JP4676920B2 - Signal separation device, signal separation method, signal separation program, and recording medium - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To suitably perform clustering even in a frequency band in which spatial aliasing may happen, and create a suitable separation signal. <P>SOLUTION: A phase is normalized in a converted frequency region signal of a mixed signal observed by a plurality of sensors. Furthermore, a frequency normalized signal is created which eliminates a frequency dependent component. A feature amount vector is clustered for every time frequency which makes the frequency normalized signal, etc. as respective elements, and a model parameter of a frequency response model is computed using a centroid of each cluster. Afterward, a phase/norm normalization vector is clustered which makes phase/norm normalized values of the frequency region signals as respective elements, in reference to the frequency response model, etc. with the model parameter substituted thereinto; and creates cluster information corresponding to the cluster to which each phase/norm normalization vector belongs. Separation signals of the frequency region are created using the frequency region signal and the cluster information, and they are converted to separation signals of the time region. <P>COPYRIGHT: (C)2008,JPO&amp;INPIT

Description

  The present invention belongs to the technical field of signal processing, and particularly relates to a technique for extracting a source signal from a mixed signal obtained by mixing a plurality of source signals in a space.

で表現できる。ここでｔはサンプリング時刻を示している。また、s_k（t）は、サンプリング時刻ｔにおいて信号源から発せられる源信号を示しており、x_q（t）は、サンプリング時刻ｔにおいてセンサｑで観測される信号を示している。また、ｒは掃引のための変数を示している。 [Blind signal separation]
Blind signal separation is a signal separation technique for estimating and separating a source signal from a mixed signal in which a plurality of source signals are mixed. First, this blind signal separation is formulated. All signals are sampled at a sampling frequency f _s and expressed discretely. Further, it is assumed that N (N ≧ 2) signals are mixed and observed by M (M ≧ 2) sensors. The following deals with a situation where the signal is attenuated / delayed depending on the distance from the signal source to the sensor, and the signal may be reflected by a wall or the like to cause distortion in the transmission path. The signal mixed in such a situation is transmitted from the signal source k to the sensor q (q is a sensor number [q = 1,..., M]. K is a signal source number [k = 1, ..., N].) Convolutional mixing with impulse response h _qk (r)

Can be expressed as Here, t indicates the sampling time. Further, s _k (t) indicates a source signal emitted from the signal source at the sampling time t, and x _q (t) indicates a signal observed by the sensor q at the sampling time t. R represents a variable for sweeping.

The general impulse response h _qk (r) has a strong pulse-like response after an appropriate time has elapsed and decays with time. The purpose of blind signal separation is the source signal s ₁ (t), ..., s _N (t) and impulse response h ₁₁ (r), ..., h _1N (r), ..., h _M1 (r), ..., h Without knowing _MN (r), only source signals s ₁ (t), ..., s _N (t) from the observed signals (hereinafter referred to as "mixed signals") x ₁ (t), ..., x _M (t) the corresponding separated signals y ₁ (t), ..., is to seek y _N (t).

を求める。ここでｆは周波数でありf=0,f_s/L,…,f_s（L-1）/Lと離散化されている（ｆ_ｓはサンプリング周波数）。また、τは離散時間であり、ｊは虚数単位である。さらにg（r）は窓関数である。窓関数としては、例えば、ハニング窓

などのg（0）にパワーの中心を持つ窓関数を用いる。この場合、周波数領域信号X_q（f,τ）は時刻t=τを中心とする混合信号x_q（t）の周波数特性を表現する。なお、周波数領域信号X_q（f,τ）はＬサンプルにわたる情報を含んでいるため、すべてのτに対して周波数領域信号X_q（f,τ）を求める必要はなく、適当な間隔のτごとにX_q（f,τ）を求める。 [Frequency domain]
Next, a conventional blind signal separation procedure will be described.
Here, the separation operation is performed in the frequency domain. For this purpose, an L-point short-time Fourier transform (STFT) is applied to the mixed signal x _q (t) at the sensor q, and the mixed signal (hereinafter referred to as “f, τ”) Called "frequency domain signal")

Ask for. Here, f is a frequency and is discretized as f = 0, f _s / L,..., F _s (L−1) / L (f _s is a sampling frequency). Also, τ is a discrete time, and j is an imaginary unit. Furthermore, g (r) is a window function. As a window function, for example, Hanning window

Use a window function with the center of power at g (0). In this case, the frequency domain signal X _q (f, τ) represents the frequency characteristics of the mixed signal x _q (t) centered at time t = τ. Since the frequency domain signal X _q (f, τ) contains information over L samples, it is not necessary to obtain the frequency domain signal X _q (f, τ) for all τ, and τ at an appropriate interval X _q (f, τ) is obtained for each.

と各周波数での単純混合に近似表現でき、分離の操作が単純になる。ここで、H_qk（f）は源信号ｋからセンサｑまでの周波数応答であり、S_k（f,τ）は式（２）と同様な式に従って源信号s_k（t）に短時間離散フーリエ変換を施したもの（周波数領域の源信号）である。ベクトルを用いて式（３）を表記すると、

となる。ここで、X（f,τ）=[X₁（f,τ）,…,X_M（f,τ）]^Tは、各センサに対応する周波数領域信号を各要素とする混合信号ベクトルであり、H_k（f）=[H_1k（f）,…,H_Mk（f）]^Tは、信号源ｋから各センサへの周波数応答を各要素とするベクトルである。なお、[*]^Tは[*]の転置ベクトルを示す。 When processing is performed in the frequency domain, convolutional mixing in the time domain represented by Equation (1) is

And simple mixing at each frequency, and the separation operation is simplified. Here, H _qk (f) is a frequency response from the source signal k to the sensor q, and S _k (f, τ) is discrete to the source signal s _k (t) for a short time according to an equation similar to the equation (2). This is a signal subjected to Fourier transform (frequency domain source signal). When expression (3) is expressed using a vector,

It becomes. Where X (f, τ) = [X ₁ (f, τ), ..., X _M (f, τ)] ^T is a mixed signal vector having frequency domain signals corresponding to each sensor as elements. , H _k (f) = [H _1k (f),..., H _Mk (f)] ^T is a vector having frequency responses from the signal source k to the sensors as elements. [*] ^T indicates a transposed vector of [*].

[Signal separation by time frequency mask]
As one of blind signal separation methods, there is a method using a time-frequency mask. This method is a signal separation and extraction method applicable regardless of the number N of signal sources and the number M of sensors. This method assumes signal sparsity. Sparse refers to the signal being zero at most discrete times τ. The sparsity of the signal is confirmed by an audio signal in the frequency domain, for example. By assuming the sparseness and mutual independence of signals, it can be assumed that even if a plurality of signals are present at the same time, there is a low probability of being observed in each time frequency slot (f, τ). Assuming signal sparsity and mutual independence, Equation (3) above is
X _q (f, τ) = H _qk (f) S _k (f, τ) (5)
The above equation (4) can be expressed as
X (f, τ) = H _k (f) S _k (f, τ) (6)
Can be written. That is, in each time frequency slot (f, τ), it can be modeled that only one of the signal sources k is active and the signals of the other signal sources are zero.

The signal separation operation in this case can be performed by determining which signal source is active for each time frequency slot (f, τ). Specifically, an appropriate feature amount is generated from the mixed signal vector, and the generated feature amount is clustered to generate a cluster C _k . Then, estimate a time frequency mask M _k (f, τ) that extracts a frequency domain signal corresponding to a member of each cluster C _k ,
Y _k (f, τ) = M _k (f, τ) X _{Q ′} (f, τ) (7)
Thus, each signal is separated and extracted. Here, X _{Q ′} (f, τ) is one of the elements of the mixed signal vector, and Q′∈ {1,..., M}.

から計算される信号の推定到来方向（Direction of Arrival : DOA）

を例示できる（例えば、非特許文献１参照）。なお、ｄはセンサｑと基準センサＱとの距離であり、ｃは信号速度である。また、クラスタリングには、k-means法（例えば、非特許文献２参照）等を用いることができる。また、時間周波数マスクM_k（f,τ）としては、例えばそれぞれのクラスタC_ｋに属するメンバの平均値θ_１ ^〜θ₂ ^〜，…，θ_N ^〜を求め、

のようにして生成したものを用いることができる。ここでΔは信号を抽出する範囲を与える。この方法では、Δを小さくすると、よい分離抽出性能が得られるが非線形型歪みは大きくなる。また、Δを大きくすると、非線形型歪みは減少するが分離性能が劣化する。
その他、クラスタリングの特徴量として、２つのセンサ（センサｑと基準センサＱ）における周波数領域信号の位相差（式（８））を周波数で除したものを用いてもよい。 As the feature amount used for clustering, for example, frequency regions in two sensors (sensor q and reference sensor Q (Q is referred to as a reference value, and a sensor corresponding to the reference value Q is referred to as a reference sensor Q)). Signal phase difference

Direction of arrival (DOA) of the signal calculated from

(For example, refer nonpatent literature 1). Here, d is the distance between the sensor q and the reference sensor Q, and c is the signal speed. Further, k-means method (for example, see Non-Patent Document 2) or the like can be used for clustering. Further, as the time frequency mask M _k (f, τ), for example, average values θ ₁ ^to θ ₂ ^to ,..., Θ _N ^to members belonging to the respective clusters C _k are obtained,

Those generated as described above can be used. Here, Δ gives a range for extracting a signal. In this method, if Δ is reduced, good separation and extraction performance can be obtained, but nonlinear distortion increases. When Δ is increased, the non-linear distortion is reduced, but the separation performance is deteriorated.
In addition, as a clustering feature amount, a value obtained by dividing a phase difference (formula (8)) of frequency domain signals in two sensors (sensor q and reference sensor Q) by a frequency may be used.

