Adaptive cross correlator apparatus comprising adaptive controller for adaptively adjusting transfer functions of two filters

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BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to an adaptive cross correlator apparatus, in particularly, to an adaptive cross correlator comprising two filters and an adaptive controller for adaptively adjusting transfer functions of the two filters.

2. Description of the Related Art

The most common method of determining the time delay between two signals x.sub.1 (t) and x.sub.2 (t) is to compute a cross correlation value Rx.sub.1 x.sub.2 (.tau.) of a cross correlation function expressed by the following Equation (1): ##EQU1## where the argument .tau. that maximizes the value of the Equation (1) provides an estimate of the delay. In order to improve this estimation, it is preferred to pre-filter the two signals x.sub.1 (t) and x.sub.2 (t) prior to the operation of cross correlation. This simple, but very important process is known as a generalized cross correlation (See, for example, G. Clifford Carter, "Coherence and time delay estimation", Proceedings of IEEE, Vol. 75, No. 2, pp. 236-255, in February, 1987; hereinafter, referred to as a reference document 1). The conventional generalized cross correlator apparatus implemented as a pre-processor for inputted waveforms is shown in FIG. 2.

As shown in FIG. 2, inputted signals x.sub.1 (t) and x.sub.2 (t) are received by, for example, finite impulse response filters (hereinafter referred to as FIR filters) 1 and 2. Then, outputted signals y.sub.1 (t) and y.sub.2 (t) showing filtering results are outputted from the FIR filters 1 and 2, and are inputted to a cross correlator 3. The cross correlator 3 performs a computation of cross correlation of the Equation (1) based on the inputted signals y.sub.1 (t) and y.sub.2 (t) so as to calculate and output a cross correlation value Ry.sub.1 y.sub.2 (.tau.).

The reference document i shows that, in the cross correlator apparatus of FIG. 2, if transfer functions H.sub.1 (.omega.) and H.sub.2 (.omega.) of the FIR filters 1 and 2 are appropriately selected, the FIR filters 1 and 2 having transfer functions H.sub.1 (.omega.) and H.sub.2 (.omega.) can be remarkably improved in the estimates of filtering time delay. The two FIR filters 1 and 2 are able to emphasize the signal passed to the cross correlator 3 at those frequencies at which the coherence therebetween or signal-to-noise ratio (SNR) is the highest. For example, it is well known to those skilled in the art how the transfer functions H.sub.1 (.omega.) and H.sub.2 (.omega.) of the FIR filters 1 and 2 should be chosen in order to achieve the time delay estimation (TDE) with minimum errors on the assumption that the two signals are Gaussian and contain Gaussian noise. Further, the reference document 1 also proposes a whole set or group of ad hoc filters.

However, this approach of the conventional method has had such a problem that errors would occur theoretically in detecting the time delay within non-Gaussian noise and estimating the signal-to-noise ratio.

SUMMARY OF THE INVENTION

An essential object of the present invention is therefore to provide an adaptive cross correlator apparatus capable of adaptively adjust transfer functions H.sub.1 (.omega.) and H.sub.2 (.omega.) of two filters so that no error occurs when detecting the time delay between two inputted signals within a non-Gaussian noise, and without giving a signal-to-noise ratio.

In order to achieve the aforementioned objective, according to one aspect of the present invention, there is provided an adaptive cross correlator apparatus comprising:

first receiving means for receiving a signal and outputting the received signal as a first signal;

second receiving means for receiving a further signal and outputting the received further signal as a second signal, said second receiving means provided at a position different from that of said first receiving means;

first filtering means for filtering the first signal outputted from said first receiving means with a first changeable transfer function and outputting a filtered first signal;

second filtering means for filtering the second signal outputted from said second receiving means with a second changeable transfer function and outputting a filtered second signal;

cross correlator means for calculating a cross correlation value by using a predetermined cross correlation function based on the filtered first signal outputted from said first filtering means and the filtered second signal outputted from said second filtering means; and

adaptive control means for calculating a discriminant function value representing a misclassification measure of the first and second signals, based on the cross correlation value outputted from said cross correlator means and a true delay between the first and second signals, and for adaptively adjusting the first transfer function of said first filtering means and the second transfer function of said second filtering means so that the calculated discriminant function value becomes a minimum.

The above-mentioned adaptive cross correlator apparatus preferably further comprises:

delay calculating means for calculating a delay between the first and second signals, based on the cross correlation value outputted from said cross correlator means, after a process of adaptive control performed by said adaptive control means.

