JP5188319B2 - Signal analysis apparatus, signal analysis method, program, and recording medium - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To perform elaborate modeling of observation data and to enable modeling to exhibit individual characteristic amplitude spectral structures existing in the observation data. <P>SOLUTION: A signal analyzer 10 includes: a time-frequency decomposing part 110 for decomposing a time series signal into time-frequency components; a storage part 100 for storing the time-frequency components, a time series signal parameter and an error distribution specific gravity factor; an initial value generating part 120 which generates each initial value of the time series signal parameter and the error distribution specific gravity factor and stores the same in the storage part 100; an updating part 130, which updates the time series signal parameter and the error distribution specific gravity factor in the storage part 100; a determination part 140 for determining whether or not the time series signal parameter meets a predetermined standard; and a parameter output part 150 for outputting the time series signal parameter when it meets the predetermined standard. The updating part 130 again updates the time series signal parameter and the error distribution specific gravity factor when it does not meet the predetermined standard. <P>COPYRIGHT: (C)2010,JPO&amp;INPIT

Description

  The present invention relates to a signal analysis device, a signal analysis method, a program, and a recording medium. In particular, the present invention relates to a signal analysis apparatus, a signal analysis method, a program, and a recording medium related to sparse signal decomposition of time series signals.

A compact basis set that can closely approximate any observation data with a sparse linear combination of bases (most of the coupling coefficients are almost zero) (this basis set is called "sparse decomposition expression"). The sparse signal decomposition is a collective approach for constructing sparse data based on statistical and informational criteria. Sparse coding (Non-patent Document 1) and non-negative matrix factorization (NMF) (non-patent) Reference 2) is a typical example. Similar to multivariate analysis methods such as principal component analysis and independent component analysis, the objective of sparse signal decomposition is to learn that each base is a basic element component of observation data. The characteristic is that characteristic patterns mixed in observed data are expressed as individual bases due to the sparsity of the coupling coefficient. Due to this property, both sparse coding and NMF have recently been expected as methodologies that have the possibility of separating and extracting constituent sounds mixed in a monaural sound signal without prior knowledge (Non-Patent Documents 3 and 4).
BAOlshausen and DJField, “Emergence of Simple-cell Receptive Field Properties by Learning a Sparse Code for Natural Images,” Nature Vol. 381, pp. 607-609, 1996. DDLee and HSSeung, “Learning the Parts of Object by Non-negative Matrix Factorization,” Nature Vol. 401, pp. 788-791, 1999. P. Smaragdis, JCBrown, “Non-Negative Matrix Factorization for Music Transcription,” In Proc. 2003 IEEE Workshop on Applications of Signal of Processing to Audio and Acoustics (WASPAA2003), pp.177-180, 2003. SAAbdallah and MDPlumbley, “Unsupervised Analysis of Polyphonic Music Using Sparse Coding,” IEEE Transactions on Neural Networks, Vol. 17, No. 1, pp. 179-196, 2006. T. Blumensath and MEDavise, “Unsupervised Learning of Sparse and Shiftinvariant Decompositions of Polyphonic Music,” In Proc. 2004 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP2004), Vol. 5, pp. 497-500, 2004. T. Blumensath and MEDavise, “On Shift-Invariant Sparse Coding,” CGPuntonet, A. Prieto (Eds.), Independent Component Analysis and Blind Signal Separation: Proc. 5th International Conference on Independent Component Analysis and Signal Separation (ICA2004), Granada , Spain, Springer, Berlin, pp.1205-1212, LNCS 3195,2004 R. Mitchell Parry and Irfan Essa, “Phase-Aware Non-negative Spectrogram Factorization,” In Proc. 7th International Conference on Independent Component Analysis and Signal Separation (ICA2007), pp.536-543, 2007.

  The reason why NMF is particularly effective in applications such as acoustic feature extraction is that base decomposition is performed using the power spectrum as observation data (Non-patent Document 3). That is, in NMF, the point is that all similar power spectra can be expressed on the same basis. For this reason, real-world acoustic signals that are various and complex phenomena can be expressed by a compact basis set. it can. Since the power spectrum is information indicating what frequency component the signal is composed of, the NMF's idea that sounds with the same power spectrum are considered to have the same attribute is probably in terms of base redundancy. Is reasonable. In addition, the non-negative constraint on the basis and coupling coefficient provided when learning the coupling coefficient of the basis and linear combination from the observation data has the effect of inducing the basis set solution to a sparse decomposition expression naturally. Another feature is that there is a very efficient iterative learning algorithm called a multiplicative update algorithm (Non-patent Document 2). However, although NMF is effective in terms of roughly grasping the characteristics of the component sounds in the mixed sound, the power spectrum is strictly non-additive, so modeling of observation data by linear combination of power spectrum bases The NMF based on the above is essentially unsuitable for sound source separation, and it is not always clear how accurately each base can express the power spectrum of mixed sound.

  On the other hand, the sparse coding approach (Non-Patent Document 4) that models an observation signal by linear combination of time domain signal bases is based on modeling that is more precise than NMF in that it considers an amount that is additive to be a base. The difficulty is that the redundancy between bases is large. That is, unlike NMF that can be regarded as a sound having the same attribute if the power spectrum is the same even if the waveforms are different, different bases are required according to subtle differences in the waveforms. On the other hand, an approach called shift invariant sparse coding (Non-Patent Documents 5 and 6) in which waveform groups having a time shift relationship can be regarded as sounds having the same attribute has been proposed. Is a small subset of all the waveforms that have the same shape as the power spectrum of the waveform, so the decomposition representation is also considered to be more redundant than that of NMF.