によって正規化する。なお、ｅｘｐはネピア数を示し、ａｒｇ［・］は偏角を示し、ｊは虚数単位を示し、ｃは信号の伝達速度を示し、ｄ_ｍａｘは基準センサＱ（Ｑ∈{1,…,M}）と他のセンサｑ（ｑ∈{1,…,M}）との距離の最大値を示す。また、X'(f,τ)=[X₁'(f,τ),…,X_M'(f,τ)]^Tであり、‖・‖はノルムを示す。 Non-Patent Document 3 discloses a method of efficiently separating information from three or more sensors and performing signal separation using a time-frequency mask. In this method, the mixed signal observed by each sensor is subjected to discrete Fourier transform for a short time, and a frequency domain signal X _q (f, τ) for each time frequency slot (f, τ) is generated.

Normalize by Here, exp represents the number of Napiers, arg [•] represents the deflection angle, j represents the imaginary unit, c represents the signal transmission speed, and d _max represents the reference sensor Q (Qε {1,..., M }) And the maximum distance between other sensors q (qε {1,..., M}). Further, X ′ (f, τ) = [X ₁ ′ (f, τ),..., X _M ′ (f, τ)] ^T , and ‖ and ‖ denote norms.

Next, clustering is performed using the normalized vector X '' (f, τ) as a feature value in this way to generate clusters that are estimated to correspond to each signal source, and the time for taking samples of each cluster Generate a frequency mask. Then, frequency domain separation signals are obtained by multiplying these time frequency masks by frequency domain signals, and time domain separation signals are obtained by performing short-time inverse Fourier transform (ISTFT) on them. .
S. Araki, S. Makino, A. Blin, R. Mukai, and H. Sawada, "Underdetermined blind separation for speech in real environments with sparseness and ICA," in Proc. ICASSP 2004, vol. III, May 2004, pp . 881-884 RO Duda, PE Hart, and DG Stork, Pattern Classification, Wiley Interscience, 2nd edition, 2000. S. Araki, H. Sawada, R. Mukai and S. Makino, "A novel blind source separation method with observation vector clustering," IWAENC2005, pp. 117-120, 2005.

However, in these prior art
f <c / (2d _max ) (d _max = d for 2 sensors) (11)
If this relationship is not satisfied, so-called spatial aliasing may occur. When this spatial aliasing occurs, there is a possibility that appropriate clustering cannot be performed. In the following, problems caused by this spatial aliasing will be described.

Assuming _sparseness and mutual independence of the signal, the frequency domain signal X _q (f, τ) is the frequency response H _qk (f) from any signal source k to the sensor q and the frequency domain source signal S. _It can be approximated to the product of _k (f, τ) (see equation (5)). That is,
X _q (f, τ) = H _qk (f) S _k (f, τ)
X _Q (f, τ) = H _Qk (f) S _k (f, τ)
Can be approximated. In this case, the relative value of the declination of the frequency domain signal X _q (f, τ) and the declination of the frequency domain signal X _Q (f, τ) is the declination of the frequency response H _qk (f) and the frequency It can be approximated that it depends only on the relative value of the response H _Qk (f) to the argument.

If the frequency response H _qk (f) is approximated by a direct wave model without reflection or reverberation,
H _qk (f) = λ _qk・ exp [−j ・ 2π ・ f ・ γ _qk ]… (12)
Can be expressed as Note that γ _qk and λ _qk > 0 are model parameters that express the arrival time from the signal source k to the sensor q and the attenuation, respectively. The arrival time γ _qk from the signal source k to the sensor q is
γ _qk = d _kq / c
Can be written. D _kq represents the distance between the signal source k and the sensor q. Therefore, equation (12) becomes
H _qk (f) = λ _qk・ exp [−j ・ 2π ・ f ・ d _kq / c] (13)
Can be written.

Here, when the relationship of Expression (11) is satisfied, the relative value 2π · f · (d _kQ -d _kq ) of the deviation angle of the frequency response H _qk (f) and the deviation angle of the frequency response H _Qk (f) / c is always −π or more and less than π, and the relative value of the declination of the frequency domain signal X _q (f, τ) and the declination of the frequency domain signal X _Q (f, τ) is always −π or more and less than π. It becomes. The relative value of the deviation angle is proportional to both the arrival time difference γ _Qk -γ _qk of the signal from the signal source k to the sensor q and the reference sensor Q and the frequency f.

In each of the conventional examples described above, the declination of the frequency domain signal X _q (f, τ) corresponding to each sensor q is used as the reference for the declination of the frequency domain signal X _Q (f, τ) corresponding to the reference sensor Q. The feature amount is generated by normalizing and dividing the normalized declination by a value proportional to the frequency f (see, for example, equations (9) and (10)). In this case, the declination of the feature value is proportional to the arrival time difference γ _Qk -γ _qk of the signal from the signal source k to the sensor q and the reference sensor Q. Since the arrival time difference γ _Qk -γ _qk depends only on the relative positions of the signal source k, the sensor q, and the reference sensor Q, the feature amount forms a cluster depending on the position of the signal source k.

On the other hand, when the relationship of Expression (11) is not satisfied, the relative value between the declination of the frequency domain signal X _q (f, τ) and the declination of the frequency domain signal X _Q (f, τ) is less than −π. There is a possibility of reaching a range of π or more. However, in the actual analysis of the mixed signal, the relative value of the declination that reaches a range of less than −π or greater than or equal to π can be determined only as an equivalent declination of a range of −π or more and less than π. In this case, the relative value of the declination jumps cyclically (jumps from π to −π or −π to π) with a predetermined period as the frequency f increases, and does not have a proportional relationship over the entire frequency f. For this reason, even if the declination is normalized as in each of the above-described conventional examples and the feature amount is generated by dividing the deviation by a value proportional to the frequency f, the cluster can correctly identify the position of each signal source by clustering. Is difficult to form. This is because even if the feature amounts correspond to the same signal source, no cluster is formed in a region exceeding the frequency at which the above-described cyclic jump occurs.

  The present invention has been made in view of these points, and can extend the conventional technique described above to perform appropriate clustering even in a frequency band where spatial aliasing can occur and generate an appropriate separated signal. Aims to provide a new technology. That is, the object of the present invention is applicable to a case where spatial aliasing does not occur, but provides a technique capable of suitably obtaining a separated signal even when spatial aliasing occurs. is there.

  In the first aspect of the present invention, in order to solve the above-described problem, first, the frequency domain conversion unit converts the mixed signals observed by a plurality of sensors into mixed signals (frequency domain signals) in the frequency domain. Next, the normalization unit normalizes the phase of the frequency domain signal and further generates a frequency normalized signal from which frequency dependent components are excluded. The frequency normalized signal may be a signal whose norm is normalized or may not. Then, the first clustering unit clusters the feature vector for each time frequency using each element as a frequency normalized signal or a value obtained by substituting the frequency normalized signal into a predetermined function. Centroid (cluster center vector) is calculated. The model parameter extraction unit calculates model parameters of the frequency response model using the centroid. Thereafter, the second clustering unit calculates the phase-norm normalized value of the frequency domain signal based on the frequency response model in which the model parameters are substituted or the frequency response model in which the model parameters are optimized. Clustering is performed on the frequency-dependent phase / norm normalized vectors as the respective elements, and cluster information corresponding to the clusters to which each phase norm normalized vector belongs is generated. Then, the separated signal generation unit uses the frequency domain signal and the cluster information to generate a frequency domain separated signal. Finally, the frequency domain separation signal is converted into a time domain separation signal.

  Here, if many of the feature vectors to be clustered by the first clustering unit do not cause the above-described cyclic jump, the centroid of each cluster to be generated is frequency normalized to the frequency response model. (Details will be described later). Therefore, the model parameter of the frequency response model can be estimated using this centroid. The second clustering unit clusters the frequency-dependent phase / norm normalized vectors with reference to the frequency response model into which the model parameter is substituted or the frequency response model into which the optimized model parameter is substituted. Here, the model parameter does not depend on the frequency, but the frequency response model into which the model parameter is substituted depends on the frequency. In this second clustering unit, frequency-dependent phase / norm normalized vectors are clustered based on this frequency-dependent frequency response model, so that even if the above-mentioned cyclic jump occurs, it corresponds to each signal source. A cluster can be suitably generated. Therefore, the separation signal can be suitably obtained by using the information of the cluster.

  Preferably, in the first aspect of the present invention, the first clustering unit clusters feature quantity vectors in a frequency band including a frequency at which spatial aliasing cannot occur, and the second clustering unit has a frequency at which spatial aliasing can occur. Cluster the phase / norm normalized vectors in the frequency band including.

  Here, the first clustering unit performs clustering of feature vectors in a frequency band including frequencies where spatial aliasing cannot occur, thereby causing many of the feature vectors to be clustered to have the above-described cyclic jumps. Can not be. As a result, a valid centroid can be generated. The second clustering unit also generates a cluster corresponding to the frequency that was not generated by the first clustering unit by clustering the phase / norm normalized vector of the frequency band including the frequency at which spatial aliasing can occur. be able to. As a result, a separation signal can be appropriately generated even for a frequency at which spatial aliasing occurs.

  In addition, the above-mentioned “frequency band including a frequency at which spatial aliasing cannot occur” may be a frequency band partially including a frequency at which spatial aliasing may occur, but preferably, spatial aliasing may occur. It is desirable that the frequency band is composed only of no frequencies. As a result, the first clustering unit can generate a centroid using only the feature vector that has not caused a cyclic jump. As a result, it is possible to prevent the accuracy of the centroid from being lowered due to the cyclic jump. Further, the above-described “frequency band including a frequency at which spatial aliasing can occur” is desirably an entire frequency band (a frequency band corresponding to all time frequency slots).

