the received signal x and the abyss s is: x = s 1 +s 2 +···+s k +s n ,s n is Gaussian white noise.

[0022] Wherein, in step 3, according to the multiphase signal x k (m) and multiple filter coefficients e k (l) Get the time domain signal y of each subband k (m) include:

[0023] y k (m) = K(IDFT[((x r (m)*e r (m))(-1) r ]); where r = k.

[0024] Wherein, constructing a variational model according to the complex variational mode decomposition and the time domain signal of each subband in step 4 includes:

[0025] Step 41: Denoise each sub-band sound source based on complex variational mode decomposition. Assume that the k-th sound source sub-band output signal is Constructing variational models;

[0026] Step 42, constructing an augmented Lagrangian function and introducing a penalty factor α to transform it into an unconstrained variational case, and solving the variational model;

[0027] Step 43: reconstruct the kth sound source subband output signal after noise suppression based on the solved modal components, that is, the sound source signals after noise suppression.

[0028] The variational model constructed in step 41 is as follows:

[0029]

[0030] in, is the subband output signal, i.e. the complex signal to be decomposed, u i (m) is each modal component, w i is the center frequency corresponding to each modal component, and I is the total number of modes.

[0031] The process of solving the variational model in step 42 includes: constructing an iterative update formula based on the constructed augmented Lagrangian function and introducing a penalty factor α:

[0032]

[0033]

[0034]

[0035]

[0036]

[0037] in, is the multiplication operator, ε is the convergence tolerance, u i (m), The frequency domain form of λ(m) is After inverse Fourier transform, it is u i (m).

[0038] Wherein, the step 43 specifically includes using all u i (m) Reconstruct the output signal of the kth sound source subband after noise suppression Right now:

[0039]

[0040] By repeatedly calculating the k sound source signal subband outputs of the polyphase filter, each sound source signal after noise suppression can be obtained.

[0041] Beneficial effects: Compared with the prior art, the present invention has the following significant improvements: by using a multi-phase filter and performing translation processing on the multi-phase filter, the received signal of multiple sound sources is divided into multiple sub-bands, so as to realize the separation of each sound source signal, fundamentally reduce the difficulty of denoising complex sound sources, and realize the extraction of a single sound source from a complex sound source environment; after each sound source signal is extracted, multiple decompositions are performed through multi-sound source sub-band complex variational modal decomposition, and the solution is performed in the constructed variational model, and the output signal of each sound source sub-band after noise suppression is reconstructed using the solved modal components, and then the entire sound source signal is subjected to denoising processing. It is found through experimental results that the signal-to-noise ratio (SNR) of each sound source after the above processing is significantly improved, and the amount of calculation data of the entire separation and denoising process is small, which is easy to implement. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 It is a schematic diagram of the process of the present invention;

[0043] Figure 2 It is a schematic diagram of the channelized structure of multi-phase filtering;

[0044] Figure 3 is the original spectrum of the signal to be processed;

[0045] Figure 4The output spectrum of the 16th to 31st subbands after polyphase filtering;

[0046] Figure 5 The corresponding spectrum diagram of each modal component decomposed in the sub-band where the first sound source is located;

[0047] Figure 6 This is the spectrum comparison diagram before and after noise reduction of the sub-band where the first sound source is located;

[0048] Figure 7 The corresponding spectrum diagram of each modal component decomposed in the sub-band where the second sound source is located;

[0049] Figure 8 This is the spectrum comparison diagram before and after noise reduction of the sub-band where the second sound source is located;

[0050] Fig. 9 This is the signal-to-noise ratio trend chart before and after denoising the sub-band where the sound source is located by 500 Monte Carlo calculations. DETAILED DESCRIPTION

[0051] The sub-band complex variation mode decomposition denoising method applied to multiple sound sources in the present invention comprises the following steps:

[0052] Step 1: Divide the entire spectrum of the received signal based on a polyphase filter (PF), and construct a low-pass filter according to the number of sub-bands and the frequency of the sound source;

[0053] Step 2, performing multi-phase decomposition on the received signal and the low-pass filter to obtain a multi-phase signal and multiple filter coefficients;

[0054] Step 3: Obtain the time domain signal of each subband according to the multi-phase signal and the multiple filter coefficients;

[0055] Step 4: construct a variational model based on complex variational mode decomposition (VMD) and the time domain signal of each subband, and perform noise suppression on the output signal of each sound source subband through the variational model.

