A Circle-Doppler-let transform method and a sound source separation method

Abstract

The present invention belongs to the technical field of moving sound source separation, and specifically relates to a Circle-Doppler-let transform method and a sound source separation method, including the following steps: The Circle-Doppler-let transform method includes: S1: Construct a circular motion model, set relevant parameters, and partition the parameters to obtain a parameter set; S2: Perform time-frequency adjustment based on the parameter set to generate a Circle-Doppler-let function library Function1; S3: Collect a sound signal x(t), use the matching pursuit algorithm and Function1 to perform sparse representation on the sound signal x(t), perform an inner product operation to find the basis function with the maximum inner product, and obtain a basis function library Function2 after iteration; The sound source separation method includes screening the basis functions in the basis function library Function2 that meet the requirements of the screening interval and storing them to obtain Function3, and then linearly combining the basis functions in Function3 to obtain a reconstructed signal x1(t). The present invention proposes a Circle-Doppler-let transform, which can be applied to the sparse representation and sound source separation of circular motion sound sources. Compared with the prior art, it has stronger in-band noise separation ability; only requires a single microphone, and the use cost is low.

Description

Technical Field

[0001] The present invention belongs to the technical field of moving sound source separation, and particularly relates to a Circle-Doppler-let transform method and a sound source separation method. Background Art

[0002] Circular motion is very common in daily life. Propellers and fan blades are typical mechanical devices with circular motion. There are often multiple sound sources in circular motion. If useful target sound sources are to be extracted, sound source separation methods need to be used to remove interfering sound sources.

[0003] For example, in the prior art, there is beamforming (Application No. CN201810648958.X discloses a method and system for separating sound sources from voice signals picked up by a microphone array). Beamforming mainly uses a microphone array to effectively identify the characteristics of sound sources and predict the radiation characteristics of the sound field. Due to the different positions of each element in the microphone array, the array can have good directivity to achieve the effect of sound source separation. However, the beamforming method requires a large number of microphones, and there are also high requirements for the placement position of each microphone, which is very inconvenient for on-site sound signal acquisition.

[0004] The prior art also includes blind source separation (Application No. CN202011529813.1, discloses a method and system for separating snoring signals of a microphone array based on a blind source separation algorithm). The blind source separation method refers to the process of obtaining the independent components of the source signal from only the observed signal according to the good statistical characteristics of the input signal under the condition of arranging the parameters of the source signal and the transmission channel. When using the blind source separation method for sound source separation, the position information between the microphone and the sound source is not required, and a good separation effect can also be obtained. However, under underdetermined conditions, that is, when the number of microphones is less than the number of sound sources, the sound source separation effect of blind source separation is not good. At the same time, the result of blind source separation is confused, that is, the order of the separated sound sources is random, and the separation result cannot be directly presented.

[0005] The prior art also includes Doppler-let transform technology (such as Application No. CN200410056802.0, discloses a passive speed measurement and ranging method and device using Doppler (Dopplerlet) transform), which is only applicable to sound sources in linear motion and cannot be applied to sound sources in circular motion.

[0006] Based on the above, there is an urgent need to design a sound source separation method applicable to circular motion. Summary of the Invention

[0007] The purpose of the present invention is to provide a simple-structured and reasonably designed Circle-Doppler-let transform method and a sound source separation method to solve the above problems.

[0008] The present invention realizes the above object through the following technical solutions:

[0009] A Circle-Doppler-let transform method, the transform method includes the following steps:

[0010] S1: Set the motion model parameters under circular motion to establish a circular motion model, and divide the motion model parameters to obtain a parameter set;

[0011] S2: Perform time-frequency adjustment based on the parameter set to generate a Circle-Doppler-let function library Function1;

[0012] S3: Collect the sound signal x(t) under the circular motion model, use the matching pursuit algorithm and Function1 to perform sparse representation on the sound signal x(t), perform an inner product operation between the signal x(t) and the basis functions in the function library Function1 to find the basis function with the maximum inner product, and obtain the basis function library Function2 after iteration.

[0013] As a further optimized solution of the present invention, in step S1, the circular motion model is selected as a single microphone - double sound source circular motion model, which includes the arrangement of the circular surface of the sound source motion and the arrangement of the microphone for collecting the sound signal. Among them, the double sound sources include a target sound source, denoted as sound source 1, and also include an interference sound source, denoted as sound source 2.