  In addition, for the purpose of correcting the additivity problem of NMF, a method of correcting the estimation result of NMF by considering the phase as a random variable with uniform distribution has been studied (Non-Patent Document 7). The handling method is ad hoc and has not yet solved the shortcomings of NMF that assumes the additivity of the power spectrum in an essential sense.

  The present invention breaks away from the concept of “modeling by linear combination of bases” common in conventional sparse signal decomposition methods such as NMF and sparse coding, while conforming to modeling in a multispectral (additive) domain. This realizes a new type of sparse signal decomposition method that has the property of expressing individual characteristic power spectrum patterns mixed in the observation signal as in NMF. The method of the present invention essentially demonstrates the advantages of sparse coding in that the basic modeling is elaborate while maintaining the effect as sparse signal decomposition, and the ability to express individual characteristic power spectrum patterns and efficiency. NMF has the advantage of being able to derive a typical iterative learning algorithm.

In order to solve the above problem, a signal analysis device according to an aspect of the present invention includes a time-series signal parameter including an amplitude spectrum base parameter, an activity coefficient parameter, and a phase spectrum parameter, a time-frequency component, an error distribution specific gravity coefficient, and A storage unit for storing the time frequency component allocation amount , a time frequency signal decomposition unit that decomposes the time series signal into time frequency components, and stores the initial values of the time series signal parameter and the error distribution specific gravity coefficient An initial value generation unit that generates and stores in the storage unit, and a time-series signal stored in the storage unit based on the time-frequency component, the time-series signal parameter, and the error distribution specific gravity coefficient stored in the storage unit Update unit for updating parameters and error distribution specific gravity coefficient, and time-series signal parameters stored in storage unit are predetermined. A determination unit that determines whether or not a criterion is satisfied, and a parameter output unit that outputs a time-series signal parameter when the determination unit determines that the time-series signal parameter satisfies a predetermined criterion; The update unit calculates a time frequency component distribution amount from a time frequency component, a time series signal parameter, and an error distribution specific gravity coefficient stored in the storage unit, based on Equation 63 described later, Amplitude spectrum base for calculating a new amplitude spectrum base parameter based on Equation 64 described later from the activity coefficient parameter stored in the storage unit and the time frequency component distribution amount calculated by the time frequency component distribution amount calculation unit. Parameter calculation unit, amplitude spectrum basis parameter and activity function stored in storage unit An activity coefficient parameter calculation unit that calculates a new activity coefficient parameter based on an equation 66 described later from the parameter and the time frequency component distribution amount calculated by the time frequency component distribution amount calculation unit; and time frequency component distribution amount calculation A phase spectrum parameter calculation unit that calculates a new phase spectrum parameter from the time frequency component allocation amount calculated by the unit based on Equation 67 described later, and the time frequency component and time series signal parameter stored in the storage unit, An error distribution specific gravity coefficient calculation unit that calculates a new error distribution specific gravity coefficient from the time frequency component distribution amount calculated by the time frequency component distribution amount calculation unit based on Equation 68 described later, and an amplitude spectrum base parameter calculation unit , Activity coefficient parameter calculator, phase spectrum A parameter calculation unit, and a reflection unit that reflects the new value calculated by the error distribution specific gravity coefficient calculation unit in the storage unit, and the update unit has a time series signal parameter that satisfies a predetermined criterion by the determination unit If it is determined that no time-series signal parameters, characterized in that updating the error distribution density coefficient and temporal frequency components distribution amount again.

In the signal analysis device, the determination unit determines whether or not the time-series signal parameter satisfies a predetermined criterion based on whether or not the rate of change of the objective function value calculated based on Equation 70 described later is equal to or less than a predetermined value. It may be what determines .

In order to solve the above problem, a signal analysis method according to one aspect of the present invention includes a time-frequency decomposition step of decomposing a time-series signal into time-frequency components and storing it in a storage unit, an amplitude spectrum base parameter, an activity An initial value generation step for generating time series signal parameters including coefficient parameters and phase spectrum parameters, and initial values of error distribution specific gravity coefficient and time frequency component allocation amount , and storing them in a storage unit; An update step for updating the time series signal parameter and the error distribution specific gravity coefficient stored in the storage unit based on the time frequency component, the time series signal parameter and the error distribution specific gravity coefficient stored in the storage unit A determination step for determining whether or not the time series signal parameter satisfies a predetermined criterion; When the time series signal parameters is determined to meet the predetermined criteria by flops, and a parameter output step of outputting the time-series signal parameters, updating step, temporal frequency components stored in the storage unit, A time frequency component distribution amount calculating step for calculating a time frequency component distribution amount from a time series signal parameter and an error distribution specific gravity coefficient based on Equation 63 described later, an activity coefficient parameter stored in the storage unit, and a time frequency component An amplitude spectrum base parameter calculating step for calculating a new amplitude spectrum base parameter based on the expression 64 described later from the temporal frequency component distribution amount calculated by the distribution amount calculating step, and an amplitude spectrum base stored in the storage unit Parameters and activity factor parameters and hours Calculated by the activity coefficient parameter calculation step for calculating a new activity coefficient parameter based on Equation 66 described later and the time frequency component distribution amount calculation step from the time frequency component distribution amount calculated by the frequency component distribution amount calculation step. A phase spectrum parameter calculation step for calculating a new phase spectrum parameter from the time frequency component allocation amount based on Equation 67 described later, a time frequency component and a time-series signal parameter stored in the storage unit, and a time frequency component From the temporal frequency component distribution amount calculated in the distribution amount calculation step, an error distribution specific gravity coefficient calculation step for calculating a new error distribution specific gravity coefficient based on Equation 68 described later, an amplitude spectrum base parameter calculation step, an activity coefficient parameter And a reflection step for reflecting the new value calculated by the error distribution specific gravity coefficient calculation step in the storage unit. If it is determined not to satisfy the predetermined criterion, the time series signal parameters, characterized in that updating the error distribution density coefficient and temporal frequency components distribution amount again.

