JPH081450B2 - Spectral analysis method - Google Patents

Description

The present invention relates to a frequency spectrum of a time-series signal in coded transmission of time-series signals such as voice and sound, and signal processing for synthesis or recognition. The present invention relates to a spectrum analysis method for extracting, particularly a spectrum analysis method for a non-stationary signal whose frequency spectrum changes with time.

(Conventional Technology) Conventionally, as a technology in such a field, the Acoustical Society of Japan (J.Acoust.Soc.Jpn), (E) 8 [6] (1987) Arai and Miura, “Annalysis of Impulsive Sound” Generated From Construction Equipment By The Wigner Distribution With A Gauss Window (An a
nalysis of impulsive sounds genera ted from constr
auction equipments by the Wingner distribution with
a Gaussian window) ”P.271-276.

As described in the above document, the frequency analysis using the Wigner distribution is used for the frequency spectrum analysis of the non-stationary signal due to its characteristics. However, the frequency spectrum analysis using the Wigner analysis has a problem that a cross spectrum, which is a kind of noise, is generated. Therefore, in the technique of the above document, in the spectrum analysis using the Wigner distribution, the cross spectrum is suppressed by performing the process of smoothing the frequency spectrum by the window function.

Here, Wigner distribution W which is a time function g (t)
_g (t, ω) is expressed by the following equation.

The pseudo Wigner distribution W _gw (t, ω) of the time function g (t) regulated by the window relation w (t) is Becomes The relation between the pseudo Wigner distribution W _gw (t, ω) and the Wigner distribution W _g (t, ω) is as follows.

However, W _w (t, ω); Wigner distribution of window function w (t) (Problems to be solved by the invention) However, in the conventional spectrum analysis method, as shown in the equation (3), the Wigner distribution W _g (t, Ω) and W _w
Since the convolution operation of (O, ω−Ω) dΩ is performed,
Instead of suppressing the cross spectrum, there is a problem that the frequency resolution of the spectrum deteriorates, and it is difficult to prevent the generation of the cross spectrum without degrading the frequency resolution.

The present invention provides a spectrum analysis method that solves the problem that the above-mentioned conventional technique has, in that it is difficult to suppress the generation of a cross spectrum without deteriorating the frequency resolution.

(Means for Solving the Problems) In order to solve the above problems, the present invention provides a spectrum analysis method in which an input time-series signal x (t) (however, t
Represents the time) and the phase of the instantaneous frequency is shifted by 90 ° to obtain the orthogonal wave (t) of this time-series signal x (t). By calculating the time series signal x (t), γ (τ, t) = x (t
-[Tau]). X (t + [tau]) (where [tau] is an integer and represents a lag). Further, by calculating the orthogonal wave (t), Second non-stationary autocorrelation signal Ask for. Then, the first non-stationary autocorrelation signal γ
(Τ, t) and the second non-stationary autocorrelation signal After calculating the autocorrelation function R (τ, t) by adding and, the autocorrelation function R (τ, t) is Fourier transformed to output the frequency spectrum.

(Operation) According to the present invention, the first non-stationary autocorrelation signal γ (τ, t) obtained from the input time-series signal x (t) and the second non-stationary autocorrelation signal γ (τ, t) obtained from the orthogonal wave (t). Autocorrelation signal And are added to calculate the autocorrelation function R (τ, t), the first nonstationary autocorrelation signal γ (τ, t) and the second nonstationary autocorrelation signal A canceling action works between and to remove the cross spectrum.

That is, since the instantaneous phase of the time-series signal x (t) and the orthogonal wave (t) differ only by 90 °, the Wigner distribution obtained based on the first non-stationary autocorrelation signal γ (τ, t) is also
Second non-stationary autocorrelation signal In principle, the Wigner distribution obtained on the basis of the above, and therefore the Wigner distribution obtained on the basis of the added value, are exactly the same. However, the cross spectrum included in the first non-stationary autocorrelation signal γ (τ, t) and the second non-stationary autocorrelation signal The cross spectrum included in the above has the property that the amplitudes are equal and the polarities of +/− are opposite to each other. Therefore, the first non-stationary autocorrelation signal γ (τ, t) and the second non-stationary autocorrelation signal By adding and to create the autocorrelation function R (τ, t), the cross spectrum is removed.

