JP2003232820A - Frequency analytical method by maximum entropy method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To realize compatibility between subdivision of the analytical width and maintenance of processing speed, in a frequency analytical method using a maximum entropy method used for analysis of an acoustic signal or the like. <P>SOLUTION: Sliced signal data based on time series, inputted through an input terminal 1 is multiplied by a window for suppressing turnup of a band zone by a window multiplier 9, and Fourier transform is applied thereto by a discrete Fourier transformer 10, to thereby generate a frequency bin having a restricted band zone. Then, coefficient prediction is performed by an MEM coefficient predictor 6, and a frequency spectrum having a desired analytical width is calculated by a frequency spectrum calculator 7 from a coefficient determined by the coefficient prediction. <P>COPYRIGHT: (C)2003,JPO

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method of performing frequency analysis of an acoustic signal by using the maximum entropy method, and is particularly suitable for use in analyzing sonar transient sound and detection sound. . The maximum entropy method is abbreviated as MEM method below.

[0002]

2. Description of the Related Art The advantage of using the MEM method for frequency analysis of an acoustic signal is that even if the observation time of the input acoustic signal data is shorter than when using the fast Fourier transform (FFT), the final The point is that the analysis width of the frequency spectrum can be obtained more finely.

FIG. 1 shows an example of a conventional frequency analysis method using the MEM method. First, the outline of this analysis method will be described below. This analysis method is roughly divided into three parts. That is, frequency shift, prefilter, and MEM analysis.

The frequency shift is a part for controlling which frequency the input acoustic signal data is analyzed as a center. here. The frequency that is the center of the analysis is called the center frequency. The pre-filter portion is a portion that limits the frequency bandwidth input to the MEM analysis portion and controls the sampling frequency rate with respect to the input acoustic signal data, and narrows the frequency bandwidth and sets the sampling frequency rate. By making it low, it becomes possible to make the analysis width of the final frequency spectrum fine. The MEM analysis part is the main body of the frequency analysis, and is a part for calculating the frequency spectrum according to the calculation order of the frequency spectrum. The calculated order will be described later.

In FIG. 1, 1 is an input terminal, 2 is an orthogonal transformer, 3-1 to 3-N are low-pass filters, 4-1.
To 4-N are 1/2 decimation processors, 5 is an input data selection processor, 6 is a MEM coefficient predictor, 7 is a frequency spectrum calculator, and 8 is an output terminal.

Time-series data obtained by converting an acoustic signal into a digital signal is input to the orthogonal transformer 2 through the input terminal 1 at a rate of the sampling frequency fs. Orthogonal transformer 2
Then, based on the center frequency fc to be analyzed,

Y (k) = x (k) e ^{−j2π · fc / fs · k} (1) where k = 1, 2, 3, ... where x (k): kth Input time series data converted to digital signals

According to the above, the frequency band (modulation) of the owned frequency band of the input time-series data converted into digital signals
To do.

The prefilter portion to which the output of the orthogonal transformation is input is one low-pass filter and one half.
A set of thinning processors is prepared for N stages. The number N of stages of this filter is determined depending on the required analysis width. The orthogonal transform output is first input to the first-stage low-pass filter 3-1 at the rate of the sampling frequency fs. In the low-pass filter 3-1, the sampling frequency fs is cut at fs / 4 in order to prevent the aliasing of the frequency when the output rate is reduced to 1/2 by the 1/2 decimation processor in the subsequent stage. The signal is filtered by the off frequency (fcl) and output to the 1/2 decimation processor 4-1.

The 1/2 decimation processor 4-1 decimates every other low pass filter output data to reduce the sampling frequency to fs / 2 and output it to the input data selection processor 5. At the same time, it also outputs to the second-stage low-pass filter 3-2. Low-pass filter 3-2 and 1/2 decimation processor 4-2
Then, by performing the same processing as the first step above,
Sampling at the cut-off frequency fs / 8 and rate reduction to the sampling frequency fs / 4 are performed.
The data is output to the input data selection processor 5 and the low pass filter of the next stage. After that, this process is repeated over N stages.

The input data selection processor 5 which receives the output of each stage selects one data corresponding to the required analysis width from the outputs of these N stages and outputs it to the MEM coefficient predictor 6. .

The MEM coefficient predictor 6 obtains the coefficients γ1, γ2, ..., γm of the m-point prediction error filter and the average output Pm from this filter by the prediction algorithm by the MEM, and the frequency spectrum calculator 7 Output to.