In the signal analysis method, the determination step determines whether or not the time-series signal parameter satisfies a predetermined criterion based on whether or not the rate of change of the objective function value calculated based on Equation 70 described later is equal to or less than a predetermined value. It may be what determines .

In order to solve the above problem, one embodiment of the present invention is a program for causing a computer to execute each step of the signal analysis method.

In order to solve the above problem, one embodiment of the present invention is a computer-readable recording medium on which the above program is recorded.

  The present invention relates to estimation of model parameters when modeling an observation signal. A feature of the present invention is that an acoustic signal is modeled with a mixture ratio and phase spectrum of each power spectrum freely time-varying with a finite type of power (amplitude) spectrum signal as a base, and the model parameters are estimated efficiently. Is to provide a simple learning method. Therefore, a special effect (similar power spectrum structure is expressed as one basis) that has been desired only in the conventional linear combination modeling (NMF) in which the amount of non-additivity does not hold is specified. This can be realized by modeling in a region where In addition, by modeling in a region where the additivity holds, observation data can be modeled precisely.

  That is, according to the present invention, observation data can be modeled precisely, and modeling that expresses individual characteristic amplitude spectrum structures (or power spectrum structures) existing in the observation data can be performed. It becomes possible. Further, according to the present invention, it is possible to provide an efficient learning method of parameters for modeling from observation data.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

A. principle
First, the principle of the present invention will be described. In the following description, the symbol ≡ means that the expression on the left side is defined by the expression on the right side. The symbol ← indicates numerical substitution. Characters with ￣ at the top of the characters in the formula are indicated with ￣ before the characters in the sentence.

A-1. Acoustic signal model _{Let Fx, t} be the time-frequency component of an arbitrary acoustic signal. However, x corresponds to a frequency or logarithmic frequency, and t is time. Here, F _{x, t} is decomposed into a sum of elements c _{x, k, t} as shown in the following equation (1).

Further, the absolute value of the element c _{x, k, t} is decomposed into a product of H _{x, k} and U _{k, t} as shown in the following equation (2).

  Also, to remove the arbitrary scale of decomposition,

Is assumed. H _{x, k} is an amplitude spectrum pattern, and is determined globally regardless of time. U _{k, t} is a coefficient of the k-th amplitude spectrum and has a degree of freedom at each time. φ _{x, k, t} is the k-th phase spectrum and has a degree of freedom at each time. In other words, the real-world acoustic signal is composed of at most K kinds of amplitude spectrum signals, and it is considered that each coefficient and phase spectrum are realized by time-varying freely. Under this model, the amplitude spectrum H _{x, k} and the coefficient U _{k, t} are set so that the coefficient U _{k, t} is sparse as much as possible and the modeling error with the observed signal is minimized as in the sparse coding concept. By learning the sparse signal decomposition of the complex spectral region having such a property that a power (amplitude) spectral structure similar to NMF is expressed as one basis can be realized. Based on the above, a sparse signal decomposition expression like the following equation (4) is proposed.

By the way, in NMF, there are K types of amplitude spectrum patterns H _{x, k that} are determined globally regardless of time, and each coefficient U _{k, t} is assumed to be freely time-varying under non-negative constraints. This is equivalent to modeling a spectrogram. That is,

Therefore, if F≡ (F _{x, t} ) _{X × T} , H≡ (H _{x, k} ) _{X × K} , U≡ (U _{k, t} ) _{K × T} , the symbol ≡ It means that it is defined by the expression on the right side.

Can be written in the form of a matrix. On the other hand, since the model of equation (4) cannot represent a matrix similar to NMF due to the presence of the three-dimensional array e ^{jφx, k, t} , it is in the form of a matrix product such as NMF or sparse coding. It is different in nature from the conventional sparse signal decomposition model represented. Hereinafter, a method for estimating the parameters H _{k, x} , U _{k, t} , φ _{x, k, t} will be described.

A-2. Sparse signal decomposition algorithm Y≡ (Y _{x, t} ) _{X × T} , H≡ (H _{x, k} ) _{X × K} , U≡ (U _{k, t} ) _{K × T} , φ≡ (φ _{x, k, t} ) _{X x K x T,} and F _{x, t}

  Put it. However,

It is. The observation time frequency component Y _{x, t} is

  I will normalize. Now, here

Assuming that the modeling error ε is white noise following a complex Gaussian distribution, the likelihood P (Y | H, U, φ, σ ² ) of H, Y, φ is given by the following equation (11).

H, U, φ, and σ ² are independent.

  Furthermore, generalized normal distribution with U prior probability representing sparsity

Assuming that P (H), P (φ), and P (σ ² ) are uniformly distributed, the posterior establishment P (H, U, φ, σ ² | Y) is

Can be written. From equation (14), the problem of maximizing the post-establishment P (H, U, φ, σ ² | Y) with respect to H, U, φ is

  Is equivalent to maximizing with respect to H, U, and φ.

You can ask for. Assuming that σ ² and b are predetermined constants, the above optimization problems can be summarized as follows.