[0056] like Figure 1 As shown, the specific implementation process includes the following steps: Multi-source separation based on polyphase filter. The polyphase filter is used to divide the entire spectrum of the received signal into K non-overlapping sub-bands. Assume that there are two sound sources, s 1 and 2 ,s 1 The frequency f 1 =1300Hz,s 2 The frequency f 2 =1510Hz, then the received signal x can be expressed as follows:

[0057] x=s 1 +s 2 +s n ;

[0058] Among them, s 1 is the first sound source, s 2 is the second sound source, s n is Gaussian white noise.

[0059] Furthermore, the sampling frequency f of the observations s =3200Hz, and its spectrum (-1600Hz, 1600Hz) is divided into K=32 sub-bands, and the bandwidth B of each sub-band is 100Hz. Ignoring the image frequency output, only the positive frequency sound source sub-band is subjected to noise suppression, then the first sound source is in the 29th sub-band, and the second sound source is in the 31st sub-band.

[0060] According to the number of subbands K and sampling frequency f s Design a prototype low-pass filter h with a bandwidth of 100 Hz and an order of 896 0 (n), assuming that the system function of the prototype low-pass filter is

[0061]

[0062] Among them, the passband cutoff frequency of H(z) is 50Hz.

[0063] For the received signal x and the prototype low-pass filter h 0 (n) multiphase decomposition, i.e.

[0064] x k (m) = x (Km + k)

[0065] e k (l) = h 0 (Kl+k)

[0066] Where, k = 0, 1, ... K-1 (K is the number of sub-bands), x k (m) is the k-th multiphase signal, e k (l) is the coefficient of the k-th polyphase filter.

[0067] Step 3: Union x k (m) and e k (l) The k-th subband time domain signal y can be quickly calculated by the following formula: k (m), i.e.

[0068] y k (m) = K(IDFT[((x r (m)*e r (m))(-1) r ])

[0069] Here, IDFT stands for Inverse Discrete Fourier Transform.

[0070] Based on the complex variation mode decomposition, the noise reduction of each sub-band sound source is assumed to be

[0071] Construct the following variational model

[0072]

[0073] in, is the complex signal to be decomposed, u i (m) is each modal component, w i is the center frequency corresponding to each modal component, and I is the total number of modes.

[0074] To solve the above equation, an augmented Lagrangian function is constructed and a penalty factor α is introduced to transform it into an unconstrained variational case. Its iterative update formula is:

[0075]

[0076]

[0077]

[0078]

[0079]

[0080] in, is the multiplication operator, ε is the convergence tolerance, which can generally be taken as ε = 10 -6 . u i (m), The frequency domain form of λ(m) is After inverse Fourier transform, it is u i (m).

[0081] Use all u i (m) Reconstruct the output signal of the kth sound source subband after noise suppression Right now

[0082]

[0083] Repeat step 2 for the k sound source signal subband outputs of the polyphase filter to obtain each sound source signal after noise suppression.

[0084] In this specific embodiment, the effectiveness of this method is further verified by computer simulation. The parameter settings of this simulation experiment are shown in Table 1:

[0085] Table 1 System simulation parameters

[0086] Parameter name Parameter Value Number of sub-bands (K) 32 Decomposition level (I) 4 Penalty factor (α) 1000 Convergence tolerance (ε) <![CDATA[10 -6 ]]> <![CDATA[Sampling frequency (f s )]]> 3200Hz <![CDATA[The first target signal frequency (f 1 )]]> 1300Hz <![CDATA[Second target signal frequency (f 2 )]]> 1510Hz

[0087] Figure 1 is a schematic diagram of a flow chart of the present invention, Figure 2 This is a schematic diagram of the multiphase filter channelization structure. This simulation is based on Figure 1 and Figure 2 In the combined denoising method, the received signal x is divided into multiple sub-bands after passing through a polyphase filter (PF), and the sub-band where each sound source is located is directly denoised using multi-source sub-band complex variational mode decomposition (CVMD).