  In the first aspect of the present invention, preferably, the model parameter optimizing unit uses the cluster information and a phase / norm normalization vector corresponding to a frequency band including a frequency at which spatial aliasing may occur to optimize the model parameter. Turn into. Thereby, information corresponding to a frequency at which spatial aliasing can occur can be reflected in the generation of the model parameter, and the accuracy of the model parameter can be improved.

  More preferably, the model parameter is a parameter corresponding to a set of a sensor and a signal source corresponding to a cluster. The model parameter optimization unit corresponds to a set of a sensor corresponding to each element of the phase / norm normalized vector and a signal source corresponding to the cluster to which the phase / norm normalized vector indicated by the cluster information belongs. The cost function consisting of the sum of the distances between the frequency response model into which the model parameters are assigned and the elements of the phase / norm normalized vector is subjected to partial differentiation with respect to the model parameters and is proportional to the calculated partial differential value. The model parameter is optimized by subtracting the value to be determined from the model parameter. As a result, it is possible to improve the accuracy of the model parameters by using the feature vector information that has not been used in the clustering of the first clustering unit.

  Further preferably, the model parameter optimization process and the cluster information generation process are alternately executed until a predetermined end condition is satisfied. Then, the separation signal generation unit generates a separation signal using the latest cluster information when a predetermined termination condition is satisfied. Thereby, the precision of a model parameter can be improved and a highly accurate separation signal can be generated. In addition, it is preferable that the model parameter optimization processing in the model parameter optimization unit is executed using phase / norm normalization vectors corresponding to all time frequency slots (that is, corresponding to all frequencies). This is because the accuracy of the model parameters can be further increased.

  In the first aspect of the present invention, the first clustering unit generates initial cluster information corresponding to clusters to which feature quantity vectors corresponding to frequency bands including frequencies in which spatial aliasing cannot occur, and second clustering. The unit generates cluster information corresponding to the clusters to which the phase and norm normalization vectors corresponding to the frequency bands including frequencies where spatial aliasing may occur, and the separated signal generation unit generates the initial data generated by the first clustering unit. The separation signal may be generated using the cluster information and the cluster information generated by the second clustering unit. As described above, by using the initial cluster information generated by the first clustering unit for the generation of the separation signal, the second clustering unit needs to generate cluster information having a frequency overlapping with the initial cluster generated by the first clustering unit. Disappears. As a result, the calculation amount can be reduced as a whole.

  In the second aspect of the present invention, first, the frequency domain conversion unit converts the mixed signals observed by a plurality of sensors into frequency domain signals. In addition, the model parameter selection unit selects an initial value of the model parameter of the frequency response model. Then, cluster the frequency-dependent phase / norm normalized vectors with the phase / norm normalized values of the frequency domain signal as elements, based on the frequency response model with the model parameters substituted until a predetermined termination condition is satisfied. Then, the process of generating cluster information corresponding to the cluster to which each phase / norm normalized vector belongs, and the process of optimizing the model parameters using the cluster information and the phase / norm normalized vector are repeated. Then, the separation signal generation unit generates a frequency domain separation signal by using the latest cluster information and the frequency domain signal when a predetermined termination condition is satisfied.

  Here, since the clustering of the second aspect of the present invention is only clustering with respect to the frequency-dependent phase / norm normalized vector, the problem caused by the above-described cyclic jump does not occur.

  In the present invention, it is possible to extend the conventional technique described above, and perform suitable clustering even in a frequency band where spatial aliasing can occur, and generate an appropriate separated signal.

The best mode for carrying out the present invention will be described below with reference to the drawings. In the following, after explaining the principle of each embodiment, each embodiment will be described.
[Summary of Principle]
In each embodiment, first, mixed signals observed by a plurality of sensors are converted into frequency domain signals, and feature vectors obtained by normalizing the signals are clustered. In each form example, this clustering (clustering in the “first clustering unit”) is performed only on feature vectors of frequencies at which spatial aliasing cannot occur. When this clustering result is analyzed, the model parameters of the frequency response model expressing how the signals are mixed, that is, normalized from the signal source k to the sensor q (qε {1,..., M}) The arrival time γ _qk and the amplitude gain λ _qk > 0 can be calculated. Then, based on the frequency response model into which these model parameters γ _qk and λ _qk are substituted, the above-described phase / norm normalized vectors are clustered (clustering in the “second clustering unit”). In each example, clustering in the second clustering unit is performed on the phase / norm normalized vectors in all frequency bands including frequencies at which spatial aliasing can occur. Since each cluster generated in this way corresponds to each signal source k, the separated signal can be estimated by using the information of the cluster.

However, the model parameters γ _qk and λ _qk are calculated using only feature quantity vectors of frequencies at which spatial aliasing cannot occur. Therefore, it may not be very accurate. Therefore, in the second embodiment, processing for adding / subtracting a small correction value to / from the model parameters γ _qk and λ _qk using the phase / norm normalized vector of the entire frequency band including the frequency at which spatial aliasing can occur. _Is repeated to optimize the model parameters γ _qk and λ _qk .

と正規化する。なお、αは正の実数であり、例えば、α＝１である。 [Details of Principle]
Next, the details of the principle will be described.
[Frequency response model and frequency domain signal]
Each form assumes signal sparsity and mutual independence. In this case, each frequency domain signal X _q (f, τ) has information corresponding to the frequency response from the signal source to the sensor (see equations (5) and (6)). Therefore, by analyzing the frequency domain signal X _q (f, τ), it is possible to calculate model parameters of a frequency response model that expresses the frequency response from the signal source to the sensor. In each embodiment, the frequency response from the signal source k to the sensor q is a direct wave model.
H _qk (f) = λ _qk・ exp [−j ・ 2π ・ f ・ γ _qk ]… (14)
Is approximated by Here, the model parameters γ _qk and λ _qk > 0 represent the arrival time and attenuation (amplitude gain) from the signal source k to the sensor q, respectively. However, it is difficult to actually distinguish the phase and amplitude of the source signal S _k (f, τ) in the frequency domain from the phase and amplitude of the frequency response H _qk (f). Therefore, in each embodiment, λ _qk and γ _qk are considered as relative ones, and some kind of normalization is performed. The arrival time γ _qk is 0 for a certain reference sensor Q, that is, the arrival time γ _Qk = 0. The amplitude gain λ _qk is

And normalize. Α is a positive real number, for example, α = 1.

により達成できる。なお、ａｒｇ［・］は、・の偏角を示す。 Such normalization is also reflected in the mixed signal vector X (f, τ) = [X ₁ (f, τ),..., X _M (f, τ)] ^T. This is done by normalizing the phase and norm of the mixed signal vector X (f, τ). That is, mixed signal vector X (f, τ) with respect to the element X _Q (f, tau) corresponding to a reference sensor Q declination as 0, the elements _{X 1 (f, τ),} ..., The deviation angle of X _M (f, τ) is normalized, and further normalized so that the norm is α (for example, 1). The vector normalized in this way is called a phase / norm normalized vector X ′ (f, τ) = [X ₁ ′ (f, τ),..., X _M ′ (f, τ)] ^T. Such normalization is, for example,

Can be achieved. Note that arg [•] indicates the declination of •.

  When normalization is performed as described above, a certain phase / norm normalization vector X ′ (f, τ) is expressed by an equation (14) (hereinafter “frequency response”) that models the frequency response from a certain signal source k to the sensor q. Called a model). That is, the phase that minimizes the sum of the distances between the elements of the phase / norm normalized vector X ′ (f, τ) and the frequency response model (sum of each time frequency slot (f, τ) for each sensor). It can be estimated that the norm normalized vector X ′ (f, τ) corresponds to the signal source k, and the separated signal can be estimated using this result.

Here, which phase / norm normalization vector X ′ (f, τ) corresponds to which frequency response model H _qk (f) is different for each time frequency slot (f, τ), and this phase / norm The correspondence relationship between the normalized vector X ′ (f, τ) and the frequency response model H _qk (f) can be expressed as minimizing the following cost function.

  Here, C (f, τ) (referred to as “cluster information”) clusters any feature quantity (eg, phase / norm normalization vector or feature quantity vector) corresponding to each time frequency slot (f, τ). It is the information corresponding to each cluster obtained in this way. That is, C (f, τ) = k for a certain time frequency slot (f, τ) means that some feature quantity corresponding to the time frequency slot (f, τ) belongs to the kth cluster. To do. Further, the summation Σ with the condition of C (f, τ) = k means that the summation is performed for all time frequency slots (f, τ) where C (f, τ) = k.

[Solution of cost function G]
In each form, in solving the problem of minimizing the cost function G of Equation (16), first, a cluster is determined for each frequency f of the frequency band F _L ⊆F where spatial aliasing cannot occur, The initial values of the model parameters λ _qk and γ _qk of the frequency response model H _qk (f) (Equation (14)) from each signal source k to each sensor q are calculated. Note that F is a set in which all the frequencies to be considered are collected, that is, F = {0, f _s / L,..., F _s (L−1) / L} (f _s is a sampling frequency). Further, the frequency band F _L that would not occur spatial aliasing,
F _L = {f: 0 <f <c / (2d _max )}… (17)
Can be calculated. D _max is the maximum distance between the reference sensor Q and another sensor q.