  An algorithm for solving this optimization problem is derived by the auxiliary function method. As preparation, first, the principle of the auxiliary function method is shown. For the objective function G (z)

If G ⁺ (z, ￣z) is defined as an auxiliary function of G (z) and ￣z is defined as an auxiliary variable, the following theorem holds.

Theorem (auxiliary function method): When the step of minimizing the auxiliary function G ⁺ (z, ￣z) with respect to ￣z and the step of minimizing with respect to z are repeated, the objective function value contracts monotonously.

Proof: Let ￣z _{t + 1} = argmin _￣z G ⁺ (z _t ,） z) and let z _{t + 1} = argmin _z G ⁺ (z, ￣z _{t + 1} ). However, t represents the number of steps of iterative calculation. _{z = z t, ¯z = ¯z} t from _z = z _{t + 1,} when it is updated _¯z = ¯z _{t + 1,} indicating that G (z) does not increase. Obviously G (z _t ) = G ⁺ (z _t , ￣z _{t + 1} ), and from z _{t + 1} argmin _z G ⁺ (z, ￣z _{t + 1} ), G ⁺ (z _t , ￣z _{t + 1} ) ≧ G ⁺ (Z _{t + 1} , ￣z _{t + 1} ). Furthermore, since G ⁺ (z _{t + 1} , ￣z _{t + 1} ) ≧ G (z _{t + 1} ) by the definition of the auxiliary function, G (z _t ) ≧ G (z _{t + 1} ) in the end.

  In order to apply the above objective function, the auxiliary function of the objective function f (H, U, φ) given by Expression (17) is derived using the following two inequalities.

  However, Formula (20) is

It is established under the conditions of Β _{x, k, t} is an arbitrary constant satisfying 0 <β _{x, k, t} <1, Σ _k β _{x, k, t} = 1. ￣Y≡ (￣Y _{x, k, t} ) _{X × K × T} , ￣U≡ (￣U _{k, t} ) _{K × T} , from Equation (20) and Equation (21),

  given that,

  Holds. Furthermore,

Since f (H, U, φ) = f ⁺ (H, U, φ, ￣ Y, ￣ U), f ⁺ (H, U, φ, ￣ Y, ￣ U) is an auxiliary function definition. Meet. Using the above results, update formulas for H, U, and φ are obtained. As for H _{x, k} , f ⁺ (H, U, φ, ￣ Y, ￣ U) must be minimized under the condition of equation (18). H _{x, k} that minimizes ⁺ (H, U, φ, ￣ Y, ￣ U) is obtained analytically, and is normalized so as to satisfy Equation (18).

  Is set to 0,

  Get. However,

  It is. here,

Therefore, it can be seen that Expression (29) is an update that minimizes f ⁺ (H, U, φ, ￣ Y, ￣ U). This is normalized to satisfy equation (18) and approximated as H _{x, k} that minimizes f ⁺ (H, U, φ, ￣ Y, ￣ U) under the condition of equation (18). Consider. Next, for U _{k, t} ,

  And set to 0 and solve

  Is given as follows. here,

Thus, it can be seen that the equation (34) is an update that minimizes f ⁺ (H, U, φ, ￣ Y, ￣ U).

Next, an update formula for φ _{x, k, t} is derived. First, if f ⁺ (H, U, φ, ￣ Y, ￣ U) and terms that do not depend on φ _{x, k, t} are put together as d, then f ⁺ (H, U, φ, ￣ Y, ￣ U)

  Can be written. However,

It is. COS (φ _{x, k, t} −C _{x, k, t} ) = COSφ _{x, k, t} COSC _{x, k, t} + SINφ _{x, k, t} SINC _{x, k, t} = 1, that is,

Then f ⁺ (H, U, φ, ￣ Y, ￣ U) is minimal with respect to φ _{x, k, t} . Therefore, the update formula for e ^{jφx, k, t} is

Given in. This update equation easily indicates non-negativeness of the updated values of H _{x, k} and U _{k, t} . Substituting equation (41) into equations (29) and (34),

If the initial values of H _{x, k} , U _{k, t} are positive, it can be seen that H _{x, k} , U _{k, t} is always updated to a non-negative value.

  The algorithm derived above is formally equivalent to the NMF multiplicative update algorithm derived by Lee et al. Under certain conditions. First, instead of iteratively updating the phase spectrum A according to equation (40), here, when A is initialized,

  Let us consider a case where only H and U are repetitively updated with the value fixed thereafter. This

  Therefore, when substituting this into equation (27), ￣Y becomes

  An update like this will be made. Substituting this and equation (44) into equation (32),

It becomes. By the way, β _{x, k, t} is a constant that can be arbitrarily determined within the range satisfying β _{x, k, t} > 0 and Σ _k β _{x, k, t} = 1. Does not affect the convergence of the algorithm. Therefore, _let β _{x, k, t} be

_Then, the updateability of H _{x, k} is

Which is consistent with the multiplicative update formula under the Frobenius norm criterion derived by Lee et al. The same can be said for U 1. From the above consideration, the invention method is
(1) To be as efficient and stable as NMF,
(2) It is effective to update β _{x, k, t} together with H, U, and A as shown in equation (48),
(3) When performing (2), if A is fixed to Equation (44), the algorithm is equivalent to NMF. Therefore, if H and U are estimated by NMF at the initial stage of iterative calculation, the local solution problem can be solved. It is expected that it can be avoided very effectively.

From the above, the algorithm can be summarized as follows.
1. Initial setting (a) H ′ and U ′ are initialized by random number generation, and φ ′ and β ′ are initially set by the following equations (50) and (51).

(B) Using Y and H ′, U ′, φ ′, and β ′ set in the previous stage, initial setting of ￣Y ′ is performed by the following equation (52).