[0014] As a further optimized solution of the present invention, for the circular motion model established in step S1, the motion model parameters are divided as follows:

[0015]

[0016] Among them, r is the radius of the sound source circle, r 1 、r 2 are the minimum and maximum radii of the circular radius respectively, and Δr is the change amount of the circular radius; d0 is the set of vertical lengths of the microphone from the circular plane, d0 1 、d0 2 are the nearest and farthest lengths between the microphone and the sound source respectively, and Δd is the change amount of the lateral distance, w is the set of angular velocities, w 1 、w 2 are the minimum and maximum values of the sound source speed respectively, and Δw is the change amount of the sound source speed; f c is the sound source center frequency interval, f c 1 、f c 2 are the maximum and minimum values of the sound source center frequency respectively, and Δf cis the change in the center frequency of the sound source, θ is the angle at the starting moment of movement, θ 1 , θ 2 are the minimum and maximum values of the angle, and Δθ is the change in the angle.

[0017] As a further optimized solution of the present invention, in the step S2:

[0018] S2-1: Generate the set of basis functions F(n):

[0019] F(n) = sin(2πf c i t s (n))

[0020] where t s (n) = N0 / f s , 1f s , ···, (N - 1 + N0) / f s , t s (n) is the set of sampling times, f s is the sampling frequency of the signal, N0 is the sampling point corresponding to the starting moment θ, N is the signal length of the signal x(t), and f c i is the set of center frequencies of the sound source;

[0021] S2-2: Calculate respectively the set of times t r (n) when the microphone receives the sound source, the set of delay times t d (n) between the sound source and the microphone, and the set of amplitudes S r (n) corresponding to t r (n):

[0022]

[0023] where D1(t) = 2·r i ·cos(θ / 2), which is the real-time distance of the projection of the connection line between the sound source 1 and the microphone on the circumferential plane, and c is the speed of sound;

[0024]

[0025] where is the Mach number, and α is the angle between the real-time movement speed direction of the sound source 1 and the connection line between the real-time position of the sound source 1 and the microphone;

[0026] S2-3: Use cubic spline interpolation resampling processing, and after standardization, obtain the Circle-Doppler-let basis function u R (n);

[0027] S2-4: Make F(n) = cos(2πf ci t s (n)), repeat steps S2-1 - S2-3 to obtain the Circle-Doppler-let basis function u l (n);

[0028] S2-5: Generate the parameterized Circle-Doppler-let basis function U0(i) = u R (n) + j * u l (n);

[0029] S2-6: Change the value of i, repeat S2-1 and S2-2, replace with the parameter set in step 1 to obtain the circular motion Circle-Doppler-let function library: Function1 = {U0(i), i = 1, 2,..., n}.

[0030] As a further optimized solution of the present invention, in the said step S3, the steps of sparse representation are as follows:

[0031] (1) Set the starting number of iterations K = 1;

[0032] (2) Perform an inner product operation between the signal x(t) and each Circle-Doppler-let basis function in Function1 to find the maximum inner product C(K) opt and its corresponding optimal basis function Function K :

[0033] C(K) opt = MAX(|x(t) · U1(K)|)

[0034] Function K = real(C(K) opt ) * real(U1(i2)) + imag(C(K) opt ) * imag(U1(i2))(3) Obtain the signal x(t)' for the next iteration:

[0035] x(t)' = x(t) - Function K

[0036] (4) K = K + 1, loop (2)-(3) until the termination criterion is met:

[0037] K < σ1

[0038] where σ1 is the set maximum number of iterations;

[0039] (5) After K iterations, the basis function library is obtained: Function2 = {U2(K), K = 1, 2…m} and the coefficients corresponding to each basis function: C = {C(K) opt , K = 1, 2,…, m}.

[0040] A method for separating sound sources using the Circle-Doppler-let transform method described in any one of the above, the method comprising:

[0041] S1: Determine a screening interval that meets the requirements of each parameter according to the motion model parameters, screen the basis functions in the basis function library Function2 that meet the requirements of the screening interval, and store the basis functions to obtain Function3;

[0042] S2: Linearly combine the basis functions in Function3 to obtain a reconstructed signal x1(t).