[0088] Figure 3 is the original spectrum of the signal to be processed, Figure 4 : This is the spectrum of the 16th to 31st sub-band output after polyphase filtering. It can be seen that the first sound source is in the 29th sub-band, and the second sound source is in the 31st sub-band. Figure 5 and Figure 7 The sub-band signal spectrum synthesized by each modal component and the atomic band signal spectrum are shown in Figure 1. Figure 6 and Figure 8 It is shown in the figure that the noise in the sub-band is significantly reduced after CVMD processing. The SNR of the first target signal sub-band before processing is 23.58dB, and the SNR after processing is 30.25dB; the SNR of the second target signal sub-band before processing is 17.78dB, and the SNR after processing is 24.62dB. The SNR in the two sub-bands is increased by 6.67dB and 6.84dB respectively.

Claims

1. A sub-band complex variational mode decomposition denoising method applied to multiple sound sources, characterized in that: The following steps are involved: Step 1: Divide the entire spectrum of the received signal based on a polyphase filter, and construct a low-pass filter according to the number of sub-bands and the sound source frequency; Step 2, performing multi-phase decomposition on the received signal and the low-pass filter to obtain a multi-phase signal and multiple filter coefficients; Step 3: Obtain the time domain signal of each subband according to the multi-phase signal and the multiple filter coefficients; Step 4: construct a variational model based on the complex variational mode decomposition and the time domain signal of each subband, and perform noise suppression on the output signal of each sound source subband through the variational model; specifically, the steps include: Step 41: Denoise each sub-band sound source based on complex variational mode decomposition. Assume that the k-th sound source sub-band output signal is Construct a variational model; the constructed variational model is as follows: in, is the subband output signal, i.e. the complex signal to be decomposed, u i (m) is each modal component, w i is the center frequency corresponding to each modal component, and I is the total number of modes; Step 42, construct an augmented Lagrangian function and introduce a penalty factor α to transform it into an unconstrained variational case, and solve the variational model; the process of solving the variational model includes: constructing an iterative update formula according to the constructed augmented Lagrangian function and the introduction of the penalty factor α: in, is the multiplication operator, ε is the convergence tolerance, u i (m), The frequency domain form of λ(m) is After inverse Fourier transform, it is u i (m); Step 43: reconstruct the k-th sound source subband output signal after noise suppression based on the solved modal components, that is, the sound source signals after noise suppression; use all u i (m) Reconstruct the output signal of the kth sound source subband after noise suppression Right now: The calculation is repeated on the k sound source signal subband outputs of the polyphase filter to obtain each sound source signal after noise suppression.

2. The sub-band complex variation mode decomposition denoising method applied to multiple sound sources according to claim 1, characterized in that: The division of the entire spectrum of the received signal in step 1 includes using a polyphase filter to divide the entire spectrum of the received signal x into K non-overlapping sub-bands, and dividing the received signal x into K non-overlapping sub-bands according to the number of sub-bands K and the sampling frequency f s Design a prototype low-pass filter h0(n) with a bandwidth of B and an order of N. The system function of the prototype low-pass filter is: Among them, the passband cutoff frequency of H(z) is B / 2, and f s =BK.

3. The sub-band complex variation mode decomposition denoising method applied to multiple sound sources according to claim 2, characterized in that: The prototype low-pass filter h0(n) is translated to obtain each sub-band filter, and the filter response of the k-th sub-band is: Where k = 0, 1, ... K-1, w k is the center frequency of the kth subband, w k =-π+2πk / K.

4. The sub-band complex variation mode decomposition denoising method applied to multiple sound sources according to claim 3, characterized in that: The multi-phase decomposition based on the received signal x and the prototype low-pass filter h0(n) in step 2 includes: x k (m)=x(Km+k); yes k (l)=h0(Kl+k); Where k = 0, 1, ... K-1, x k (m) is the k-th multiphase signal, e k (l) is the coefficient of the k-th polyphase filter.

5. The sub-band complex variation mode decomposition denoising method applied to multiple sound sources according to claim 2, characterized in that: The relationship between the received signal x and the sound source s is: x=s1+s2+···+s k +s n ,s n is Gaussian white noise.

6. The sub-band complex variation mode decomposition denoising method applied to multiple sound sources according to claim 4, characterized in that: In step 3, according to the multi-phase signal x k (m) and multiple filter coefficients e k (l) Get the time domain signal y of each subband k (m) include: y k (m) = K(IDFT[((x r (m)*e r (m))(-1) r ]); where r = k.

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