(Embodiment) FIG. 1 shows an embodiment of the present invention and is a functional block diagram of a spectrum analyzer for analyzing a frequency spectrum.

This spectrum analyzer is equipped with a low-pass filter 1 that limits the band of an analog signal Ain such as voice and sound.
An analog / digital converter (hereinafter referred to as A / D converter) 2 is connected to the output side thereof. The output side of the A / D converter 2 has a first unsteady autocorrelation calculator.
4a is connected, and the second unsteady autocorrelation calculator 4b is connected via the orthogonal transformer 3. Orthogonal transformer 3
Has a function of shifting the phase of the instantaneous frequency by 90 ° with respect to the output of the A / D converter 2 and converting the output of the A / D converter 2 into a quadrature wave, and is composed of, for example, a Hilbert filter. The first non-stationary autocorrelation calculator 4a uses A / D
It has a function of calculating the output of the converter 2 and outputting the first non-stationary autocorrelation signal, and is configured by a multiplier or the like.
The second non-stationary autocorrelation calculator 4b has a function of calculating the output of the orthogonal transformer 3 and outputting a second non-stationary autocorrelation signal, and is composed of a multiplier or the like.

A Fourier transformer 6 is connected via an autocorrelation calculator 5 to the output sides of the first and second unsteady autocorrelation calculators 4a and 4b. The autocorrelation calculator 5 is a circuit that calculates the autocorrelation function from the outputs of the first and second non-stationary autocorrelation calculators 4a and 4b, and is composed of an adder or the like. The Fourier transformer 6 has a function of performing Fourier transform on the output of the autocorrelation calculator 5 to output the frequency spectrum X (ω, t), and is configured by a product-sum calculator or the like.

Next, a spectrum analysis method using the apparatus of FIG. 1 will be described.

The band of the analog signal Ain is limited to FoHz by the low pass filter 1. The band-limited analog signal is sampled by the A / D converter 2 at a sampling frequency FsHz which is, for example, four times or more the band of the low-pass filter 1 and is converted to a digitized time series signal x (t). , The time series signal x (t) is given to the orthogonal transformer 3 and the first non-stationary autocorrelation calculator 4a. The quadrature converter 3 shifts the phase of the instantaneous frequency of the time series signal x (t) by 90 ° by, for example, a Hilbert filter, and supplies the quadrature waveform (t) to the second non-stationary autocorrelation calculator 4b. Here, the transfer characteristic H of the Hilbert filter
(E ^jω ) is However, ω is the angular frequency.

In the first non-stationary autocorrelation calculator 4a, the time series signal x
(T) is input and the following equation is calculated to calculate the first unsteady autocorrelation signal γ (τ, t), which is calculated by the autocorrelation calculator 5
Output to.

 γ (τ, t) = x (t−τ) ・ x (t−τ) …… (4) where τ; is an integer (0,1, ..., N) and represents a lag. .

t; time In the second non-stationary autocorrelation calculator 4b, the orthogonal transformer 3
The second non-stationary autocorrelation signal is calculated by inputting the quadrature wave (t) output by And outputs it to the autocorrelation calculator 5.

However, τ = 0,1, ..., N The autocorrelation calculator 5 uses the first and second non-stationary autocorrelation signals γ (τ, t), Input and calculate the following equation to calculate the autocorrelation function R (τ, t)
Ask for.

However, τ = 0,1, ..., N −τ = −1, −2, ……, −N The autocorrelation function R (τ, t) obtained by the equation (6) (however,
τ = −N, ..., 0, 1, ..., N) is subjected to Fourier transform as shown by the following equation by the Fourier transformer 6, and the frequency spectrum X (ω, t) is calculated.

As a result, the Fourier transformer 6 causes the frequency spectrum X
(Ω, t) is output as the spectrum of the time-series signal x (t).

Then, the input time-series signal x (n) (where, n is an integer in the sampling time) as the signal of a single frequency f ₀ cos (2
πf ₀ T _s n) (where T _s is a sampling period), the cross spectrum canceling action will be described.

Non-stationary autocorrelation signal γ (m, of input time series signal x (n)
n) (where m is a lag and an integer) can be expressed by the following equation.