[0043] As a further optimized solution of the present invention, in step S1, the steps of obtaining Function3 are as follows:

[0044] Determine the interval of parameters that meet the requirements through the geometric relationship between the circular motion plane and the microphone:

[0045]

[0046] where r is the interval of the circular radius of the sound source that meets the requirements, dr is the change amount of the new circular radius, r s 、r s +dr are the upper and lower bounds of the circular radius of the sound source; d is the interval of the vertical distance from the microphone to the circular plane that meets the requirements, dd is the change amount of the new vertical distance, ds, ds + dd are the upper and lower bounds of the vertical distance from the microphone to the circular plane; w is the set of initial angular velocities that meet the requirements, w 11 、w 22 are the upper and lower bounds of the angular velocity respectively; f c is the interval of the central frequency of the sound source that meets the requirements, f c 11 、f c 22 11 、θ 22 are the upper and lower bounds of the new starting angle; θ is the angle of the starting moment of the motion that meets the requirements, θare the upper and lower bounds of the new starting angle respectively.

[0047] Search each basis function in Function2. When the parameters used to generate the basis function meet the screening interval in (1), store it to obtain Function3 = {U3(i3), i3 = 1, 2…N}.

[0048] In the step S2, the steps of obtaining the reconstructed signal x1(t) are as follows:

[0049] The reconstructed signal x1(t) is obtained through linear combination:

[0050]

[0051] The beneficial effects of the present invention are as follows:

[0052] By establishing a circular motion model, the present invention creatively proposes a new Circle-Doppler-let transform applicable to circular motion sound sources, and elaborates in detail on its transformation method. At the same time, aiming at the deficiencies of existing sound source separation methods, the idea of sparse representation and signal reconstruction is adopted to achieve sound source separation. The present invention creatively utilizes the characteristic that the signal components from different sound sources in circular motion follow different time-frequency variation laws in the mixed signal to separate the target sound source signal. Compared with the existing beamforming method, the present invention uses only a single microphone, with low cost and strong practicability. Compared with the existing blind source separation method, the present invention is not affected by underdetermined conditions, and the separation result is direct and clear. Compared with the existing Doppler-let transform technology, the present invention can be applied to the separation and denoising of various circular motion sound sources. Brief Description of the Drawings

[0053] Figure 1 It is a flowchart of a Circle-Doppler-let transform method and a sound source separation method proposed by the present invention;

[0054] Figure 2 It is a single microphone - dual sound source circular motion model of the present invention;

[0055] Figure 3 It is a single microphone - dual sound source circular motion model (physical object) of the present invention;

[0056] Figure 4 It is the time domain diagram, frequency spectrum diagram and envelope spectrum diagram of the mixed signal x(t) of the present invention;

[0057] Figure 5 It is the time domain diagram, frequency spectrum diagram and envelope spectrum diagram of the theoretical signal x0(t) of the present invention;

[0058] Figure 6 It is the relationship between the number of iterations and the projection coefficient and energy residual of the present invention;

[0059] Figure 7 It is a schematic diagram of the screening range of the basis function parameters of the present invention;

[0060] Figure 8 It is the time domain diagram, frequency spectrum diagram and envelope spectrum diagram of the reconstructed signal x1(t) of the present invention;

[0061] Figure 9 This is a waveform comparison diagram of the reconstructed signal x1(t) and the theoretical signal X0(t) in the present invention. Specific implementation manners

[0062] The following further describes the present application in conjunction with the accompanying drawings. It is necessary to point out here that the following specific implementation manners are only used to further illustrate the present application and cannot be construed as limiting the protection scope of the present application. Those skilled in the art can make some non-essential improvements and adjustments to the present application according to the above application content.

[0063] Embodiment 1

[0064] In combination with Figure 1 , the present invention provides a Circle-Doppler-let transform method, and the transform method includes the following steps:

[0065] S1: Set the motion model parameters under circular motion to establish a circular motion model, and divide the motion model parameters to obtain a parameter set;

[0066] Among them, the circular motion model is selected as a single microphone - dual sound source circular motion model, which includes the arrangement of the circular surface of the sound source motion and the arrangement of the microphone for collecting sound signals. Its dual sound sources include sound source 1 - the target sound source and sound source 2 - the interference sound source.