2. Update of H (a) ￣H is calculated by the following equation (53) using U ′, ￣Y ′, φ ′, and β ′ obtained in the previous stage.

(B) Normalize ￣H by the following equation (54) and substitute it into H.

3. Update U Update U using the following formula (55) using H = H ′, φ ′, ￣Y ′, and β ′ obtained in the previous stage.

4. Update of φ Update U by the following formula (56) using ￣Y ′ obtained in the previous stage.

5. Update of β β is updated by the following equation (57) using H and U obtained in the previous stage.

6. Update ￣Y ￣Y is updated by the following equation (58) using Y, H, U, φ, and β obtained in the previous stage.

7. Return to 2 as H ′ ← H, U ′ ← U, φ ′ ← φ, β ′ ← β, ￣Y ′ ← ￣Y.
8. After convergence, H, U, and φ are output.

B. Signal Analysis Device According to Embodiment of the Present Invention Based on the above, the signal analysis device 10 according to the embodiment of the present invention will be described. FIG. 1 is a functional block diagram of a signal analysis apparatus 10 according to an embodiment of the present invention. The signal analysis apparatus 10 analyzes a time-series signal and includes a storage unit 100, a time frequency decomposition unit 110, an initial value generation unit 120, an update unit 130, a determination unit 140, and a parameter output unit 150, as shown in FIG. . Further, the update unit 130 includes a time frequency component distribution amount calculation unit 131, an amplitude spectrum base parameter calculation unit 132, an activity coefficient parameter calculation unit 133, a phase spectrum parameter calculation unit 134, an error distribution specific gravity coefficient calculation unit 135, and a reflection unit 136. It is configured.

  The storage unit 100 is a storage area for storing a time-series signal parameter including an amplitude spectrum base parameter, an activity coefficient parameter, and a phase spectrum parameter, a time frequency component, and an error distribution specific gravity coefficient. The storage unit 100 also stores a time frequency component distribution amount.

  The time-frequency decomposition unit 110 decomposes the time-series signal into time-frequency components and stores (outputs) them in the storage unit 100.

More specifically, the time-frequency decomposition unit 110 receives a time-series signal and outputs a time-frequency component Y _{x, t} . x = 1,..., X, t = 1,..., T are indices corresponding to frequency and time, respectively. The time-frequency component Y _{x, t} is calculated by time-frequency decomposition means using a filter bank output of a plurality of channels, such as short-time Fourier transform and wavelet transform. Also, the time frequency component Y _{x, t} is

  Standardize so that

  The initial value generation unit 120 generates initial values of the time series signal parameter and the error distribution specific gravity coefficient, and stores (outputs) them in the storage unit 100.

More specifically, the initial value generation unit 120 includes an amplitude spectrum base parameter H≡ (H _{x, k} ) _{X × K} , an activity coefficient parameter U≡ (U _{k, t} ) _{K × T} , a phase spectrum parameter φ≡ (φ _{x, k, t} ) _{X × K × T} , error distribution specific gravity coefficient β≡ (β _{x, k, t} ) Set the initial value of _{X × K × T} , and set the respective set values to H ′, U ′, φ Let ', β'.

In addition, the selectable range of each initial value is the following equation (60) for the amplitude spectrum base parameter H≡ (H _{x, k} ) _{X × K} and the activity coefficient parameter U≡ (U _{k, t} ) _{K × T.} And The phase spectrum parameter φ≡ (φ _{x, k, t} ) _{X × K × T} is expressed by the following equation (61), and the error distribution specific gravity coefficient β is expressed by the following equation (62).

  The time frequency component distribution amount calculation unit 131 calculates the time frequency component distribution amount from the time frequency component, the time series signal parameter, and the error distribution specific gravity coefficient stored in the storage unit 100.

More specifically, the time frequency component allocation amount calculation unit 131 uses the H ′, U ′, φ ′, β ′ obtained in the previous stage and the time frequency component Y _{x, t} to calculate the time according to the following equation (63). Frequency component allocation amount ￣Y′≡ (￣Y ′ _{x, k, t} ) _{X × K × T} is calculated.

  Also, the time frequency component distribution amount calculation unit 131 recalculates a new time frequency component distribution amount when the determination unit 140 determines that the time series signal parameter does not satisfy a predetermined criterion.

  The amplitude spectrum base parameter calculation unit 132 calculates a new amplitude spectrum base parameter from the activity coefficient parameter stored in the storage unit 100 and the time frequency component allocation amount calculated by the time frequency component allocation amount calculation unit 131. To do.

More specifically, the amplitude spectrum basis parameter calculation unit 132 uses the U ′, φ ′, and ￣Y ′ obtained in the previous stage to calculate the amplitude spectrum basis parameter ￣H≡ (H _{x, k} ) Calculate _{X × K.}

However, (•) ^* represents the complex conjugate of (•), and Re [(•)] represents the real part of (•). Next, ￣H is normalized by the following equation (65) and substituted for H.

  The amplitude spectrum base parameter calculation unit 132 calculates a new amplitude spectrum base parameter again when the determination unit 140 determines that the time-series signal parameter does not satisfy a predetermined criterion.

  The activity coefficient parameter calculation unit 133 calculates a new activity coefficient from the amplitude spectrum base parameter and the activity coefficient parameter stored in the storage unit 100 and the time frequency component distribution amount calculated by the time frequency component distribution amount calculation unit 131. Calculate the parameters.

More specifically, the activity coefficient parameter calculation unit 133 uses the H ′, U ′, φ ′, ￣Y ′, and β ′ obtained in the previous stage and the activity coefficient parameter U≡ (U _{k, t} ) _{K × T} is calculated.