In the frequency spectrum calculator 7, based on these coefficients γ1, γ2, ..., γm and the average output Pm,

[0014]

[Equation 1]

[0015] Where g is the calculation order of the frequency spectrum         fs': Sampler of data selected by the input data selection processor Frequency         Δf: analysis width of frequency spectrum         γk: γ1, γ2, ..., γm (when k ≦ m)                   0 (when k> m)     ... (2)

According to the above, the frequency spectrum is calculated and output to the output terminal 8. Here, the analysis width Δf of the frequency spectrum in the MEM analysis is the fast Fourier transform FFT.
Similar to how the analysis width in the analysis depends on the sampling frequency of the input data and the FFT order,

[0017]

[Equation 2]

However, g: order of calculation of frequency spectrum fs': sampling frequency of data selected by the input data selection processor (3)

Is determined by

As is clear from this equation, the analysis width Δf of the frequency spectrum is calculated by
And the sampling frequency of the data selected by the input data selection processor.

Therefore, in the frequency analysis method using the MEM of the conventional method, generally, the calculation order g of the frequency spectrum is fixed in advance, and the sampling frequency of the input data to the MEM analysis section is set in the prefilter section. The frequency spectrum of the required analysis width was obtained by changing the.

[0022]

The frequency analysis method using the conventional MEM described so far has the following problems.

In order to obtain the necessary analysis width in the conventional method, it is indispensable to rate down the sampling frequency of the acoustic signal data input in the pre-filter portion, as shown in the above description. is there. However, in this method, there are several analysis widths that can be analyzed, and if the analysis width is made finer, the number of filter stages required increases proportionally. The processing amount of this increasing filter is, for example, the analysis width from the basic analysis width to 1 /
In the case of setting to 16, if the total processing amount of the low-pass filter and the 1/2 thinning-out process is S, the amount of S ¹⁶ will be reached.

That is, the analysis width is 1/2 ^{n of the} basic width
Therefore, the total throughput of S ⁿ is required to
The total throughput increases at the power level. The purpose of the present invention is to solve such problems.

[0025]

In order to solve such a problem, in the first invention of the present application, band folding is suppressed with respect to signal data cut out based on time series. The signal data multiplied by the window is subjected to Fourier transform to generate a frequency bin limited to a band required for frequency analysis, and coefficient prediction is performed on the frequency bin by a MEM algorithm. Then, the frequency spectrum having a desired analysis width is calculated from the coefficient obtained by this coefficient prediction.

Further, in the second invention of the present application,
When the signal data is cut out, while cutting out the signals while overlapping them, after obtaining the frequency bin, a compensation process for compensating the frequency shift occurring at the time of the overlap is performed. is there.

Further, in the third invention of the present application, the signal data cut out based on the time series is multiplied by a window of an order higher than a predetermined order for suppressing the aliasing of the band. The signal data multiplied by the window,
The signal data divided by the predetermined order and subjected to the window is subjected to Fourier transform to generate frequency bins limited to the band required for frequency analysis, and the MEM algorithm is applied to the frequency bins. Coefficient prediction by
The frequency spectrum having a desired analysis width is calculated from the coefficient obtained by the coefficient prediction.

[0028]

BEST MODE FOR CARRYING OUT THE INVENTION An example of an embodiment of the present invention will be described below with reference to the drawings.

FIG. 2 shows a first embodiment of the frequency analysis method of the present invention. The analysis method of the first embodiment differs from the above-mentioned conventional method in that the frequency shift function is incorporated in the prefilter portion. This part controls the center frequency to be analyzed, the frequency bandwidth as well as the input sampling frequency rate to the MEM analysis.

In FIG. 2, 1 is an input terminal, 9 is a window multiplier, 10 is a discrete Fourier transformer (DFT), 11 is a phase compensator, 6 is a MEM coefficient predictor, 7 is a frequency spectrum calculator, and 8 is It is an output terminal.

Through the input terminal 1, the window multiplier 2 is supplied with time-series data obtained by converting the acoustic signal into a digital signal at a rate of the sampling frequency fs. Window multiplier 9
Then, the digital signal-converted time-series data is cut out with the same order as the order N required by the discrete Fourier transformer in the subsequent stage while performing overlap processing if necessary, and the time-series data is adjacent to the required frequency analysis band. A window of the same order as this order N to reduce the aliasing from the band
The cut out data is multiplied and output to the discrete Fourier transformer 10.