[0067] For the above-established circular motion model, the motion model parameters are divided as follows:

[0068]

[0069] Among them, r is the circular radius of the sound source, r 1 , r 2 are respectively the minimum and maximum radii of the circular radius, and Δr is the change amount of the circular radius; d0 is the set of vertical lengths of the microphone from the circular plane, d0 1 , d0 2 are respectively the nearest and farthest lengths between the microphone and the sound source, Δd is the change amount of the lateral distance, w is the set of angular velocities, w 1 , w 2 are respectively the minimum and maximum values of the sound source velocity, and Δw is the change amount of the sound source velocity; f c is the sound source center frequency interval, f c 1 , f c 2 are respectively the maximum and minimum values of the sound source center frequency, Δf c is the change amount of the sound source center frequency, θ is the angle at the starting moment of motion, θ 1 , θ 2The minimum and maximum values of the angle are, and Δθ is the change in the angle.

[0070] S2: Perform time-frequency adjustment based on the parameter set to generate the Circle-Doppler-let function library Function1;

[0071] S2-1: Generate the set of basis functions F(n):

[0072] F(n) = sin(2πf c i t s (n))

[0073] where t s (n) = N0 / f s , 1f s , ···, (N - 1 + N0) / f s , t s (n) is the set of sampling times, f s is the sampling frequency of the signal, N0 is the sampling point corresponding to the starting time θ, N is the signal length of the signal x(t), and f c i is the set of center frequencies of the sound source;

[0074] S2-2: Calculate respectively the set of times t r (n) when the microphone receives the sound source, the set of delay times t d (n) between the sound source and the microphone, and the set of amplitudes S r (n) corresponding to t r (n):

[0075]

[0076] where D1(t) = 2·r i ·cos(θ / 2), which is the real-time distance of the projection of the line connecting the sound source 1 and the microphone on the circumferential plane, and c is the speed of sound;

[0077]

[0078] where is the Mach number, and α is the angle between the real-time movement speed direction of the sound source 1 and the line connecting the real-time position of the sound source 1 and the microphone;

[0079] S2-3: Use cubic spline interpolation resampling processing, and after standardization, obtain the Circle-Doppler-let basis function u R (n);

[0080] S2-4: Let F(n) = cos(2πf c i ts (n)), repeat steps S2-1 - S2-3 to obtain the Circle-Doppler-let basis function u l (n);

[0081] S2-5: Generate the parameterized Circle-Doppler-let basis function U0(i) = u R (n) + j * u l (n);

[0082] S2-6: Change the value of i, repeat S2-1 and S2-2, replace with the parameter combinations in step 1, to obtain the circular motion Circle-Doppler-let function library: Function1 = {U0(i), i = 1, 2,..., n}.

[0083] S3: Collect the sound signal x(t) under the circular motion model, use the matching pursuit algorithm and Function1 to perform sparse representation on the sound signal x(t), perform an inner product operation between the signal x(t) and the basis functions in the function library Function1 to find the basis function with the maximum inner product, and obtain the basis function library Function2 after iteration.

[0084] Among them, the steps of sparse representation are as follows:

[0085] (1) Set the starting iteration number K = 1;

[0086] (2) Perform an inner product operation between the signal x(t) and each Circle-Doppler-let basis function in Function1 to find the maximum inner product C(K) opt and its corresponding optimal basis function Function K :

[0087] C(K) opt = MAX(|x(t) · U1(K)|)

[0088] Function K = real(C(K) opt ) * real(U1(i2)) + imag(C(K) opt ) * imag(U1(i2))

[0089] (3) Obtain the signal x(t)' for the next iteration:

[0090] x(t)' = x(t) - Function K

[0091] (4) K = K + 1, loop (2) - (3) until the termination criterion is met:

[0092] K < σ1

[0093] Wherein, σ1 is the set maximum number of iterations;

[0094] (5) After K iterations, the basis function library is obtained: Function2 = {U2(K), K = 1, 2…m} and the coefficients corresponding to each basis function: C = {C(K) opt , K = 1, 2,…, m}.

[0095] A method for separating sound sources using any one of the above Circle-Doppler-let transform methods, the method comprising:

[0096] S1: Determine the screening interval that meets each parameter requirement according to the motion model parameters, screen the basis functions in the basis function library Function2 that meet the requirements of the screening interval, and store the basis functions to obtain Function3;

[0097] S2: Linearly combine the basis functions in Function3 to obtain the reconstructed signal x1(t).