  The activity coefficient parameter calculation unit 133 calculates a new activity coefficient parameter again when the determination unit 140 determines that the time series signal parameter does not satisfy a predetermined criterion.

  The phase spectrum parameter calculation unit 134 calculates a new phase spectrum parameter from the time frequency component distribution amount calculated by the time frequency component distribution amount calculation unit 131.

More specifically, the phase spectrum parameter calculation unit 134 calculates the phase spectrum parameter φ≡ (φ _{x, k, t} ) _{X × K × T} by the following equation (67) using ￣Y ′ obtained in the previous stage. To do. However, arg (·) represents the declination of (·).

  The phase spectrum parameter calculation unit 134 calculates a new phase spectrum parameter again when the determination unit 140 determines that the time-series signal parameter does not satisfy a predetermined criterion.

  The error distribution specific gravity coefficient calculation unit 135 calculates a new error from the time frequency component and time series signal parameter stored in the storage unit 100 and the time frequency component distribution amount calculated by the time frequency component distribution amount calculation unit 131. The distribution specific gravity coefficient is calculated.

  If the error distribution specific gravity coefficient is not constant and is updated for each iteration, the update rule is

  like,

  You may decide arbitrarily within the limits which satisfy | fill.

  The error distribution specific gravity coefficient calculation unit 135 calculates a new error distribution specific gravity coefficient again when the determination unit 140 determines that the time-series signal parameter does not satisfy a predetermined criterion.

  The reflection unit 136 causes the storage unit 100 to reflect the new values calculated by the amplitude spectrum base parameter calculation unit 132, the activity coefficient parameter calculation unit 133, the phase spectrum parameter calculation unit 134, and the error distribution specific gravity coefficient calculation unit 135. . That is, the reflecting unit 136 substitutes H, U, φ, and β obtained in the previous stage into H ′, U ′, φ ′, and β ′.

  In addition, when the determination unit 140 determines that the time-series signal parameter does not satisfy a predetermined criterion, the reflection unit 136 reflects the new value calculated again in the storage unit 100.

  The determination unit 140 determines whether or not the time-series signal parameter stored in the storage unit 100 satisfies a predetermined criterion.

  More specifically, the determination unit 140 determines whether or not the iterative calculation has satisfied a predetermined number of times, or whether or not the change rate of the parameter update in the iterative calculation is equal to or less than a predetermined value, or changes in the objective function value. It is determined whether the rate has become a predetermined value or less. The objective function is calculated by the following equation (70).

  The parameter output unit 150 outputs the time series signal parameter when the judgment unit 140 determines that the time series signal parameter satisfies a predetermined criterion.

  Subsequently, the operation of the signal analyzing apparatus 10 will be described. FIG. 2 is a flowchart showing an example of the operation of the signal analyzing apparatus 10 according to the embodiment of the present invention.

  The time-frequency decomposition unit 110 decomposes the time-series signal into time-frequency components, and stores (outputs) the decomposed time-frequency components in the storage unit 100 (step S100). The initial value generation unit 120 generates initial values of the time series signal parameter and the error distribution specific gravity coefficient, and stores (outputs) the generated initial values in the storage unit 100 (step S110).

  The time frequency component distribution amount calculation unit 131 calculates the time frequency component distribution amount from the time frequency component, the time series signal parameter, and the error distribution specific gravity coefficient stored in the storage unit 100 (step S120).

  The amplitude spectrum base parameter calculation unit 132 calculates a new amplitude spectrum base parameter from the activity coefficient parameter stored in the storage unit 100 and the time frequency component allocation amount calculated by the time frequency component allocation amount calculation unit 131. (Step S130). The activity coefficient parameter calculation unit 133 calculates a new activity coefficient from the amplitude spectrum base parameter and the activity coefficient parameter stored in the storage unit 100 and the time frequency component distribution amount calculated by the time frequency component distribution amount calculation unit 131. A parameter is calculated (step S140). The phase spectrum parameter calculation unit 134 calculates a new phase spectrum parameter from the time frequency component distribution amount calculated by the time frequency component distribution amount calculation unit 131 (step S150). The error distribution specific gravity coefficient calculation unit 135 calculates a new error from the time frequency component and time series signal parameter stored in the storage unit 100 and the time frequency component distribution amount calculated by the time frequency component distribution amount calculation unit 131. A distribution specific gravity coefficient is calculated (step S160). Note that the order of each step from step S130 to step S160 may be changed.

  The reflection unit 136 causes the storage unit 100 to reflect the new values calculated by the amplitude spectrum base parameter calculation unit 132, the activity coefficient parameter calculation unit 133, the phase spectrum parameter calculation unit 134, and the error distribution specific gravity coefficient calculation unit 135. (Step S170).

  The determination unit 140 determines whether or not the time series signal parameter stored in the storage unit 100 satisfies a predetermined criterion (step S180).

  When the determination unit 140 determines that the time series signal parameter stored in the storage unit 100 satisfies a predetermined criterion (step S180: Yes), the parameter output unit 150 sets the time series signal parameter. Output (step S190). Then, this flowchart ends.

  On the other hand, when the determination unit 140 determines that the time-series signal parameter stored in the storage unit 100 does not satisfy the predetermined criterion (step S180: No), the process returns to step S120. That is, steps S120 to S180 are repeatedly executed until the time-series signal parameters stored in the storage unit 100 satisfy a predetermined criterion (until they converge to the predetermined criterion).