に従い、位相・ノルム正規化ベクトルX'(f,τ)の周波数依存成分を排除する周波数正規化を行う。各形態では、このように正規化された各要素X_q''(f,τ)からなるベクトルX''(f,τ)=[X₁''(f,τ),..., X_M''(f,τ)]^Tを特徴量ベクトルとする。 When considering only the frequency band F _L where spatial aliasing does occur, the cost function G of the formula (16) can be easily minimized by the following steps.
First, For all frequencies f that belong to the frequency band F _L, for example,

The frequency normalization is performed to eliminate the frequency dependent component of the phase / norm normalization vector X ′ (f, τ). In each form, the vector X '' (f, τ) = [X ₁ '' (f, τ), ..., X consisting of each element X _q '' (f, τ) normalized in this way Let _M ″ (f, τ)] ^T be a feature vector.

と変更される。ここでH_qk’は、式（１４）に示した周波数応答モデルH_qk(f)の周波数依存成分を排除する正規化を、式（１８）と同様に行ったものであり、例えば、

と表現されるものである。なお、H_qk’を正規化周波数応答モデルと呼ぶ。
また、式（１９）をベクトル表記すると、

となる。なお、H_k'=[ H_1k',..., H_Mk']^Tは、正規化周波数応答モデルH_qk’を要素とするベクトルである。 When each element X _q ″ (f, τ) of such a feature vector X ″ (f, τ) is used, the cost function G shown in Expression (16) is

And changed. Here, H _qk ′ is _{obtained by performing} normalization for eliminating the frequency dependent component of the frequency response model H _qk (f) shown in the equation (14) in the same manner as in the equation (18).

It is expressed as H _qk ′ is called a normalized frequency response model.
Further, when expression (19) is expressed in vector,

It becomes. H _k ′ = [H _1k ′,..., H _Mk ′] ^T is a vector whose elements are normalized frequency response models H _qk ′.

[Determination of cluster for each frequency f of frequency band F _L ⊆F]
Here, considering only the frequency f of the frequency band F _L ⊆F, the feature vector X ″ (f, τ) forms a cluster for each signal source k (see, for example, Non-Patent Document 3). The vector H _k '= [H _1k ', ..., H _Mk '] ^T whose elements are the normalized frequency response model H _qk ' described above is regarded as the centroid of each cluster (cluster center vector). be able to. Therefore, similarly to the well-known k-means method (see, for example, Non-Patent Document 2), the following <Calculation 1><Calculation2> is alternately applied repeatedly, whereby the cost function G of Equation (19) is applied. Each cluster that minimizes 'and their centroid H _k ' can be calculated.

に従って算出する。この演算は、最新のクラスタ情報C(f,τ)に基づき、最適なセントロイドH_k’を算出するものである。なお、特徴量ベクトルX''（f,τ）と同様に、セントロイドH_k’もベクトルとしてのノルムがα（式（２１）の例ではα＝１）になるように正規化される。 <Calculation 1> Based on the latest cluster information C (f, τ), the centroid H _k ′ of each cluster is calculated.

Calculate according to This calculation calculates an optimal centroid H _k ′ based on the latest cluster information C (f, τ). Similar to the feature vector X ″ (f, τ), the centroid H _k ′ is also normalized so that the norm as a vector is α (α = 1 in the example of Expression (21)).

に従い、各特徴量ベクトルX''（f,τ）に最も近いセントロイドH_k’を選択し、選択したセントロイドH_k’の添字ｋを、特徴量ベクトルX''（f,τ）に対応する時間周波数スロット（f,τ）のクラスタ情報C(f,τ)とする（C(f,τ)=k）。式（２２）におけるargmin_k・は、・を最小にするｋを意味する。 <Calculation 2> The cluster information C (f, τ) is updated based on the latest centroid H _k ′. That is,

The centroid H _k ′ closest to each feature vector X ″ (f, τ) is selected according to the above, and the subscript k of the selected centroid H _k ′ is used as the feature vector X ″ (f, τ). The cluster information C (f, τ) of the corresponding time frequency slot (f, τ) is assumed (C (f, τ) = k). Argmin _k · in Equation (22) means k that minimizes ·.

Either <Calculation 1> or <Calculation 2> may start first. The initial value of the cluster information C (f, τ) when <Calculation 1> is performed first and the setting method of the initial value of the centroid H _k ′ when <Calculation 2> is performed first Although there is no limitation, cluster information C (f, τ) such that feature vector X '' (f, τ) distributed over a wide range belongs to the same cluster and centroid H _k ′ concentrated in a narrow range are initially set It is not preferable to use a value. This is because an appropriate cluster may not be generated. Such a preferable initial value setting method is not particularly limited, and examples thereof include the following methods.

Example of initial value setting for Centroid H _k ':
(1) A plurality of combinations of initial value candidate combinations of centroid H _k ′ (k∈ {1,..., N}) are randomly generated.
(2) For each combination, the inner product of the initial value candidates of the centroid H _k ′ is obtained, and the combination having the smallest inner product is set as the initial value of the centroid H _k ′.

Example of initial value setting for cluster information C (f, τ):
(1) A plurality of patterns of random combinations of initial value candidates for cluster information C (f, τ) are generated.
(2) For each combination, a combination of initial value candidates of centroid H _k ′ is calculated according to equation (21).
(3) 'for each combination of initial value options of the centroid H _k' centroid H _k obtains an inner product of the initial value candidates, the cluster information corresponding to a combination of the inner product becomes minimum C of (f, tau) The initial value candidate is set as the initial value of the cluster information C (f, τ).

[Initial value calculation of model parameters λ _qk and γ _qk ]
<Calculation 1> and <Calculation 2> are repeated until a predetermined termination condition is satisfied, and the frequency response of Expression (14) is used according to the following expression using the centroid H _k ′ when the predetermined condition is satisfied. The model parameters λ _qk and γ _qk of the model H _qk (f) are calculated.

に従い、クラスタ情報(f,τ)を生成し、位相・ノルム正規化ベクトルX'(f,τ)を各クラスタに割り当てる。 [Solution of cost function G]
Next, using the obtained model parameters λ _qk and γ _qk , the phase / norm normalized vector X ′ (f, τ) is set so as to minimize the cost function G of Equation (16) for all frequencies f∈F. ). As a simple method, the obtained model parameters λ _qk and γ _qk are used as _they are,

Then, cluster information (f, τ) is generated, and a phase / norm normalized vector X ′ (f, τ) is assigned to each cluster.

However, the model parameter lambda _qk calculated only in the frequency band F _L, gamma _qk is likely less accurate. Therefore, as a better method, more accurate model parameters λ _qk and γ _qk are calculated using the phase / norm normalized vector X ′ (f, τ) of all frequencies f∈F. This can be realized by repeating the following corrections using partial differential values related to the model parameters λ _qk and γ _qk of the cost function G in Expression (16).

は、それぞれ、式（１６）のコスト関数Ｇのモデルパラメータλ_ｑｋ，γ_ｑｋに関する偏微分である。また、 (f,τ)=C_k ^fの条件を付加した総和Σは、C(f,τ)=kであって周波数がｆである全ての時間周波数スロット(f,τ)について総和をとることを意味する。また、ｉｍａｇ［・］とｒｅａｌ［・］は、それぞれ、複素数・の虚部と実部を抽出する関数を意味する。 Note that μ is a real number indicating a step size parameter. Also,

_Are partial derivatives with respect to the model parameters λ _qk and γ _qk of the cost function G in the equation (16), respectively. The sum Σ with the condition of (f, τ) = C _k ^f is summed for all time frequency slots (f, τ) with C (f, τ) = k and frequency f. Means that. Further, imag [•] and real [•] mean functions for extracting the imaginary part and real part of the complex number, respectively.

By repeatedly applying the calculation of the cluster information C (f, τ) according to Equation (24) and the correction of the model parameters λ _qk and γ _qk according to Equation (25), better cluster information C (f, τ ) And model parameters λ _qk and γ _qk can be calculated. This repetition is performed until a predetermined end condition is satisfied.

そして、得られた周波数領域の分離信号Y_k(f,τ)を短時間逆フーリエ変換等によって時間領域の分離信号y_k(t)を求める。 [Separate signal generation]
Thereafter, using the cluster information C (f, τ) obtained as described above, a frequency domain separation signal Y _k (f, τ) is generated. Specifically, for example, the frequency domain separation signal Y _k (f, τ) is generated as follows.

Then, a time domain separation signal y _k (t) is obtained from the obtained frequency domain separation signal Y _k (f, τ) by short-time inverse Fourier transform or the like.

[First Embodiment]
Next, a first embodiment of the present invention will be described. In this embodiment, the cluster information C (f, τ) is generated according to the equation (24) for all frequencies fεF without optimization of the model parameters λ _qk and γ _qk .
<Hardware configuration>
FIG. 1 is a block diagram illustrating a hardware configuration of a signal separation device 1 according to the first embodiment.
As illustrated in FIG. 1, a signal separation device 1 of this example includes a CPU (Central Processing Unit) 10, an input unit 20, an output unit 30, an auxiliary storage device 40, a RAM (Random Access Memory) 10d, and a ROM (Read Only). Memory) 50 and bus 70.
The CPU 10 in this example includes a control unit 11, a calculation unit 12, and a register 13, and executes various calculation processes according to various programs read into the register 13. The input unit 20 in this example is an input port for inputting data, a keyboard, a mouse, and the like, and the output unit 30 is an output port for outputting data, a display, and the like. The auxiliary storage device 40 is, for example, a hard disk, an MO (Magneto-Optical disc), a semiconductor memory, or the like, and is observed by a signal separation program area 41 storing a signal separation program for executing the signal separation processing of this embodiment and a sensor. And a data area 42 in which various data such as mixed signals in the time domain are stored. The RAM 50 is, for example, an SRAM (Static Random Access Memory), a DRAM (Dynamic Random Access Memory) or the like, and has a signal separation program area 51 in which a signal separation program is written and a data area 52 in which various data are written. Yes. The bus 70 in this example connects the CPU 10, the input unit 20, the output unit 30, the auxiliary storage device 40, the RAM 50, and the ROM 60 so that they can communicate with each other.