In the above-mentioned adaptive cross correlator apparatus, said adaptive cross correlator apparatus is provided for separating a first speech signal generated by a first sound source and a second speech signal generated by a second sound source, from each other, the first and second speech signals having spectral characteristics different from each other and being generated at locations different from each other,

wherein said adaptive cross correlator apparatus preferably further comprises:

delay means for delaying the filtered first signal outputted from said first filtering means, by a delay amount equal to a delay between said first and second receiving means which is calculated by said delay calculation means when the first speech signal generated by the first sound source is received by said first and second receiving means, and for outputting a delayed signal; and

adding means for adding up the delayed signal outputted from said delay means and the filtered second signal outputted from said second filtering means, and for outputting a signal representing the addition result, thereby outputting an improved first speech signal.

In the above-mentioned adaptive cross correlator apparatus, the discriminant function representing the misclassification measure of the first and second signals is preferably a linearly differentiable function, and

wherein said adaptive control means adaptively adjusts the first transfer function of said first filtering means and the second transfer function of said second filtering means by using a gradient descent method so that said calculated discriminant function value becomes a minimum.

In the above-mentioned adaptive cross correlator apparatus, said first and second filtering means are preferably finite impulse filters; and

wherein said adaptive control means adaptively adjusts a filter coefficient of the finite impulse filter of said first filtering means and a filter coefficient of the finite impulse filter of said second filtering means so that said calculated discriminant function value becomes a minimum.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other objects and features of the present invention will become clear from the following description taken in conjunction with the preferred embodiments thereof with reference to the accompanying drawings throughout which like parts are designated by like reference numerals, and in which:

FIG. 1 is a block diagram of an adaptive cross correlator apparatus of a preferred embodiment according to the present invention;

FIG. 2 is a block diagram of a cross correlator apparatus of a prior art example;

FIG. 3 is a block diagram of coefficient changeable type FIR filters 11 and 12 shown in FIG. 1;

FIG. 4 is a block diagram showing an application example of the adaptive cross correlator apparatus shown in FIG. 1 in a training mode;

FIG. 5 is a block diagram showing an application example of the adaptive cross correlator apparatus shown in FIG. 1 in a detection mode;

FIG. 6 is a block diagram showing an arrangement for implementing sound source separation by using the adaptive cross correlator apparatus shown in FIG. 1;

FIG. 7 is a graph showing a spectrum of a noise power used in a simulation of the adaptive cross correlator apparatus shown in FIG. 1;

FIG. 8 is a graph showing a spectrum of a noise-free clean signal power used in the simulation of the adaptive cross correlator apparatus shown in FIG. 1;

FIG. 9 is a graph showing a noisy inputted signal x.sub.1 (t) used in the simulation of the adaptive cross correlator apparatus shown in FIG. 1;

FIG. 10 is a graph showing a noisy inputted signal x.sub.2 (t) used in the simulation of the adaptive cross correlator apparatus shown in FIG. 1;

FIG. 11 is a graph showing a discriminant function value versus a number of accumulative sampling times (corresponding to elapsed time) when adaptation is allowed in the simulation of the adaptive cross correlator apparatus shown in FIG. 1;

FIG. 12 is a graph showing a discriminant function value versus a number of accumulative sampling times (corresponding to elapsed time) when no adaptation is allowed in the simulation of the adaptive cross correlator apparatus shown in FIG. 1;

FIG. 13 is a graph showing a detected delay .tau..sub.estimated versus a number of accumulative sampling times (corresponding to elapsed time) when adaptation is allowed in the simulation of the adaptive cross correlator apparatus shown in FIG. 1;

FIG. 14 is a graph showing a detected delay .tau..sub.estimated versus a number of accumulative sampling times (corresponding to elapsed time) when no adaptation is allowed in the simulation of the adaptive cross correlator apparatus shown in FIG. 1;

FIG. 15 is a graph showing a frequency characteristic of transfer functions H.sub.1 (.omega.)=H.sub.2 (.omega.) of the FIR filters 11 and 12 shown in FIG. 1, prior to adaptation in the simulation of the adaptive cross correlator apparatus shown in FIG. 1;

FIG. 16 is a graph showing a frequency characteristic of the transfer functions H.sub.1 (.omega.)=H.sub.2 (.omega.) of the FIR filters 11 and 12 shown in FIG. 1, after adaptation in the simulation of the adaptive cross correlator apparatus shown in FIG. 1;

FIG. 17 is a graph in which a spectrum of noise power is overlaid on the frequency characteristics of the transfer functions H.sub.1 (.omega.)=H.sub.2 (.omega.) of the FIR filters 11 and 12 shown in FIG. 1, after adaptation in the simulation of the adaptive cross correlator apparatus shown in FIG. 1; and

FIG. 18 is a graph in which a spectrum of noise-free clean signal power is overlaid on the frequency characteristics of the transfer functions H.sub.1 (.omega.)=H.sub.2 (.omega.) of the FIR filters 11 and 12 shown in FIG. 1, after adaptation in the simulation of the adaptive cross correlator apparatus shown in FIG. 1.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Preferred embodiments according to the present invention will be described below with reference to the attached drawings.