Here, the coefficient of this window is calculated by using the Kaiser-Bessel window formula to determine the window parameter α from the required amount of aliasing reduction and the ripple characteristic of the band. The discrete Fourier transformer 10 performs a Fourier transform of the Nth order on the center frequency fc required for analysis on the data that has been cut out and multiplied by the window to create frequency bins, and the phase compensator 11 Output to.

Here, the order N is set in accordance with the frequency bandwidth required for analysis and the analysis width Δf, and if the order N is changed, the phase compensator 11 and the subsequent ones of the created frequency bin are transferred. Output sampling frequency rate fs ′ of In the phase compensator 11, when the time series data converted into a digital signal by the window multiplier 9 is subjected to overlap processing, for example, a frequency shift caused in the frequency analysis result by the MEM,

Y (k) = X (k) e− ^{j2π (1-Ovp) fc / fs · k · N}

[0035] k = 1, 2, ..., N Where X (k): k-th time series data of the frequency bin output from the DFT         fc: center frequency to be analyzed         fs: sampling of time-series data obtained by converting acoustic signals into digital signals frequency         Ovp: Overlap ratio in window multiplier 9     ... (4)

As described above, the amount of compensation determined by the center frequency is multiplied in the time series direction of the frequency bin to perform compensation, and output to the MEM coefficient predictor 6. The phase compensator 11 is not necessary when the overlap processing is not performed.

In the MEM coefficient predictor 6, the phase compensator 11
The compensated frequency bins from are arranged in a time series in the order in which they are generated and buffered, and the coefficients γ1 and γ of the m-point prediction error filter are calculated by the prediction algorithm by the MEM.
2, ..., γm, and the average output Pm from this filter
And are output to the frequency spectrum calculator 7. In the frequency spectrum calculator 7, the coefficients γ1, γ2, ...
, .Gamma.m and the average output Pm

[0038]

[Equation 3]

After the frequency spectrum is calculated by the above-mentioned method, it is output to the outside through the output terminal 8.

However, the sampling frequency fs' in this equation is M in the first embodiment described here.
This is the input sampling frequency rate in the time series direction of the compensated frequency bins to the EM coefficient predictor 6.

Further, the analysis width Δf of the frequency spectrum in the MEM analysis is as described above.

[0042]

[Equation 4]

.. (3), the sampling frequency fs' in the equation (3) is also the time of the compensated frequency bin to the MEM coefficient predictor 6 in the first embodiment. It becomes the input sampling frequency rate in the stream direction. As is clear from this equation, the analysis width Δf of the frequency spectrum can be determined by the calculation order of the frequency spectrum and the input sampling frequency rate of the compensated frequency bin in the time series direction.

Therefore, in the frequency analysis method of the first embodiment, the calculation order g of the normal frequency spectrum is fixed in advance, and the order N in the discrete Fourier transformer 10 is changed to obtain a necessary analysis width Δf. The input sampling frequency rate to the MEM coefficient predictor 6 for obtaining Further, it is naturally possible to make both the calculation order g of the normal frequency spectrum and the order N in the discrete Fourier transformer 10 variable, or only the calculation order g of the normal frequency spectrum variable. The required analysis width Δf can be obtained in each case.

Next, a second embodiment different from the above-mentioned first embodiment will be described below. The second embodiment differs from the first embodiment in that an addition processor is provided between the window multiplier and the discrete Fourier transformer to perform a special discrete Fourier transform. On the other hand, in the prefilter part, the center frequency to be analyzed, the frequency bandwidth, and the ME
Similar to the first embodiment, the input sampling frequency rate to the M analysis is controlled.

FIG. 3 shows the frequency analysis method of the second embodiment. In the figure, 1 is an input terminal, 6 is a MEM coefficient predictor, 7 is a frequency spectrum calculator, 8 is an output terminal,
Reference numeral 9 is a window multiplier, 10 is a discrete Fourier transformer, 11 is a phase compensator, and 12 is an addition processor.

Through the input terminal 1, time-series data obtained by converting the acoustic signal into a digital signal is input to the window multiplier 9 at a rate of the sampling frequency fs. In the window multiplier 9, as in the first embodiment, this time series data is cut out while performing overlap processing as necessary, and the cut out data is divided into adjacent bands to the required frequency analysis band. Multiply the window to reduce the aliasing from However, the number of data cut out by the overlap processing here and the order of the window are determined by the addition processor 12 in the subsequent stage.
Is determined by the number of additions Q in and the order N in the discrete Fourier transformer 10, and the number of data and the order are

N × (Q + 1) (4)

It becomes For example, if the number of additions in the addition processor 12 is 1, the number of data cut out in this overlap processing and the order of the window are 2N. The time series data multiplied by this window is output to the addition processor 3. In the addition processor 12, the time series data multiplied by this window is x (1), x (2), x (3), x (N × (Q +
1)), the addition processing as shown in the following equation is performed and output to the discrete Fourier transformer 10.