<Cooperation between hardware and software>
The CPU 10 in this example writes the signal separation program stored in the signal separation program area 41 of the auxiliary storage device 40 in the signal separation program area 51 of the RAM 50 in accordance with the read OS (Operating System) program. Similarly, the CPU 10 writes various data such as a mixed signal in the time domain stored in the data area 42 of the auxiliary storage device 40 in the data area 52 of the RAM 50. Further, the CPU 10 stores the address on the RAM 50 where the signal separation program and various data are written in the register 13. Then, the control unit 11 of the CPU 10 sequentially reads these addresses stored in the register 13, reads a program and data from the area on the RAM 50 indicated by the read address, and sequentially executes the calculation indicated by the program to the calculation unit 12. The calculation result is stored in the register 13.

FIG. 2 is an example of a block diagram of the signal separation device 1 configured by reading the signal separation program into the CPU 10 as described above. FIG. 3 is a block diagram illustrating details of the mixed signal classifying unit 130 in FIG.
As illustrated in FIG. 2, the signal separation device 1 of this embodiment includes a memory 100, a frequency domain conversion unit 120, a mixed signal classification unit 130, a separated signal generation unit 140, a time domain conversion unit 150, a control unit 160, and a temporary memory. 170.

  Here, the memory 100 has storage areas 101 to 111. As illustrated in FIG. 3, the mixed signal classification unit 130 includes a frequency band determination unit 131, a normalization unit 132, a first clustering unit 133, a model parameter extraction unit 134, and a second clustering unit 135. . In addition, the normalization unit 132 includes a phase / norm normalization unit 132a and a frequency normalization unit 132b. Furthermore, the first clustering unit 133 includes a cluster determination unit 133a and a centroid calculation unit 133b.

<Processing>
Next, processing of the signal separation device 1 in this embodiment will be described. In the following, the situation where N source signals are mixed and observed by M sensors will be treated. In the preprocessing, the time domain mixed signal x _q (t) (q∈ {1,..., M}) observed by each sensor is stored in the storage area 101 of the memory 100, and the reference sensor Q is The indicated value Q and the maximum distance d _max between the reference sensor Q and another sensor q are stored in the storage area 105, and the initial value of the centroid H _k ′ or the initial value of the cluster information C (f, τ). Is stored in the storage area 107.

FIG. 4 is a flowchart for explaining processing of the signal separation device 1 according to the first embodiment. FIG. 5 is a flowchart for explaining details of the process in step S2 of FIG. 6 and 7 are flowcharts for explaining details of the process in step S3 of FIG. Hereinafter, the processing of this embodiment will be described with reference to these drawings.
The following processes are executed under the control of the control unit 160. Unless otherwise specified, each process data is stored and extracted in the temporary memory 170 one by one.

[Processing of Frequency Domain Transformer 120]
First, in the frequency domain transform unit 120 (FIG. 2), the mixed signal x _q (t) in the time domain is read from the storage area 101 of the memory 100, and the time frequency slot (f, τ) is read by short-time discrete Fourier transform or the like. Each signal (frequency domain signal) X _q (f, τ) (qε {1,..., M}) is converted and stored in the storage area 102 of the memory 100 (step S1).

[Processing of Mixed Signal Classification Unit 130]
Next, the normalization unit 132 of the mixed signal classification unit 130 reads the frequency domain signal X _q (f, τ) from the storage area 102 of the memory 100. Then, the normalization unit 132 normalizes the phase of the frequency domain signal X _q (f, τ) with respect to a frequency (f∈F _L ) at which spatial aliasing cannot occur, and further eliminates frequency-dependent components. Generated signal X _q ″ (f, τ) is generated (step S2). Details of step S2 will be described later. The generated frequency normalized signal X _q ″ (f, τ) is stored in the storage area 104 of the memory 100.

Next, the first clustering unit 133 of the mixed signal classifying unit 130 reads the frequency normalized signal X _q ″ (f, τ) from the storage area 104 of the memory 100. Then, the first clustering unit 133 uses the frequency normalized signal X _q ″ (f, τ) as each element, and the feature vector X ″ (f, τ) = [X ₁ ″ for each time frequency. (f, τ),..., X _M ″ (f, τ)] ^T are clustered to calculate the centroid H _k ′ of each cluster (step S3). Details of step S3 will be described later. The generated centroid H _k ′ is stored in the storage area 108 of the memory 100.

Next, the model parameter extraction unit 134 of the mixed signal classification unit 130 reads the centroid H _k ′ from the storage area 108 of the memory 100. The model parameter extraction unit 134 uses each element of the centroid H _k ′ = [H _1k ′,..., H _Mk ′] ^T and uses the frequency response model H _qk (f) according to the above equation (23). Model parameters γ _qk and λ _qk are extracted (step S4). The extracted model parameters γ _qk and λ _qk are stored in the storage area 109 of the memory 100.

Next, the second clustering unit 135 of the mixed signal classifying unit 130 reads the model parameters γ _qk and λ _qk from the storage area 109 of the memory 100. Then, the second clustering unit 135 uses the frequency response model H _k (f) into which the model parameters γ _qk and λ _qk are substituted according to the above-described equation (24) for all the frequencies F, and normalizes the frequency domain signal. of values X _q '(f, τ) phase norm normalized vector X of the frequency-dependent to the elements' (f, τ) = [ X 1 '(f, τ), ..., X M' ( f, τ)] ^T is clustered. Thus, cluster information C (f, τ) indicating the time frequency slot (f, τ) corresponding to the cluster to which each phase / norm normalized vector X ′ (f, τ) belongs is generated (step S5). The generated cluster information C (f, τ) is stored in the storage area 107 of the memory 100.

[Processing of Separation Signal Generation Unit 140]
Next, the separated signal generation unit 140 reads the frequency domain signal X _q (f, τ) and the cluster information C (f, τ) from the storage areas 102 and 107 of the memory 100, respectively. Then, the separated signal generation unit 140 uses the frequency domain signal X _q (f, τ) and the cluster information C (f, τ), for example, according to the above equation (28), the frequency domain separated signal Y _k. (f, τ) (kε {1,..., N}) is generated (step S6). The generated separated signal Y _k (f, τ) is stored in the storage area 110 of the memory 100.

[Processing of time domain conversion unit 150]
Next, the time domain transform unit 150 reads the separation signal Y _k (f, τ) from the storage area 110 of the memory 100 and converts it into the time domain separation signal y _k (t) by short-time inverse Fourier transform or the like. Then, it is stored in the storage area 111 of the memory 100 (step S7).
[Details of Step S2 Processing]
Next, details of the process of step S2 will be described.
First, the frequency band determining unit 131, from the storage area 105 of the memory 100 reads the value _{d max,} the frequency band _{F L} that can not occur spatial aliasing
F _L = {f: 0 <f <c / (2d _max )}
(Step S11). Calculated value _{F L} is stored in the storage area 106 of the memory 100.

Next, the phase / norm normalization unit 132 a of the normalization unit 132 reads the value Q indicating the reference sensor Q from the storage area 105 of the memory 100, and further, each frequency domain signal X _q (f, τ) from the storage area 102. ) And each frequency domain signal X _Q (f, τ) corresponding to the reference sensor Q is read. Then, the phase / norm normalization unit 132a normalizes the declination of the frequency domain signal X _q (f, τ) based on the declination of the frequency domain signal X _Q (f, τ) corresponding to the reference sensor Q. , The normalization vector X '(f, τ) = [X ₁ ' (f, τ), ..., X _M '(f, τ)] ^T is generated (step S12). Note that this normalization is performed, for example, according to the above-described equation (15). The generated phase / norm normalized vector X ′ (f, τ) is stored in the storage area 103 of the memory 100.

Then, the frequency normalizing section 132b of the normalization unit 132 reads from the storage area 103 and 106 of the memory 100, respectively, phase-norm normalized vector X '(f, τ) and the value _{F L.} Then, the frequency normalizing section 132b, for example, in accordance with the equation (18), the frequency band F _L for all frequencies f belonging to the phase-norm normalized vector X '(f, tau) each element of X' _q (f , τ) is normalized by dividing the declination by a value proportional to the frequency f, and the frequency normalized signal X _q '' (), which eliminates the frequency dependence of the phase / norm normalized vector X ′ (f, τ). f, τ) (fεF _L ) is generated (step S13). The generated frequency normalized signal X _q ″ (f, τ) is stored in the storage area 104 of the memory 100.

[Details of processing in step S3 (pattern A)]
Next, details (pattern A) of the processing in step S3 will be described (FIG. 6).
First, the first clustering unit 133 reads the initial value of the centroid H _k ′ from the storage area 108 of the memory 100 (step S21).
Next, the cluster determining unit 133a of the first clustering unit 133, for example, according to the above-described equation (22), the feature quantity vector X ″ (f, τ) (f∈F _L ) read from the storage area 104, A cluster corresponding to each feature vector X ″ (f, τ) is determined so that the sum of the distances from the centroid H _k ′ read from the storage area 108 is minimized, and each feature vector X ″ is determined. A value k that identifies the cluster to which the feature vector X ″ (f, τ) belongs is substituted into the cluster information C (f, τ) corresponding to the time frequency slot (f, τ) of (f, τ). (Step S22). Each piece of cluster information C (f, τ) subjected to such processing is stored in the storage area 107 of the memory 100.