[0098] In step S1, the steps to obtain Function3 are as follows:

[0099] Determine the interval of parameters that meet the requirements through the geometric relationship between the circular motion plane and the microphone:

[0100]

[0101] Wherein, r is the interval of the circular radius of the sound source that meets the requirements, dr is the change amount of the new circular radius, r s 、r s +dr are the upper and lower bounds of the circular radius of the sound source; d is the interval of the vertical distance from the microphone to the circular plane that meets the requirements, dd is the change amount of the new vertical distance, ds, ds + dd are the upper and lower bounds of the vertical distance from the microphone to the circular plane; w is the set of initial angular velocities that meet the requirements, w 11 、w 22 are the upper and lower bounds of the angular velocity respectively; f c is the interval of the center frequency of the sound source that meets the requirements, f c 11 、f c 22 11 22 、θ 22 are the upper and lower bounds of the new starting angle.

[0102] Search for each basis function in Function2. When the parameters used to generate the basis function satisfy the screening interval of (1), store it to obtain Function3 = {U3(i3), i3 = 1, 2…N}.

[0103] In step S2, the steps to obtain the reconstructed signal x1(t) are as follows:

[0104] Obtain the reconstructed signal x1(t) through linear combination:

[0105]

[0106] The Circle-Doppler-let transform method and the sound source separation method proposed in the present invention mainly include two parts. One is the construction steps of the Circle-Doppler-let transform:

[0107] (1) Establish a circular motion model and set relevant parameters;

[0108] (2) Traverse the parameter combinations to perform time-frequency adjustment on the harmonic basis function F(n) and generate the function library Function1;

[0109] (3) Use the matching pursuit algorithm and Function1 to perform sparse representation on the mixed signal x(t), and put the F(n) participating in the sparse representation into Function2.

[0110] The other is the steps of sound source separation:

[0111] (1) According to the sound source position and frequency characteristics, set a new parameter interval, and screen the F(n) that meets the parameter interval from the obtained Function2 and store it in Function3;

[0112] (2) Perform linear combination on the F(n) of Function3 to obtain the reconstructed signal x1(t).

[0113] The present invention will be further described below in conjunction with the accompanying drawings and experimental data. The specific steps are as follows:

[0114] Step 1:

[0115] Establish a single microphone - dual sound source circular motion parameter model as Figure 2 shown, Figure 3 which is its physical model. When the rod makes a high-speed circular motion, it drives the two sound sources to make high-speed circular motions. Due to the different relative positions of the two sound sources and the microphone, the signals received by the microphone will have different Doppler distortion laws. Among them, two different types of signals are selected for the two sound sources.

[0116] The sound source 1 selects a periodic impact signal as the fault signal, and its expression is:

[0117]

[0118] t = {0:1 / f s :(N - 1)f s}, where A = 3 represents the amplitude of the signal, ξ = 0.05 represents the damping ratio, f c1 = 2000 represents the center frequency of the signal, fs = 20 kHz represents the sampling frequency, and N = 11000 represents the signal length.

[0119] The sound source 2 is a multi-frequency sine signal, used as the interference noise signal, and its expression is:

[0120] Y(t) = q0sin(2πf c2 t)

[0121] where q0 = 9×10 -1 represents the signal intensity, f c2 = 1500:200:2500 represents the signal frequency. This signal overlaps with the center frequency of 2000 Hz of the sound source type 1.

[0122] The detailed parameters of the circular motion model are shown in the following table (Table 1 is the parameter setting of the circular motion model, Table 2 is the detailed parameter setting of the sound source 1, and Table 3 is the detailed parameter setting of the sound source 2):

[0123]

[0124] Table 1

[0125]

[0126] Table 2

[0127]

[0128] Table 3

[0129] Play the sound source 1 and the sound source 2 simultaneously, and the microphone collects the mixed signal x(t). Its waveform diagram, time-frequency diagram, spectrogram, and envelope spectrogram are as Figure 4 . It can be seen from the spectrogram the frequency shift phenomenon caused by the movement of the sound source, and the fault frequency of 111.1 Hz and the interference noise frequency of 200 Hz can be seen from the envelope spectrogram. Turn off the sound source 2 and only play the sound source 1. The microphone collects the theoretical signal x0(t). Its waveform diagram, time-frequency diagram, spectrogram, and envelope spectrogram are as Figure 5 .

[0130] Then, according to the circular motion model established in step 1, divide the important motion parameters:

[0131]

[0132] The detailed parameter settings of sound source 1 and sound source 2 are shown in Table 1 and Table 2. In the experimental data, the angular velocity w = 11.94 m / s is selected as a fixed value. The lower limit of the parameter range of sound source 1 is set to (0.15, 0.45, 1201, -3), and the upper limit of the parameter range is set to (1.10, 0.55, 2800, 3); the lower limit of the parameter range of sound source 2 is set to (0.68, 0.45, 1201, -3), and the upper limit of the parameter range is set to (1.08, 0.55, 2800, 3).