  The flowchart shown in FIG. 2 is also expressed by the flowchart shown in FIG. FIG. 3 is a flowchart showing an example of the operation of the signal analyzing apparatus 10 according to the embodiment of the present invention.

  Frequency analysis process: A time-frequency signal is output by inputting a time-series signal (step S200). This corresponds to step S100 in FIG.

  Initial time-series signal parameter generation process: Generates time-series signal parameters including amplitude spectrum base parameters, activity coefficient parameters, and phase spectrum parameters, and initial values of error distribution specific gravity coefficients (step S210). This corresponds to step S110 in FIG.

  Time frequency component allocation amount output process: The time frequency component allocation amount is output using the time frequency component output in the frequency analysis process, the time series signal parameter obtained in the previous stage, and the error distribution specific gravity coefficient (step S220). This corresponds to step S120 in FIG.

  Amplitude spectrum base parameter update value calculation process: The update value of the amplitude spectrum base parameter is calculated using the activity coefficient parameter obtained in the previous stage and the time frequency component allocation amount as inputs (step S230). This corresponds to step S130 in FIG.

  Activity coefficient parameter update value calculation process: The activity coefficient update value is calculated by inputting the amplitude spectrum base parameter, the activity coefficient parameter, and the time-frequency component allocation amount obtained in the previous stage (step S240). This corresponds to step S140 in FIG.

  Phase spectrum parameter update value calculation process: The update value of the phase spectrum parameter is calculated using the time frequency component allocation amount obtained in the previous stage (step S250). This corresponds to step S150 in FIG.

  Error distribution specific gravity coefficient update value calculation process: The update value of the error distribution specific gravity coefficient is input using the observation time frequency component output in the frequency analysis process, the time series signal parameter obtained in the previous stage, and the time frequency component distribution amount as inputs. Calculate (step S260). This corresponds to step S160 in FIG.

  Parameter update process: The value calculated in the amplitude spectrum base parameter update value calculation process, activity coefficient parameter update value calculation process, and phase spectrum parameter update value calculation process is substituted into the time series signal parameter, and in the error distribution specific gravity coefficient update calculation process The calculated value is substituted into the error distribution specific gravity coefficient (step S270). This corresponds to step S170 in FIG.

  Convergence determination process: It is determined whether or not the time series signal parameter satisfies a predetermined criterion. If not, the time frequency component allocation amount update process, the amplitude spectrum base parameter update value calculation process, and the activity coefficient parameter An update value calculation process, a phase spectrum parameter update value calculation process, an error distribution specific gravity coefficient update value calculation process, and a parameter update process are performed (step S280). This corresponds to step S180 (No) in FIG.

  Time-series parameter output process: A time-series signal parameter determined to satisfy a predetermined criterion in the convergence determination process is output (step S290). This corresponds to step S180 (Yes) and step S190 in FIG.

  As described above, according to the present invention, observation data can be modeled precisely, and modeling that expresses individual characteristic amplitude spectrum structures (or power spectrum structures) existing in the observation data can be performed. It becomes possible. In addition, it is possible to obtain an effect that it is possible to provide an efficient learning method of parameters for modeling from observation data.

  2 is recorded on a computer-readable recording medium, and the program recorded on the recording medium is read into a computer system and executed, thereby executing a signal analyzing apparatus. 10 may be performed. Here, the “computer system” may include an OS and hardware such as peripheral devices. Further, the “computer system” includes a homepage providing environment (or display environment) if a WWW system is used. The “computer-readable recording medium” means a flexible disk, a magneto-optical disk, a ROM, a writable nonvolatile memory such as a flash memory, a portable medium such as a CD-ROM, a hard disk built in a computer system, etc. This is a storage device.

  Further, the “computer-readable recording medium” means a volatile memory (for example, DRAM (Dynamic DRAM) in a computer system that becomes a server or a client when a program is transmitted through a network such as the Internet or a communication line such as a telephone line. Random Access Memory)), etc., which hold programs for a certain period of time. The program may be transmitted from a computer system storing the program in a storage device or the like to another computer system via a transmission medium or by a transmission wave in the transmission medium. Here, the “transmission medium” for transmitting the program refers to a medium having a function of transmitting information, such as a network (communication network) such as the Internet or a communication line (communication line) such as a telephone line. The program may be for realizing a part of the functions described above. Furthermore, what can implement | achieve the function mentioned above in combination with the program already recorded on the computer system, and what is called a difference file (difference program) may be sufficient.

  The embodiment of the present invention has been described in detail with reference to the drawings. However, the specific configuration is not limited to this embodiment, and includes designs and the like that do not depart from the gist of the present invention.

1 is a functional block diagram of a signal analysis device 10 according to an embodiment of the present invention. It is a flowchart which shows an example of operation | movement of the signal analyzer 10 which concerns on embodiment of this invention. It is a flowchart which shows an example of operation | movement of the signal analyzer 10 which concerns on embodiment of this invention.