Next, the centroid calculation unit 133b of the first clustering unit 133 reads the feature vector X ″ (f, τ) and the cluster information C (f, τ) from the storage areas 104 and 107 of the memory 100, respectively. . Then, the centroid calculation unit 133b, for example, according to the above-described equation (21), the feature vector X ″ (f, τ) corresponding to the time frequency slot (f, τ) where C (f, τ) = k. ) And the norm of the addition result normalized to a predetermined value is set as a new centroid H _k ′ (step S23). The generated new centroid H _k ′ is stored in the storage area 108 of the memory 100.

Next, the control unit 160 determines whether or not a predetermined end condition is satisfied (step S24). As the termination condition, for example, “the process of steps S22 and S23 is alternately repeated a predetermined number of times” or “the displacement between the centroid H _k ′ updated in step S23 and the centroid H _k ′ before update Is within a predetermined range. " If the control unit 160 determines that the predetermined end condition is not satisfied, the control unit 160 returns the process to step S22. On the other hand, when the control unit 160 determines that the predetermined end condition is satisfied, the control unit 160 ends the process of step S3. Note that the centroid H _k ′ stored in the storage area 108 of the memory 100 at the time when the processing of step S3 is completed is treated as a regular centroid H _k ′ ([Details of processing of step S3 (pattern A) ] End of explanation).

[Details of processing in step S3 (pattern B)]
Next, details (pattern B) of the process of step S3 will be described (FIG. 7).
First, the first clustering unit 133 reads the initial value of the cluster information C (f, τ) from the storage area 107 of the memory 100 (step S31).
Next, the centroid calculation unit 133b of the first clustering unit 133, for example, according to the above-described equation (21), the feature quantity vector corresponding to the time frequency slot (f, τ) where C (f, τ) = k. X ″ (f, τ) is added, and the norm of the addition result is normalized to a predetermined value as a new centroid H _k ′. The generated new centroid H _k ′ is stored in the storage area 108 of the memory 100 (step S32).

Next, the cluster determining unit 133a of the first clustering unit 133, for example, according to the above-described equation (22), the feature quantity vector X ″ (f, τ) (f∈F _L ) read from the storage area 104, A cluster corresponding to each feature vector X ″ (f, τ) is determined so that the sum of the distances from the centroid H _k ′ read from the storage area 108 is minimized, and each feature vector X ″ is determined. A value k that identifies the cluster to which the feature vector X ″ (f, τ) belongs is substituted into the cluster information C (f, τ) corresponding to the time frequency slot (f, τ) of (f, τ). (Step S33). Each piece of cluster information C (f, τ) subjected to such processing is stored in the storage area 107 of the memory 100.

Next, the control unit 160 determines whether or not a predetermined end condition is satisfied (step S34). As the termination condition, for example, “the process of steps S32 and S33 is alternately repeated a predetermined number of times” or “the displacement between the centroid H _k ′ updated in step S32 and the centroid H _k ′ before update is used. Is within a predetermined range. " If the control unit 160 determines that the predetermined end condition is not satisfied, the control unit 160 returns the process to step S32. On the other hand, when the control unit 160 determines that the predetermined end condition is satisfied, the control unit 160 ends the process of step S3. Note that the centroid H _k ′ stored in the storage area 108 of the memory 100 at the time when the processing of step S3 is completed is treated as a regular centroid H _k ′ ([Details of processing of step S3 (pattern A) ] End of explanation).

[Second Embodiment]
Next, a second embodiment of the present invention will be described. In this embodiment, the model parameters λ _qk and γ _qk are optimized to generate cluster information C (f, τ) for all frequencies fεF according to the equation (24).
<Configuration>
The difference from the first embodiment is only the mixed signal classification unit. In the following, only the configuration of the mixed signal classification unit is shown.
FIG. 8 is a block diagram illustrating details of the mixed signal classifying unit 230 according to the second embodiment. In FIG. 8, portions common to the first embodiment are denoted by the same reference numerals as those in FIG. 3, and description thereof is omitted.
As illustrated in FIG. 8, the mixed signal classification unit 230 of this embodiment includes a frequency band determination unit 131, a normalization unit 132, a first clustering unit 133, a model parameter extraction unit 134, and a second clustering unit 235. Yes. Here, the second clustering unit 235 of the present embodiment includes a cluster determination unit 235a and a model parameter optimization unit 235b.

<Processing>
Next, processing of the signal separation device in this embodiment will be described. In the following, the situation where N source signals are mixed and observed by M sensors will be treated. Further, it is assumed that the same preprocessing as in the first embodiment is performed.
FIG. 9 is a flowchart for explaining processing of the signal separation device according to the second embodiment. FIG. 10 is a flowchart for explaining details of the process in step S105 shown in FIG.

Hereinafter, the processing of this embodiment will be described with reference to these drawings. The following processes are executed under the control of the control unit 160. Unless otherwise specified, each process data is stored and extracted in the temporary memory 170 one by one.
[Processing of Frequency Domain Transformer 120, Frequency Band Determining Unit 131, Normalizing Unit 132, First Clustering Unit 133, and Model Parameter Extracting Unit 134]
These processes are the same as steps S1 to S4 in the first embodiment (steps S101 to S104).

[Processing of Second Clustering Unit 235]
The second clustering unit 235 of this embodiment uses the frequency response model H _qk (f) into which the model parameters γ _qk and λ _qk are substituted for all frequencies fεF as a reference, and a phase / norm normalized vector X ′ (f , τ) are clustered to generate cluster information C (f, τ), cluster information C (f, τ), and phase / norm normalized vector X ′ (f, τ). The process of optimizing γ _qk and λ _qk is alternately repeated (step S105). Thus, the optimized model parameter gamma _qk, lambda _qk and the optimized model parameter gamma _qk, lambda _qk assignment frequency response model H _qk cluster information generated based on (f) C (f , τ). Hereinafter, the details of the process of step S105 will be described with reference to FIG.

First, the second clustering unit 235 reads the phase / norm normalized vector X ′ (f, τ) and the model parameters γ _qk and λ _qk from the storage areas 103 and 109 of the memory 100, respectively. Then, the cluster determining unit 235a of the second clustering unit 235, in accordance with the aforementioned equation (24), the phase norm normalized vector X '(f, tau) each element of X _q' (f, tau) and model parameters The frequency response model λ _qk · exp (−j · 2π · f · γ _qk ) to which γ _qk and λ _qk are substituted, and k that minimizes the sum of the distances are set to the phase / norm normalized vector X ′ (f , τ) as the value of the cluster information C (f, τ) (step S111). The cluster information C (f, τ) subjected to such processing is stored in the storage area 107 of the memory 100.

Next, the model parameter optimization unit 235b of the second clustering unit 235 follows each of the elements X _q ′ (f, τ) of the phase / norm normalized vector X ′ (f, τ) according to the above-described equations (26) and (27). model parameter corresponding to the set of the sensor q corresponding to τ) and the signal source k corresponding to the cluster to which the phase / norm normalized vector X ′ (f, τ) indicated by the cluster information C (f, τ) belongs Frequency response model λ _qk・ exp (-j ・ 2π ・ f ・ γ _qk ) substituted with γ _qk , λ _qk and each element X _q ′ () of the phase / norm normalized vector X ′ (f, τ) A partial differentiation with respect to the model parameters γ _qk and λ _qk is performed on the cost function (equation (16)) consisting of the sum of the distances to f, τ) (step S112). Then, the model parameter optimizing unit 235b subtracts a value proportional to each partial differential value from the model parameters γ _qk and λ _qk according to the above equation (25), respectively, and the model parameters γ _qk and λ _qk. Is optimized (step S113).

  Next, the control unit 160 determines whether or not a predetermined end condition is satisfied (step S114). Examples of the termination condition include “the processing of steps S111 and S112 being alternately repeated a predetermined number of times” and “the knitting differential values calculated in step S112 being equal to or less than a predetermined threshold”. . Here, when the control unit 160 determines that the predetermined end condition is not satisfied, the control unit 160 returns the process to step S111. On the other hand, when the control unit 160 determines that the predetermined end condition is satisfied, the control unit 160 ends the process of step S105.

[Processing of Separation Signal Generation Unit 140 and Time Domain Conversion Unit 150]
These processes are the same as steps S6 and S7 of the first embodiment (steps S106 and 107).
[Third Embodiment]
Next, a third embodiment of the present invention will be described. This embodiment is a modification of the second embodiment. In this embodiment, the initial values of the model parameters λ _qk and γ _qk are arbitrarily selected, and the model parameters λ _qk and γ _qk are optimized as in the second embodiment to obtain the model parameters λ _qk and γ _qk . decide. Then, cluster information C (f, τ) is generated for all frequencies fεF according to equation (24). Only differences from the first and second embodiments will be described below.

<Configuration>
The difference from the first embodiment is only the mixed signal classification unit. In the following, only the configuration of the mixed signal classification unit is shown.
FIG. 11 is a block diagram illustrating details of the mixed signal classification unit 330 according to the third embodiment. In FIG. 11, portions common to the first and second embodiments are denoted by the same reference numerals as in FIGS. 3 and 8, and description thereof is omitted.
As illustrated in FIG. 1, the mixed signal classification unit 330 according to the present exemplary embodiment includes a phase / norm normalization unit 132 a, a second clustering unit 235, and a model parameter selection unit 333.

<Processing>
Next, processing of the signal separation device in this embodiment will be described. In the following, the situation where N source signals are mixed and observed by M sensors will be treated. Further, it is assumed that the same preprocessing as in the first embodiment is performed.
FIG. 12 is a flowchart for explaining processing of the signal separation device according to the third embodiment. Hereinafter, the processing of this embodiment will be described with reference to these drawings.
[Processing of Frequency Domain Transformer 120]
This process is the same as step S1 of the first embodiment (step S201).