γ (m, n) = x (n−m) × x (n + m) = cos (2πf ₀
T _s (n−m)) · cos (2πf ₀ T _s (n−m)) = (1/2)
_{· Cos (2πf 0 T s n} ) + (1/2) · cos (2πf 0 T s m) ......
(8) The second term of the equation (8) does not depend on the time n and corresponds to the frequency of the power spectrum as the analysis result. On the other hand, the first term depends on the time n and is called a cross spectrum, which adversely affects the frequency analysis.

Also, the orthogonal wave (n) of the time series signal x (n) and its non-stationary autocorrelation signal (N) = sin (2πf ₀ T _s n) (9) here, Can be expressed by the following equation.

Considering the defining autocorrelation function R (m, n), R (m, n)
_{= Cos (2πf 0 T s m} ) , and the cross spectrum is removed.

2A and 2B are spectrum analysis measurement diagrams, FIG. 2A is a spectrum analysis example by a conventional Wigner distribution, and FIG. 2B is a spectrum analysis example of the present embodiment. The horizontal axis of FIG. 2 represents the frequency (Hz) and the vertical axis represents the amplitude of the spectrum, which is displayed by shifting the spectrum every 125 μsec. That is, the lowest waveform is the spectrum at time 0, the upper waveform is the spectrum at time 125 μsec, the upper waveform is the spectrum at time 250 μsec, and so on.

As shown in FIGS. 2A and 2B, the input analog signal Ain is a sine wave having a frequency of 1000 Hz. In FIG. 2 (a), a cross spectrum exists near the direct current having a frequency of 0 Hz. On the other hand, in FIG. 2 (b), the first and second non-stationary autocorrelation signals x (τ, t) and (τ, t) are canceled out, so that the cross spectrum is removed. Moreover, the width of the spectrum peak at 1000 Hz in FIG. 2 (b) is the same as the width of the spectrum peak at 1000 Hz in FIG. 2 (a). Therefore, in this embodiment, it is possible to suppress the cross spectrum generated in the spectrum analysis by the Wigner distribution without lowering the frequency resolution,
Accurate spectrum analysis can be performed. Moreover, like the Wigner distribution, it is a spectrum analysis method in which the center of two samplings for correlation, such as x (t−τ) · x (t + τ), is always fixed at the time t, so Suitable for spectrum analysis of stationary signals.

It should be noted that the present invention is not limited to the illustrated embodiment, and various modifications can be made, for example, by performing the fast Fourier transform instead of the equation (6).

(Effects of the Invention) As described in detail above, according to the present invention, the time series signal x (t) is converted into the orthogonal wave (t), and the first non-stationary signal of the time series signal x (t) is converted. The autocorrelation signal γ (τ, t),
A second non-stationary autocorrelation signal (τ, t) of the orthogonal wave (t) is obtained, and the first and second non-stationary autocorrelation signals γ (τ, t), Since the autocorrelation function R (τ, t) is calculated from
The first and second non-stationary autocorrelation signals x (τ, t), (τ,
t) is canceled out, and the cross spectrum can be accurately removed without lowering the frequency resolution. Therefore, accurate spectral analysis of non-stationary signals can be expected.

[Brief description of drawings]

FIG. 1 is a functional block diagram of a spectrum analyzer showing an embodiment of the present invention, and FIGS. 2 (a) and 2 (b) are spectrum analysis measurement diagrams of the conventional example and the example of FIG. 3 ... Orthogonal transformer, 4a, 4b ... First and second non-stationary autocorrelation calculator, 5 ... Autocorrelation calculator, 6 ... Fourier transformer, x (t) ... Time series signal, X (ω, t) …… Frequency spectrum.

Claims (1)

[Claims] 1. A quadrature wave (t) of the time series signal x (t) is obtained by shifting the phase of the instantaneous frequency of the input time series signal x (t) (where t represents time) by 90 °. , Γ (τ, t) = x by calculating the time series signal x (t)
A first non-stationary autocorrelation signal γ (τ, t) of (t−τ) · x (t + τ) (where τ represents an integer lag) is calculated, and the orthogonal wave (t) is calculated, Second non-stationary autocorrelation signal To obtain the first non-stationary autocorrelation signal γ (τ, t) and the second non-stationary autocorrelation signal A spectrum analysis method comprising calculating the autocorrelation function R (τ, t) by adding and, and then Fourier transforming the autocorrelation function R (τ, t) to output a frequency spectrum.