[0133] Step 2:

[0134] Perform time-frequency adjustment according to the parameter set obtained in Step 1 to construct a complete Circle-Doppler-let function library Function1, which contains 470,400 basis functions.

[0135] Step 3:

[0136] Using the sparse representation method, sparsely represent the mixed signal x(t) using the Circle-Doppler-let function library Function1 generated in Step 1, with a total of 500 iterations. Thus, Function2 is obtained, which contains 500 basis functions. Figure 6 For the relationship between the number of iterations and the projection coefficients and energy residuals, Figure 6 (a) represents the 500 optimal basis functions selected in the sparse representation, where the dashed line represents the basis functions used to form the reconstructed signal x1(t). Figure 6 (b) represents 500 iterations. After each iteration of decomposition, the energy residual of the mixed signal x(t) will decrease.

[0137] Step 4:

[0138] According to parameters such as the angle at the starting moment and the circumferential radius, screen the basis functions selected after 500 iterations, Figure 7 This is the basis function parameter screening diagram proposed by the present invention. The screening range used in the experimental data is as follows: r = [0.25, 0.35], d = [0.45, 0.55], w = 11.94, fc = [1201, 2800], θ = [-3, 3]. Finally, Function3 is obtained, which contains 134 basis functions. Linearly combine the screened basis functions to obtain the reconstructed signal x1(t).

[0139]

[0140] Its waveform diagram, time-frequency diagram, frequency spectrum diagram and envelope spectrum diagram are as Figure 8As shown. Through the spectrogram and the envelope spectrogram, it can be seen that the present invention has a good sound source separation effect, and the 200 Hz interference noise frequency existing in the mixed signal is removed in the reconstructed signal x0(t). Figure 9 Fig. Figure 9 is a waveform comparison diagram of the reconstructed signal x1(t) and the theoretical signal x0(t). The dashed line represents the waveform diagram x0(t) of the theoretical signal, and the solid line represents the waveform diagram x1(t) of the reconstructed signal. Observing the waveforms at three different positions, it can be seen that the matching effect of the waveforms is good. The above demonstrates the effectiveness of the method of the present invention.

[0141] The above-described embodiments only represent one implementation manner of the present invention, and the description thereof is relatively specific and detailed, but it should not be construed as a limitation on the scope of the patent of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several modifications and improvements can still be made, and these all belong to the protection scope of the present invention.

Claims

1. A Circle-Doppler-let transform method, characterized in that: The transformation method includes the following steps: S1: Set the motion model parameters under circular motion to establish a circular motion model, and divide the motion model parameters to obtain a parameter set; S2: Perform time-frequency adjustment based on the parameter set to generate the Circle-Doppler-let function library Function1; S3: Collect the sound signal x(t) under the circular motion model, use the matching pursuit algorithm and Function1 to perform sparse representation on the sound signal x(t), perform an inner product operation between the signal x(t) and the basis functions in the function library Function1 to find the basis function with the maximum inner product, and obtain the basis function library Function2 after iteration; In the step S3, the steps of sparse representation are as follows: (1) Set the starting iteration number K = 1; (2) Perform the inner product operation between the signal x(t) and each Circle-Doppler-let basis function in Function1 to obtain the maximum inner product C(K) opt and its corresponding optimal basis function Function K : C(K) opt = MAX(|x(t)·U1(K)|) Function K = real(C(K) opt ) * real(U1(i2)) + imag(C(K) opt ) * imag(U1(i2)) (3) Obtain the signal x(t)' for the next iteration: x(t)' = x(t) - Function K (4) K = K + 1, loop (2)-(3) until the termination index is satisfied: K < σ1 where σ1 is the set maximum number of iterations; (5) After K iterations, the basis function library is obtained: Function2 = {U2(K), K = 1, 2…m} and the coefficients corresponding to each basis function: C = {C(K) opt , K = 1, 2,…, m}.

2. The Circle-Doppler-let transform method according to claim 1, characterized in that: In the step S1, the circular motion model is selected as a single microphone - dual sound source circular motion model, which includes the arrangement of the circular surface of the sound source motion and the arrangement of the microphone for collecting the sound signal. Among them, the dual sound sources include a target sound source, denoted as sound source 1, and also include an interference sound source, denoted as sound source 2.