[Processing of phase / norm normalization unit 132a]
This process is the same as step S12 of the first embodiment (step S202).
[Process of Model Parameter Selection Unit 333]
The model parameter selection unit 333 arbitrarily selects initial values of the model parameters γ _qk and λ _qk . The initial values of the selected model parameters γ _qk and λ _qk are stored in the storage area 109 of the memory 100 (step S203).
[Processing of Second Clustering Unit 235]
This process is the same as step S105 of the second embodiment (step S204).

[Processing of Separation Signal Generation Unit 140 and Time Domain Conversion Unit 150]
These processes are the same as steps S6 and S7 in the first embodiment (steps S205 and 206).
〔Experimental result〕
Next, in order to show the effects of the above-described embodiments, an experiment is performed to separate a plurality of sounds under the experimental condition A shown in FIG. 13 (a) and the experimental condition B shown in FIG. 13 (b). The results are shown. These conditions are conditions under which spatial aliasing can occur. For comparison, the experiment was performed by the following three types of procedures.

Procedure I: Spatial aliasing was not considered, and clustering by the first clustering unit, that is, Expressions (21) and (22) were repeatedly applied to the mixed signal vectors of all frequencies fεF (conventional configuration). Therefore, in the high region where spatial aliasing occurs, there is a high possibility that the generated cluster is largely incorrect.
Procedure II: The clustering by the first clustering unit, that is, the expressions (21) and (22) are repeatedly applied to only the mixed signal vector of the low frequency fεF _L where no spatial aliasing occurs, and the cent Model parameters were calculated using Lloyd (formula (23)). Then, using the calculated model parameters as they are, clustering was performed for all frequencies fεF according to Expression (24) (first embodiment).
Step III: Using the model parameters λ _qk and γ _qk optimized by repeatedly applying the equations (24) and (25) by the model parameter optimizing unit, for all frequencies fεF, the equation (24) is used. Clustering was performed (second and third embodiments).

ここで、分離性能は、SIR（Signal-to-Interference Ratio，分離信号における目的信号成分と干渉信号成分のパワー比）で測定した。値が大きいほど良い結果を示す。双方の実験条件において、手順II、手順IIIと分離性能が向上していくことが見受けられ、各形態の効果が確認できた。なお、入力SIRとは、センサでの観測信号のSIRである。 The following is a table showing the average value of the separation performance corresponding to each condition performed for 16 combinations of sounds.

Here, the separation performance was measured by SIR (Signal-to-Interference Ratio, the power ratio between the target signal component and the interference signal component in the separated signal). Larger values indicate better results. Under both experimental conditions, it was observed that the separation performance was improved as in Procedure II and Procedure III, and the effects of each form could be confirmed. The input SIR is the SIR of the signal observed by the sensor.

[Effect of each embodiment]
The effects of the above embodiments are summarized as above. With each form of technique, even in Takashiro, where spatial aliasing occurs, the mixed signal vectors can be correctly classified, resulting in improved separation performance. Further, as in the second embodiment, the accuracy is improved by improving the model parameters λ _qk and γ _qk using the phase / norm normalized vector in all bands. Further, as in the third embodiment, spatial aliasing is also _achieved by a _{method of} arbitrarily selecting model parameters λ _qk and γ _qk and improving them using a frequency-dependent phase / norm normalization vector. High-precision signal separation can be performed in Takashiro where this occurs.

[Modifications, etc.]
The present invention is not limited to the embodiment described above. For example, in the first and second embodiments, the first clustering unit clusters only the feature quantity vectors having the frequency fεF _L at which spatial aliasing cannot occur. However, the first clustering unit may perform clustering of a feature vector having a frequency fεF _L at which spatial aliasing cannot occur, and a feature vector having a frequency at which spatial aliasing may occur. . Even if feature vectors that have undergone the above-mentioned cyclic jumps are mixed together, if the ratio is small when viewed from the whole feature vectors, clustering can be performed with a certain degree of accuracy and model parameters can be generated. It is. That is, the first clustering unit only needs to cluster feature quantity vectors in a frequency band including frequencies where spatial aliasing cannot occur.

  Further, for example, in the first and second embodiments, the second clustering unit clusters the phase / norm normalized vectors of all frequencies fεF. However, if separation signals at some frequencies are not necessary, the second clustering unit may calculate a normalized mixed signal vector of a frequency band that includes a frequency that is a part of the entire frequency band and that may cause spatial aliasing. A configuration for clustering may be used.

  Further, even when separated signals at all frequencies are required, the cluster information generated by the first clustering unit (corresponding to “initial cluster information”) is also used for the generation of separated signals, and the second clustering is performed. The unit may generate only cluster information of a frequency for which cluster information is not generated by the first clustering unit. Thereby, the calculation amount of clustering can be reduced. Further, the cluster information generated by the first clustering unit and the cluster information generated by the second clustering unit may overlap at some frequencies. Furthermore, the cluster information generated by the first clustering unit and the cluster information generated by the second clustering unit may not cover the entire frequency band F. That is, the first clustering unit generates initial cluster information corresponding to clusters to which feature vectors corresponding to frequency bands including frequencies where spatial aliasing cannot occur, and the second clustering unit performs spatial aliasing. Cluster information corresponding to clusters to which each of the normalized mixed signal vectors corresponding to frequency bands including frequencies that may occur belongs, and the separated signal generation unit includes initial cluster information generated by the first clustering unit, and a second clustering unit. The configuration may be such that the separated signal is generated using the cluster information generated by.

ただし、・^＊は、・の複素共役である。また、ψ｛・｝は関数であり、クラスタリング精度の観点から好ましくは単調増加関数であることが望ましい。 In the first and second embodiments described above, the method of generating each element of the phase / norm normalized vector by Expression (15) is exemplified. However, the frequency domain signal declination is not particularly limited as long as it normalizes the declination of the frequency domain signal corresponding to the reference sensor and normalizes the norm of the normalized value to a predetermined value. . For example, each element of the phase / norm normalized vector may be generated by the following expression.

However, ^* is a complex conjugate of. Also, ψ {·} is a function, and preferably a monotonically increasing function from the viewpoint of clustering accuracy.

を最小値化するクラスタを生成する。なお、セントロイドH_k'は、各クラスタのメンバの平均として算出する。 In the first and second embodiments, the frequency normalized signal is obtained by eliminating the frequency dependent component of the phase / norm normalized vector. However, the frequency normalized signal may be configured without performing norm normalization. That is, the frequency domain signal deviation angle may be normalized based on the deviation angle of the frequency domain signal corresponding to the reference sensor, and the frequency-dependent component may be excluded without performing norm normalization. In this case, the first clustering unit performs clustering of frequency normalized vectors whose norms are not normalized. The clustering criterion in this case is not whether the vectors are similar including the norm, but only whether the vectors are similar. This is an evaluation using the similarity. Cosine distance as one of the similarities
^{cosθ = | X 'H (f} , τ) · H k' | / (‖X '(f, τ) || · ‖H _k' ||) ... (29)
Can be illustrated. Here, θ is an angle formed by the frequency normalization vector and the vector of the centroid H _k ′. Here, · ^H indicates a complex conjugate transposed vector of vector ·. When using the cosine distance, the first clustering unit calculates the sum of the cosine distances.

Generate a cluster that minimizes. The centroid H _k ′ is calculated as the average of the members of each cluster.

  In the first and second embodiments, the frequency normalization signal is used as each element, and the feature quantity vector is configured. However, the value vector obtained by substituting the frequency normalized signal into a predetermined function may be used as each element to form the feature vector. For example, a frequency normalization signal that has not been norm-normalized may be substituted into a function that performs norm normalization, and values obtained thereby may be used as elements to form a feature vector. Further, when the number of sensors is 2 (N = 2), a feature quantity vector having each value obtained by the above equation (9) as an element, and a frequency domain signal in two sensors (sensor q and reference sensor Q). A feature amount vector having each element obtained by dividing the phase difference (equation (8)) by the frequency may be used. In addition, when using the feature-value vector which makes each value obtained by above-mentioned Formula (9) an element, a 1st clustering part performs clustering using Formula (29) (30), for example.

In each of the above-described embodiments, the method of generating a frequency domain separation signal using Equation (28) is exemplified. Equation (28) shows that when C (f, τ) = k, the frequency domain signal X _Q (f, τ) (corresponding to the reference sensor Q) of the corresponding time frequency slot (f, τ) is The separated signal Y _k (f, τ) is used. However, when C (f, τ) = k, a frequency domain signal corresponding to a sensor other than the reference sensor Q may be used as the frequency domain separation signal Y _k (f, τ). For example, when C (f, τ) = k in a certain time frequency slot (f, τ), the largest one of the frequency domain signals in that time frequency slot (f, τ) is separated signal Y _k (f, τ ). However, even in this case, the sensor corresponding to the frequency domain signal selected as the separated signal Y _k (f, τ) is the same in each time frequency slot (f, τ). That is, if the sensor corresponding to the frequency domain signal to be selected as the separation signal Y _k (f, τ) is determined in a certain time frequency slot (f, τ), the same sensor is supported in the other time frequency slot (f, τ). The frequency domain signal to be selected is selected as the separation signal Y _k (f, τ).

In addition, the various processes described above are not only executed in time series according to the description, but may be executed in parallel or individually according to the processing capability of the apparatus that executes the processes or as necessary. Needless to say, other modifications are possible without departing from the spirit of the present invention.
Further, the program describing the above-described processing contents can be recorded on a computer-readable recording medium. The computer-readable recording medium may be any medium such as a magnetic recording device, an optical disk, a magneto-optical recording medium, or a semiconductor memory. Specifically, for example, the magnetic recording device may be a hard disk device or a flexible Discs, magnetic tapes, etc. as optical disks, DVD (Digital Versatile Disc), DVD-RAM (Random Access Memory), CD-ROM (Compact Disc Read Only Memory), CD-R (Recordable) / RW (ReWritable), etc. As the magneto-optical recording medium, MO (Magneto-Optical disc) or the like can be used, and as the semiconductor memory, EEP-ROM (Electronically Erasable and Programmable-Read Only Memory) or the like can be used.

The program is distributed by selling, transferring, or lending a portable recording medium such as a DVD or CD-ROM in which the program is recorded. Furthermore, the program may be distributed by storing the program in a storage device of the server computer and transferring the program from the server computer to another computer via a network.
As another execution form of the program, the computer may directly read the program from a portable recording medium and execute processing according to the program, and the program is transferred from the server computer to the computer. Each time, the processing according to the received program may be executed sequentially. Also, the program is not transferred from the server computer to the computer, and the above-described processing is executed by a so-called ASP (Application Service Provider) type service that realizes the processing function only by the execution instruction and result acquisition. It is good. Note that the program in this embodiment includes information that is used for processing by an electronic computer and that conforms to the program (data that is not a direct command to the computer but has a property that defines the processing of the computer).

  In this embodiment, the present apparatus is configured by executing a predetermined program on a computer. However, at least a part of these processing contents may be realized by hardware.

  Industrial applications of the present invention include spatial aliasing, such as a video conference system in which microphones are arranged at intervals of several tens of centimeters, and a system that separates audio signals sampled at a high sampling frequency. A system used in an easy-to-occur environment can be exemplified. According to the present invention, signal separation can be correctly performed for all frequencies even in an environment where spatial aliasing is likely to occur.

FIG. 1 is a block diagram illustrating a hardware configuration of a signal separation device according to the first embodiment. FIG. 2 is an example of a block diagram of the signal separation device according to the first embodiment. FIG. 3 is a block diagram illustrating details of the mixed signal classifying unit in FIG. FIG. 4 is a flowchart for explaining the processing of the signal separation device according to the first embodiment. FIG. 5 is a flowchart for explaining details of the process in step S2 of FIG. FIG. 6 is a flowchart for explaining details of the process in step S3 of FIG. FIG. 7 is a flowchart for explaining details of the process in step S3 of FIG. FIG. 8 is a block diagram illustrating details of the mixed signal classification unit in the second embodiment. FIG. 9 is a flowchart for explaining processing of the signal separation device according to the second embodiment. FIG. 10 is a flowchart for explaining details of the process in step S105 shown in FIG. FIG. 11 is a block diagram illustrating details of the mixed signal classifying unit in the third embodiment. FIG. 12 is a flowchart for explaining processing of the signal separation device according to the third embodiment. FIG. 13A is a table showing the experimental condition A, and FIG. 13B is a diagram showing the experimental condition B.

Explanation of symbols

1 Signal separation device 130, 230, 330 Mixed signal classification unit

Claims (13)

A signal separation device that separates a mixed signal composed of a mixture of source signals emitted from a plurality of signal sources into a separated signal that is an estimate of the source signal,
A frequency domain converter that converts the mixed signals observed by a plurality of sensors into frequency domain signals, and
A normalization unit that normalizes the phase of the frequency domain signal and further generates a frequency normalized signal that excludes frequency-dependent components;
Clustering feature vectors for each time frequency using the frequency normalized signal or a value obtained by assigning the frequency normalized signal to a predetermined function as each element, and calculating a centroid for each cluster One clustering unit;
Using the centroid, a model parameter extraction unit that calculates model parameters of a frequency response model,
A frequency response model in which the model parameter is substituted or a frequency response model in which the model parameter optimized by the model parameter is substituted as a reference, and a frequency having a phase / norm normalized value of the frequency domain signal as each element. Clustering dependent phase / norm normalized vectors and generating cluster information corresponding to clusters to which each phase / norm normalized vector belongs;
Using the frequency domain signal and the cluster information, a separation signal generation unit that generates a frequency domain separation signal;
A signal separation device comprising: The signal separation device according to claim 1,
The first clustering unit includes:
Clustering the above feature vectors in a frequency band that includes frequencies where spatial aliasing cannot occur,
The second clustering unit includes
Clustering the phase-norm normalized vectors in a frequency band that includes frequencies where spatial aliasing can occur,
A signal separation device. The signal separation device according to claim 2,
The frequency band including the frequency where the spatial aliasing cannot occur is
A frequency band consisting only of frequencies where spatial aliasing cannot occur,
A signal separation device. The signal separation device according to claim 2 or 3,
The frequency band including the frequency at which the spatial aliasing can occur is
All frequency bands,
A signal separation device. The signal separation device according to any one of claims 2 to 4,
The second clustering unit includes
A model parameter optimization unit that optimizes the model parameter using the cluster information and the phase / norm normalization vector in a frequency band including a frequency at which spatial aliasing may occur;
A signal separation device. The signal separation device according to claim 5,
The model parameters above are
A parameter corresponding to a set of the sensor and a signal source corresponding to the cluster;
The model parameter optimization unit
The model parameter corresponding to the set of the sensor corresponding to each element of the phase / norm normalized vector and the signal source corresponding to the cluster to which the phase / norm normalized vector indicated by the cluster information belongs is substituted. The partial differential with respect to the above model parameter is performed on the cost function consisting of the sum of the distances between the frequency response model and each element of the phase / norm normalized vector, and a value proportional to the calculated partial differential value is obtained. Optimize the model parameter by subtracting from the model parameter,
A signal separation device. The signal separation device according to claim 6,
The second clustering unit includes
Until the predetermined end condition is satisfied, the process of generating the cluster information and the process of optimizing the model parameter are alternately executed,
The separated signal generator is
When the predetermined termination condition is satisfied, the latest cluster information is used to generate the separation signal.
A signal separation device. The signal separation device according to claim 2,
The first clustering unit includes:
Generating initial cluster information corresponding to each cluster to which the feature vector corresponding to a frequency band including a frequency in which spatial aliasing cannot occur;
The second clustering unit includes
Generating the cluster information corresponding to the clusters to which the phase and norm normalization vectors corresponding to frequency bands including frequencies where spatial aliasing may occur;
The separated signal generator is
Generating the separation signal using the initial cluster information generated by the first clustering unit and the cluster information generated by the second clustering unit;
A signal separation device. A signal separation device that separates a mixed signal composed of a mixture of source signals emitted from a plurality of signal sources into a separated signal that is an estimate of the source signal,
A frequency domain converter that converts the mixed signals observed by a plurality of sensors into frequency domain signals, and
A model parameter selection unit for selecting initial values of model parameters of the frequency response model;
Clustering frequency-dependent phase / norm normalization vectors with each element as the phase / norm normalization value of the above frequency domain signal based on the frequency response model into which model parameters are substituted, and each phase / norm normalization vector is A cluster determination unit that generates cluster information corresponding to the cluster to which the cluster belongs;
A model parameter optimization unit that optimizes the model parameter using the cluster information and the phase / norm normalization vector;
Until the predetermined termination condition is satisfied, a control unit that alternately executes the processing of the cluster determination unit and the model parameter optimization unit,
A separation signal generation unit that generates a separation signal in the frequency domain using the latest cluster information and the frequency domain signal at the time when the predetermined termination condition is satisfied;
A signal separation device comprising: A signal separation method for separating a mixed signal composed of a mixture of source signals emitted from a plurality of signal sources into a separated signal that is an estimation of the source signal,
A frequency domain conversion process for converting the mixed signals observed by a plurality of sensors into frequency domain signals,
Normalization process for generating a frequency normalized signal that normalizes the phase of the frequency domain signal and further eliminates frequency dependent components;
Clustering feature vectors for each time frequency using the frequency normalized signal or a value obtained by assigning the frequency normalized signal to a predetermined function as each element, and calculating a centroid for each cluster 1 clustering process,
Using the centroid, a model parameter calculation process for calculating a model parameter of a frequency response model,
A frequency response model in which the model parameter is substituted or a frequency response model in which the model parameter optimized by the model parameter is substituted as a reference, and a frequency having a phase / norm normalized value of the frequency domain signal as each element. Clustering dependent phase / norm normalized vectors and generating cluster information corresponding to clusters to which each phase / norm normalized vector belongs;
Using the frequency domain signal and the cluster information, a separation signal generation process for generating a frequency domain separation signal;
A signal separation method comprising: A signal separation method for separating a mixed signal composed of a mixture of source signals emitted from a plurality of signal sources into a separated signal that is an estimation of the source signal,
A frequency domain conversion process for converting the mixed signals observed by a plurality of sensors into frequency domain signals,
Model parameter selection process for selecting initial values of model parameters of the frequency response model,
Repeated alternately until a predetermined termination condition is satisfied,
(A) Clustering frequency-dependent phase / norm normalized vectors having the phase / norm normalized values of the frequency domain signal as elements, based on the frequency response model into which model parameters are substituted, and each phase / norm normal A clustering process for generating cluster information corresponding to the cluster to which the quantization vector belongs;
(B) a model parameter optimization process for optimizing the model parameter using the cluster information and the phase / norm normalization vector;
A separation signal generation process for generating a separation signal in the frequency domain using the latest cluster information and the frequency domain signal at the time after satisfying the predetermined termination condition;
A signal separation method comprising:   A signal separation program for causing a computer to function as the signal separation device according to claim 1.   A computer-readable recording medium storing the signal separation program according to claim 12.

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