Explanation of symbols

DESCRIPTION OF SYMBOLS 10 Signal analysis apparatus 100 Storage part 110 Time frequency decomposition part 120 Initial value generation part 130 Update part 131 Time frequency component allocation amount calculation part 132 Amplitude spectrum base parameter calculation part 133 Activity coefficient parameter calculation part 134 Phase spectrum parameter calculation part 135 Error distribution Specific gravity coefficient calculation unit 136 reflection unit 140 determination unit 150 parameter output unit

Claims (6)

A signal analyzer for analyzing time series signals,
A storage unit for storing a time series signal parameter composed of an amplitude spectrum base parameter, an activity coefficient parameter and a phase spectrum parameter, a time frequency component, and an error distribution specific gravity coefficient and a time frequency component distribution amount ;
A time-frequency decomposition unit that decomposes a time-series signal into time-frequency components and stores the time-series signal in the storage unit;
Generating initial values of the time-series signal parameters and the error distribution specific gravity coefficient, and storing the initial values in the storage unit;
Based on the time frequency component, the time series signal parameter, and the error distribution specific gravity coefficient stored in the storage unit, the time series signal parameter and the error distribution specific gravity coefficient stored in the storage unit are An update section to update;
A determination unit that determines whether or not the time-series signal parameter stored in the storage unit satisfies a predetermined criterion;
A parameter output unit that outputs the time-series signal parameter when the determination unit determines that the time-series signal parameter satisfies a predetermined criterion;
The update unit
A time frequency component distribution amount calculation unit that calculates a time frequency component distribution amount from the time frequency component stored in the storage unit, the time series signal parameter, and the error distribution specific gravity coefficient based on the following equation 1.

Based on the activity coefficient parameter stored in the storage unit and the temporal frequency component allocation amount calculated by the temporal frequency component allocation amount calculation unit, a new amplitude spectrum base parameter is calculated based on the following Equation 2. An amplitude spectrum basis parameter calculation unit;

From the amplitude spectrum base parameter and the activity coefficient parameter stored in the storage unit and the time frequency component allocation amount calculated by the time frequency component allocation amount calculation unit, a new activity coefficient parameter is expressed by the following equation (3). An activity coefficient parameter calculation unit to calculate based on

A phase spectrum parameter calculation unit that calculates a new phase spectrum parameter from the time frequency component distribution amount calculated by the time frequency component distribution amount calculation unit based on the following Equation 4.

From the time frequency component and the time-series signal parameter stored in the storage unit and the time frequency component distribution amount calculated by the time frequency component distribution amount calculation unit, a new error distribution specific gravity coefficient is expressed by the following equation: An error distribution specific gravity coefficient calculation unit to calculate based on 5,

A reflection unit for reflecting the new value calculated by the amplitude spectrum base parameter calculation unit, the activity coefficient parameter calculation unit, the phase spectrum parameter calculation unit, and the error distribution specific gravity coefficient calculation unit to the storage unit;
Have
The update unit
When the determination unit determines that the time series signal parameter does not satisfy a predetermined criterion, the time series signal parameter, the error distribution specific gravity coefficient, and the time frequency component distribution amount are updated again . A signal analyzer characterized by being a thing. The determination unit determines whether or not the time series signal parameter satisfies a predetermined criterion based on whether or not the rate of change of the objective function value calculated based on the following equation 6 is equal to or less than a predetermined value. is there

The signal analysis apparatus according to claim 1. A signal analysis method for analyzing a time series signal,
A time-frequency decomposition step of decomposing the time-series signal into time-frequency components and storing the time-series signal in a storage unit;
An initial value generation step of generating respective initial values of a time series signal parameter composed of an amplitude spectrum base parameter, an activity coefficient parameter and a phase spectrum parameter, and an error distribution specific gravity coefficient and a time frequency component allocation amount , and storing them in a storage unit;
Based on the time-frequency component, the time-series signal parameter, and the error distribution specific gravity coefficient stored in the storage unit, the time-series signal parameter and the error distribution specific gravity coefficient stored in the storage unit are updated. An update step;
A determination step of determining whether or not the time-series signal parameter stored in the storage unit satisfies a predetermined criterion;
A parameter output step for outputting the time-series signal parameter when the time-series signal parameter is determined to satisfy a predetermined criterion by the determination step;
The update step includes:
A time frequency component distribution amount calculating step for calculating a time frequency component distribution amount from the time frequency component stored in the storage unit, the time series signal parameter, and the error distribution specific gravity coefficient based on the following equation 7;

Amplitude for calculating a new amplitude spectrum base parameter from the activity coefficient parameter stored in the storage unit and the temporal frequency component allocation amount calculated in the temporal frequency component allocation amount calculating step based on the following equation 8. A spectral basis parameter calculating step;

From the amplitude spectrum base parameter and the activity coefficient parameter stored in the storage unit, and the time frequency component allocation amount calculated by the time frequency component allocation amount calculation step, a new activity coefficient parameter is expressed by the following equation (9). An activity coefficient parameter calculation step to be calculated based on,

A phase spectrum parameter calculation step of calculating a new phase spectrum parameter based on the following equation 10 from the time frequency component distribution amount calculated by the time frequency component distribution amount calculation step;

From the time frequency component and time series signal parameter stored in the storage unit and the time frequency component distribution amount calculated by the time frequency component distribution amount calculation step, a new error distribution specific gravity coefficient is expressed by the following equation (11). An error distribution specific gravity coefficient calculating step to calculate based on

A reflection step of reflecting the new value calculated by the amplitude spectrum basis parameter calculation step, the activity coefficient parameter calculation step, the phase spectrum parameter calculation step, and the error distribution specific gravity coefficient calculation step in a storage unit;
Have
The updating step includes
When the time-series signal parameter by said determining step is determined not to satisfy the predetermined criterion, the time-series signal parameters, said is to error distribution density coefficient and updating the time-frequency component distribution amount again A signal analysis method characterized by the above. The determination step determines whether or not the time series signal parameter satisfies a predetermined criterion based on whether or not the rate of change of the objective function value calculated based on the following equation 12 is equal to or less than a predetermined value. is there

The signal analysis method according to claim 3.   The program for making a computer perform each step of the signal analysis method of Claim 3 or 4.   A computer-readable recording medium on which the program according to claim 5 is recorded.

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