3. The Circle-Doppler-let transform method according to claim 1, characterized in that: For the circular motion model established in the step S1, the motion model parameters are divided as follows: where r is the radius of the sound source circle, r 1 , r 2 are respectively the minimum and maximum radii of the circular radius, and Δr is the change in the circular radius; d0 is the set of the vertical lengths of the microphones from the circular plane, d0 1 , d0 2 are respectively the nearest and farthest lengths between the microphone and the sound source, Δd is the change in the lateral distance, w is the set of angular velocities, w 1 , w 2 are respectively the minimum and maximum values of the sound source velocity, and Δw is the change in the sound source velocity; f c is the central frequency range of the sound source, f c 1 , f c 2 are respectively the maximum and minimum values of the central frequency of the sound source, and Δf c is the change in the central frequency of the sound source, θ is the angle at the starting moment of the movement, θ 1 , θ 2 are respectively the minimum and maximum values of the angle, and Δθ is the change in the angle.

4. A Circle-Doppler-let transform method according to claim 1, characterized in that: In the step S2: S2-1: Generate a set of basis functions F(n): where t s (n) = N0 / f s , 1 / f s , ···, (N - 1 + N0) / f s , t s (n) is the set of sampling times, f s is the sampling frequency of the signal, N0 is the sampling point corresponding to the starting time θ, N is the signal length of the signal x(t), f c i is the set of center frequencies of the sound source; S2-2: Calculate the time set t r (n) received by the microphone from the sound source, the delay time set t d (n), and the amplitude set S r (n) corresponding to t r (n): where D1(t) = 2·r i ·cos(θ / 2), which is the real-time distance of the projection of the line connecting the sound source 1 and the microphone on the circumferential plane, and c is the speed of sound; wherein, is the Mach number, and α is the angle between the direction of the real-time movement speed of the sound source 1 and the line connecting the real-time position of the sound source 1 and the microphone; S2-3: Resample using cubic spline interpolation, and obtain the Circle-Doppler-let basis function u(n) after standardization; R (n); S2-4: Make Repeat steps S2-1 - S2-3 to obtain the Circle-Doppler-let basis function u l (n); S2-5: Generate the parameterized Circle-Doppler-let basis function U0(i) = u R (n) + j * u l (n); S2-6: Change the value of i, repeat S2-1 and S2-2, replace with the parameter set in step 1, and obtain the circular motion Circle-Doppler-let function library: Function1 = {U0(i), i = 1, 2,..., n}.

5. A method for separating sound sources using the Circle-Doppler-let transform method according to any one of claims 1 to 4, characterized in that: The method includes: S1: Determine the screening interval that meets the requirements of each parameter according to the motion model parameters, screen the basis functions in the basis function library Function2 that meet the requirements of the screening interval, and store the basis functions to obtain Function3; S2: Linearly combine the basis functions in Function3 to obtain the reconstructed signal x1(t).

6. A sound source separation method according to claim 5, characterized in that: In the step S1, the steps to obtain Function3 are as follows: Determine the interval of parameters that meet the requirements through the geometric relationship between the circular motion plane and the microphone: Among them, r is the circular radius interval of the sound source that meets the requirements, dr is the change in the new circular radius, r s , r s +dr are the upper and lower bounds of the circular radius of the sound source; d is the vertical distance interval of the microphone from the circular plane that meets the requirements, dd is the change in the new vertical distance, ds, ds+dd are the upper and lower bounds of the vertical distance of the microphone from the circular plane; w is the set of initial angular velocities that meet the requirements, w 11 , w 22 are the upper and lower bounds of the angular velocity respectively; f c is the central frequency interval of the sound source that meets the requirements, f c 11 , f c 22 are the upper and lower bounds of the new central frequency of the sound source; θ is the angle at the starting moment of the movement that meets the requirements, θ 11 , θ 22 are the upper and lower bounds of the new starting angle; Search each basis function in Function2. When the parameters used to generate the basis function satisfy the screening interval in (1), store it, so as to obtain Function3 = {U3(i3), i3 = 1, 2... N}; In the step S2, the steps to obtain the reconstructed signal x1(t) are as follows: Obtain the reconstructed signal x1(t) through linear combination:

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