[0050]

[Equation 5]

However, Q: the number of additions in the addition processor 12 N: Order in the discrete Fourier transformer 10

In the discrete Fourier transformer 10, the added data is subjected to an Nth-order Fourier transform with respect to the center frequency fc required for analysis to create a frequency bin, and the frequency bin is output to the phase compensator 11. The operation after the phase compensator 11 is the same as the operation of the corresponding portion in the first embodiment.

Furthermore, the first and second embodiments described above
As a modification to the above embodiment, the following contents can be considered. That is, in each of the above-described embodiments, the average output Pm is obtained by the MEM coefficient predictor. However, when only the relative power of the frequency spectrum is required, the average output Pm is not obtained, and an appropriate constant is used for this. It is also possible to replace.

In addition, the frequency spectrum calculator is used to calculate the spectrum.

[0055]

[Equation 6]

Although the above method has been described, as a method for speeding up the processing instead of this, for example, the calculation in the parentheses of the denominator of the above equation (2) is performed by an inverse FFT of the same order as the frequency spectrum calculation order g. May be.

Further, the data format and data processing format in the methods described so far may be either analog format or digital format, and either may be adopted. Also, regarding the circuit configuration, it may be configured by a combination of integrated circuits or the like, or may be configured by software using an arithmetic processor such as a digital signal processor. These modifications are included in the scope of the present invention.

[0058]

According to the method described above, in the present invention, even when the analysis width necessary for the analysis becomes fine,
There is almost no increase in the amount of processing, and a decrease in processing speed can be effectively avoided.

Particularly in the method of the second embodiment, the addition processor 12 adds the time-series data multiplied by the window once. Therefore, the effect of reducing aliasing from the adjacent band to the frequency analysis band can be obtained in the same manner as when the window order is 2N, and the Fourier transform order can be N. Therefore, as compared with the first embodiment, the processing amount of the Fourier transform can be suppressed, and thus the entire processing amount can be significantly reduced.

Alternatively, if the order of the Fourier transform is increased in the second embodiment, the order of the window can be increased and the effect of reducing aliasing can be expected to be enhanced. As a result, in the second embodiment, a significant improvement in performance can be expected even when compared with the first embodiment.

[Brief description of drawings]

FIG. 1 is a block diagram showing a conventional frequency analysis method.

FIG. 2 is a block diagram showing a first embodiment of the present invention.

FIG. 3 is a block diagram showing a second embodiment of the present invention.

[Explanation of symbols]

1 input terminal 2 Orthogonal transformer 3 Low-pass filter 4 1/2 thinning processor 5 Input data selection processor 6 MEM coefficient predictor 7 Frequency spectrum calculator 8 output terminals 9 window multiplier 10 Discrete Fourier Transform 11 Phase compensator

Claims (3)

[Claims] 1. A method for performing frequency analysis of an acoustic signal or the like by using the maximum entropy method, wherein signal data converted into data based on a time series is cut out, and band folding is performed on the cut out signal data. The suppression window is multiplied, and the window-multiplied signal data is subjected to Fourier transform to generate frequency bins limited to the band required for frequency analysis. Coefficients are calculated by the MEM algorithm for the frequency bins. A frequency analysis method, which comprises performing a prediction and calculating a frequency spectrum having a desired analysis width from the coefficient obtained by the coefficient prediction. 2. The frequency analysis method according to claim 1, wherein when the signal data is cut out, the signals are cut out while being overlapped, and the frequency bin is obtained, and then the overlap A frequency analysis method, characterized by performing a compensation process for compensating for a frequency shift that occurs at the time. 3. A method for frequency-analyzing an acoustic signal or the like using the maximum entropy method, wherein signal data converted into data based on a time series is cut out, and band folding is performed on the cut out signal data. Multiply a window of an order higher than a predetermined order to be suppressed, divide the signal data multiplied by the window for each of the predetermined orders, apply a Fourier transform to the signal data multiplied by the window, A frequency bin limited to the band required for frequency analysis is generated, coefficient prediction is performed on the frequency bin by the MEM algorithm, and a frequency spectrum having a desired analysis width is calculated from the coefficient obtained by the coefficient prediction. A frequency analysis method comprising: