JPH0580795A - Signal processing method - Google Patents

Abstract

PURPOSE:To estimate a signal corresponding to a given wavelet coefficient. CONSTITUTION:An amplitude wavelet coefficient ¦Y(n, j)¦ is set (S1). A random number is regarded as an initial temporary estimation signal x<0>(l) (S2). This is used as a temporary estimation signal x<k>(l) to perform wavelet conversion (S3). It is decided (S4) whether the square of the amplitude difference between the obtained wavelet coefficient x<k>(n, j) and ¦Y(n, j)¦ is less than a specific value or not. When not, the amplitude ¦X<k>(n, j)¦ of X<k>(n, j) is substituted (S5) with ¦Y(n, j)¦. The substituted coefficient is processed (S5) by inverse wavelet conversion. The inversely converted signal x<k+1>(l) is put back to the step S3 as x<k>(l) and the steps S3, S4, S5, and S6 are repeated. When it is decided in the step S4 that the difference is less than the specific value, the current x<k>(l) is outputted (S7) as an estimation signal.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to pitch conversion of sounds such as voices and musical instrument sounds, time compression / expansion, voice quality conversion, hearing aid signal processing, sound source creation for electronic musical instruments, signal extraction from outputs of sensors and measuring instruments, The present invention relates to a signal processing method that is generally used for signal processing such as signal enhancement and signal modulation / decoding, and estimates a signal corresponding to a given wavelet coefficient.

[0002]

2. Description of the Related Art A process that could not be performed by directly processing a signal in the past is converted into a space different from that of the signal, the transformed one is transformed, and the transformed one is inversely transformed. There is a processing by short time Fourier transform as a method of performing signal processing by returning to a signal by (Oppenheim AVand Shafer RW "Digital Processin
g "Prentice-Hall, NJ, USA1975. Japanese translation, Date translation" Digital Signal Processing "Corona, Tokyo 1978). In particular, the amplitude and phase of the Fourier coefficient (frequency space) obtained by the Fourier transform is manipulated and transformed. Several methods have been proposed for estimating the signal (time space) corresponding to the manipulated Fourier coefficient, or estimating the corresponding signal (time space) only from the amplitude of the directly applied Fourier coefficient (Griffin DWandLim JS "Signal Estimation from
Modified Short-Time Fourier Transform ".IEEE Tran
s. Vol.ASSP-32, No.2, April 1984).

However, in this paper, it is assumed that the short-time Fourier transform is used as the center of the basic operation and that a window function having a fixed length is used in the signal space. Therefore, there are the following problems. (1) Generally, in a time-frequency space obtained by a short-time Fourier transform with such a fixed window, the time-frequency resolution is constant regardless of the time and frequency band, and the time-frequency resolution is appropriately adjusted according to the frequency. I can't make a plan. As a signal expression, it is impossible to realize a high frequency resolution and a low time resolution in a low frequency component and a low frequency resolution and a high time resolution in a high frequency component, which are considered to have a much wider application range.

(2) In the human auditory system, low frequency components have high frequency resolution, low time resolution, and high frequency components have low frequency resolution and high time resolution. It is difficult to do because of (3) In order to solve the problems (1) and (2) in the range of short-time Fourier transform, it is easy to think of using a band-pass filter set (bank) in which frequencies are logarithm-linearly arranged. , The filter characteristics are fixed, and it is impossible to change the filter characteristics.

(4) Therefore, in the method of adjusting the frequency to the human auditory system by using a set of logarithmic-linearly arranged band filters, the amplitude and phase of the Fourier coefficient are modified and then the time domain It cannot be applied to estimating a signal or giving a completely new frequency domain amplitude information to estimate a signal in the time domain. By the way, it has been proposed to use a wavelet transform for analysis and synthesis of signals. For the mathematical background of the Wavelet transformation theory, see [Combes, JM et al. Eds. "WA
VELETS ", Springer-Verlag, 1989, Masaaki Sato:" Mathematical Basics of Wavelet Theory Part 1-Non-orthogonal Wavelets ", Journal of Acoustical Society of Japan, Vol.46, No.6, June 1991] I will briefly explain this Wavelet transformation.

A time-series signal to be analyzed is represented by a discrete system and is represented by x (l). The coefficient obtained by Wavelet transforming the signal x (l), so-called Wavelet transform X (n, j), is defined by the following equation. X (n, j) = Σφ ^* _{n, j} (m) x (m) (1) Σ is m = −∞ to ∞ where {φ _{n, j} (m) | n, j: integer} is a wavelet Function, basic wavelet function (analyzing wavelet) φ
From (m), scale parameter a _n and shift parameter b
_It is created by the following equation using _nj . Note that φ ^* _{n, j} (m) represents the complex conjugate of φ _{n, j} (m).

[0007]

[Equation 1]

At the zero frequency of the Fourier transform φ '(ω) of φ (m), the admissibility condition of zero (φ' (0) = 0) must be satisfied, and conversely Any function that satisfies the above may be freely used as the basic wavelet function. This wavelet transform can define an inverse transform,

[0009]

[Equation 2]

Can be written as Here, C is a constant that can be calculated from φ '(ω). Although the above discussion has described the case where φ '(ω) is symmetric with respect to ω, it can be easily extended to the case where it is localized in the positive frequency region. In the above wavelet conversion, the time-frequency resolution is a conversion system that changes in a logarithmic-linear manner, and high frequency resolution with low frequency components, low time resolution, low frequency resolution with high frequency components, and high time resolution can be realized. Like That is, the problem (1) is solved in principle.

Since the method of determining the basic wavelet function φ (m) is free as long as the admittability condition is satisfied, the problem (3) can be naturally solved.
Examples of basic wavelet functions include (1) Mexican-
hat (Laplacian Gaussian) function, (2) Gabor function,
(3) Orthogonal wavelet For example, S. Mallat: "A theory for mul
tisignal decomposition: The wavelet representatio
n, "IEEE Trans.PAMI, Vol.11, No.7, pp.674-693,1989.,
(4) Auditory impulse response [Toshio Irino, Hidenori Kawahara:
"Analysis and synthesis by wavelet transform using auditory impulse response," Proceedings of Spring Meeting of ASJ, 1-
8-1, March 1991]. The imaginary part of the basic wavelet function may be determined by the Hilbert transform after determining the real part according to the purpose of analysis. The problem (2) can be solved by using the last basic wavelet function in consideration of the characteristics of the auditory system.

[0012]

However, it has not been proposed to estimate a signal corresponding to a wavelet coefficient whose amplitude and phase are modified, or a signal corresponding to a wavelet coefficient which is newly given. The purpose of this invention is wavel
It is to provide a signal processing method for estimating a signal corresponding to a given wavelet coefficient by using the et transform.

[0013]

According to the invention of claim 1, the first process for wavelet transforming the temporary estimated signal, the difference between the wavelet coefficient obtained by the wavelet transform and the given wavelet coefficient. Second process for determining whether the square of is less than or equal to a predetermined value, and when the second process is determined to be greater than or equal to the predetermined value, a signal that minimizes the square of the difference is calculated to perform the next provisional estimation. If the third square of the signal and the first to third processes are repeated and the square of the difference is determined to be less than or equal to a predetermined value in the second process, the temporary estimated signal at that time is the estimated signal for the given wavelet coefficient. And a fourth process.

According to the second aspect of the present invention, the first process for wavelet transforming the temporary estimated signal and the first process for judging whether or not the wavelet coefficient obtained by the wavelet transform is sufficiently close to the given wavelet coefficient. If it is not determined that the two processes are sufficiently close to each other, the amplitude of the wavelet coefficient obtained in the first process is replaced by the amplitude of the given wavelet coefficient, and the third process is performed. The fourth process in which the generated wavelet coefficient is subjected to the inverse wavelet transform and the obtained signal is the next temporary estimated signal and the first to fourth processes are repeated, and when it is determined in the second process that they are sufficiently close, And a fifth process for converting the temporary estimated signal into an estimated signal for a given wavelet coefficient.

In any of the first and second aspects of the invention,
For a given wavelet coefficient, a case where a completely new wavelet coefficient amplitude is directly given from the beginning, or a case where a signal to be processed is wavelet transformed and at least one of the amplitude and phase of the wavelet coefficient is modified is given. There is.

[0016]

DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the invention of claim 1 will be described with reference to FIG. This embodiment uses a given wavelet coefficient Y
(n, j), (amplitude of wavelet coefficient obtained by wavelet transforming the signal to be processed, wavelet coefficient Y (n, j) obtained by modifying at least one of the phases, or only the amplitude of wavelet coefficient from the beginning is directly given. The present invention estimates the signal corresponding to the obtained amplitude wavelet coefficient | Y (n, j) |).

First, given wavelet coefficient Y
(n, j) is set (S ₁ ), and then an arbitrary value, for example, a random number value is set as the signal initial value (first temporary estimated signal) x ⁰ (l) (S ₂ ). The temporary estimated signal x ^k (l) (k =
0) is wavelet transformed (S ₃ ). The square of the difference between the converted wavelet coefficient X ^k (n, j) and the given wavelet coefficient Y (n, j), that is, it is determined whether the following expression is less than or equal to a predetermined value, that is, estimation repetition processing operations it is determined whether sufficiently converged (S _4).

[0018]

[Equation 3]

When it is determined that the square of this difference is greater than or equal to a predetermined value, a signal that minimizes the square of this difference is calculated and used as the next temporary estimated signal x ^{k + 1} (l). That is, in equation (4), (1)
By substituting the relation of the equation into the equation (5), the equation (5) is partially differentiated with respect to x (l) as in the equation (6), and this is set to zero.

[0020]

[Equation 4]

[0021]

[Equation 5]

This equation (6) is arranged for each sample point in the time series of the temporary estimated signal to obtain x (1), x (2), ... X.
Make P equations for (p), obtain simultaneous equations for x (l), solve this for x (l), and solve the solution x
Let (l) be the next temporary estimated signal x ^{k + 1} (l). That is, this x ^{k + 1} (l) is used as the temporary estimated signal x ^k (l), and the process returns to step S ₃ . Thus, step S _3, S ₄ until the determination in Step S ₄ becomes below a predetermined value, S ₅ are repeated. That is, the signal x ^k (l) closest to the given wavelet coefficient Y (n, j) is obtained by the method of least squares. In this case,
The iterative process is constrained to converge using Y (n, j) so as to find the one that minimizes the square of the difference between the wavelet coefficients given by the equation (6).

Step S_FourAnd the formula (4) is less than or equal to a predetermined value.
If it is determined, that is, it is determined that it has converged sufficiently
And x at that time^k(l) given wavelet coefficient Y
The estimated signal corresponding to (n, j) is used (S₆). Next claim
Amplitude wavelet coefficient | Y given by the second invention
See FIG. 2 for an example of obtaining an estimated signal corresponding to (n, j) |
I will explain. Also in this embodiment, the steps of FIG.
S₁, S₂, S₃, S_FourPerforms the same process as
S _FourIf it is judged to be more than a predetermined value (non-convergence),
Bullet coefficient X^kAmplitude of (n, j) ｜ X^k(n, j) |
Replace with the obtained amplitude wavelet coefficient | Y (n, j) |
The obtained wavelet coefficient X ′ (n, j) is calculated (S_Five).
That is, the following replacement is performed.

[0024]

[Equation 6]

The wavelet coefficient X '(n, j) whose amplitude has been replaced is subjected to inverse wavelet transform to obtain x (l),
This is used as the next temporary estimated signal x ^{k + 1} (l) (S ₆ ). This x ^{k + 1} (l) is set again as x ^k (l) in step S ₃ , and the following S
₃ , S ₄ , S ₅ , and S ₆ are repeatedly processed. Step S
_When it is determined that | X ^k (n, j) | is sufficiently close to | Y (n, j) | in 4, that is, when it is determined that the above iterative processing has sufficiently converged, x ^k (l) at that time is determined. Is output as an estimated signal for | Y (n, j) | (S ₇ ). In step S ₅ | Y (n, j)
The iterative process converges due to the constraint that amplitude replacement is performed with |. In step S ₄ , | X
Amplitude wavelet coefficient given by ^k (l) | Y (n, j)
The determination as to whether or not it is sufficiently close to | may be performed by a method other than obtaining the square of the difference. A concrete example of performing the time compression of the voice by utilizing the estimation of the voice signal only from the amplitude information of the wavelet coefficient given by the embodiment of FIG. 2 will be shown.
The voice waveform of / kanojowa / uttered by a man (FIG. 3A) is taken into the computer as discrete time series data at a sampling frequency of 48 KHz. The length of this voice waveform is 50 including the silent section.
It was set to 0 mS. Next, change this waveform from about 56Hz to about 14.4KHz
The 128-channel auditory wavelet (wavelet having the auditory impulse response as a basic wavelet function) is analyzed to obtain wavelet coefficients. This wavelet coefficient is obtained each time one sample value (data) is input, and every other time series of the obtained wavelet coefficient is extracted, and its amplitude is taken out (the time axis is halved). Let the given amplitude wavelet coefficient | Y (n, j) |.

The process shown in FIG. 2 was executed using a random number as the initial value x ⁰ (l) of the temporary estimated signal. In curve 8 of FIG.
Amplitude of wavelet coefficient of provisional estimated signal x ^k (l) | X
^k (n, j) | and the given wavelet coefficient | Y (n, j
j) Indicates the normalized squared distance from |. Number of iterations k
It is understood that | X ^k (n, j) | approaches | Y (n, j) | Curve 9 shows the normalized square of the difference between the ^k- th temporary estimated signal x ^k (l) and the (k-1) -th temporary estimated signal x ^k-1 (l). It can be seen from curve 9 that the change in x ^k (l) decreases as the number of iterations increases, and curve 8 shows | Y for k = 4 or more.
It seems that the approach to (n, j) | is very slight, but from curve 9, it can be seen that even if k = 4 or more, it approaches to | Y (n, j) | at a considerable rate.

[0027] Thus given amplitude wavelet coefficients | approaching accordance repetition of the process ^{| X k (n, j)} | of Y (n, j) | amplitude wavelet coefficients starting from the random number to the estimated signal x (l) It is understood that it will continue. The waveform of the final estimated signal x (l) is shown in FIG. 3B. It can be seen that FIG. 3B is similar to FIG. 3A in that the time axis is half and the waveform is similar, and thus the time axis of the speech waveform can be compressed. When actually listening to the compressed voice of FIG. 3B, (1) the pitch of the voice does not change and the speed increases, (2) the naturalness of the voice is not impaired, and (3) each phoneme It was characterized by being audible (4) no noisy sounds.

[0028]

As described above, according to the present invention,
By including the theory of wavelet transform in its basic operation and performing iterative processing that imposes a constraint condition that approaches the given wavelet coefficient, it is possible to estimate the signal corresponding to the given wavelet coefficient and Since the conversion is also equivalent to the operating principle of the auditory mechanism, when applied to a voice signal, the edited and processed signal has the effect of being heard naturally by humans. Claim 2
According to the invention of (1), the amount of calculation can be significantly reduced and the memory capacity to be used is smaller than that of the invention of claim 1.

[Brief description of drawings]

FIG. 1 is a flowchart showing an embodiment of the invention of claim 1;

FIG. 2 is a flow chart showing an embodiment of the invention of claim 2;

3B is a diagram showing a voice waveform, and FIG. 3A is a diagram showing a waveform obtained by time-compressing the waveform of B by applying the embodiment of FIG.

FIG. 4 is a diagram showing how the wavelet coefficient of the temporary estimation signal approaches a given wavelet coefficient by iterative processing.

Claims (2)

[Claims] 1. A first process of wavelet transforming a temporary estimated signal and determining whether a square of a difference between a wavelet coefficient obtained by the wavelet transform and a given wavelet coefficient is a predetermined value or less. If the second process and the second process determines that the value is equal to or more than the predetermined value, the difference of 2 is obtained.
The third process for calculating the signal that minimizes the power to obtain the next temporary estimated signal and the first, second, and third processes are repeated, and in the second process, the square of the difference is equal to or less than a predetermined value. If it is determined that
A signal processing method comprising: a fourth process of using a temporary estimated signal at that time as an estimated signal for the given wavelet coefficient. 2. A first process of wavelet transforming a temporary estimated signal, a second process of determining whether a wavelet coefficient obtained by the wavelet transform is sufficiently close to a given wavelet coefficient, and a second process thereof. If it is not determined that the wavelet coefficients are sufficiently close in the processing, a third processing for replacing the amplitude of the wavelet coefficient obtained in the first processing with the amplitude of the given wavelet coefficient, and the wavelet coefficient replaced in the third processing are reversed. If it is determined in the second process that the fourth process in which the signal obtained by the wavelet transformation and the obtained signal is the next temporary estimated signal and the first, second, third and fourth processes are repeated are sufficiently close to each other in the second process, A signal processing method comprising: a fifth process of using the provisional estimated signal at that time as an estimated signal for the given wavelet coefficient.