FIG. 1 is a block diagram of an adaptive cross correlator apparatus 100 of a preferred embodiment according to the present invention. The adaptive cross correlator apparatus 100 of the preferred embodiment has both of:

(a) a training mode or a learning mode in which transfer functions H.sub.1 (.omega.) and H.sub.2 (.omega.) of coefficient changeable type FIR filters 11 and 12 are adaptively adjusted based on inputted signals x.sub.1 (t) and x.sub.2 (t) which are generated by the same sound source and are transmitted along different propagation paths, wherein a relative delay occurs therebetween so that the two signals x.sub.1 (t) and x.sub.2 (t) are different from each other; and

(b) a detection mode in which a delay .tau..sub.estimated between two inputted signals x.sub.1 (t) and x.sub.2 (t) is detected based on those inputted signals x.sub.1 (t) and x.sub.2 (t).

Referring to FIG. 1, the adaptive cross correlator apparatus 100 of the present preferred embodiment comprises:

(a) coefficient changeable type FIR filters 11 and 12 for filtering the inputted signals x.sub.1 (t) and x.sub.2 (t), respectively;

(b) a cross correlator 13 for computing or calculating a cross correlation value by performing a calculation of the Equation (1) based on the outputted signals y.sub.1 (t) and y.sub.2 (t) outputted from the FIR filters 11 and 12;

(c) an adaptive controller 10, which operates in the training mode, for adaptively adjusting the transfer functions H.sub.1 (.omega.) and H.sub.2 (.omega.) of the FIR filters 11 and 12, more specifically, for adaptively adjusting filter coefficients of the FIR filters 11 and 12 so as to set those filter coefficients to optimal values based on an outputted signal Ry.sub.1 y.sub.2 (.tau., t) outputted from the cross correlator 13, so that no error occurs when detecting the time delay within a non-Gaussian noise, that is, a discriminant function value representing a misclassification measure therebetween becomes a minimum value; and

(d) a delay detector 14, which operates in the detection mode, for detecting and outputting a delay .tau..sub.estimated between the inputted signals x.sub.1 (t) and x.sub.2 (t) based on the outputted signal Ry.sub.1 y.sub.2 (.tau., t) outputted from the cross correlator 13.

The adaptive cross correlator apparatus 100 of the present preferred embodiment is characterized in that the apparatus 100 adaptively adjusts the transfer functions H.sub.1 (.omega.) and H.sub.2 (.omega.) of the FIR filters 11 and 12 so that an error caused in the delay estimation is minimized. Each pair of inputted signals x.sub.1 (t) and x.sub.2 (t) is classified by the cross correlator 13 using the delay .tau..sub.estimated. The delay .tau..sub.estimated is expressed by the following Equation (2): ##EQU2## where the function "argmax" with respect to .tau. is a function that represents a value of argument .tau. at which Ry.sub.1 y.sub.2 (.tau.) becomes a maximum. In the conventional technical field of pattern recognition, Ry.sub.1 y.sub.2 (.tau.) is referred to as a discriminant function for a pair of inputted signals x.sub.1 (t) and x.sub.2 (t) . A pair of inputted signals x.sub.1 (t) and x.sub.2 (t) can be expressed, for example, by the following Equation (3):

x.sub.1 (t)=n.sub.1 (t)+s(t) x.sub.2 (t)=n.sub.2 (t)+s(t+.tau..sub.true) (3 )

where n.sub.1 (t) and n.sub.2 (t) are noise signals from noise sources, and s(t) is a signal whose delay .tau..sub.true which we, inventors try to estimate. When the delay .tau..sub.estimated differs from the true delay .tau..sub.true, namely, when .tau..sub.estimated .noteq..tau..sub.true, an estimation error occurs. In the preferred embodiment according to the present invention, a degree of misclassification, namely, a misclassification measure dx.sub.1,x.sub.2 (H.sub.1 (.omega.), H.sub.2 (.omega.)) is introduced to quantify the error in the delay estimation. The misclassification measure dx.sub.1,x.sub.2 (H.sub.1 (.omega.), H.sub.2 (.omega.)) is so set as to be positive when .tau..sub.estimated .noteq..tau..sub.true, and the misclassification measure dx.sub.1,x.sub.2 (H.sub.1 (.omega.), H.sub.2 (.omega.)) is so set as to be negative when .tau..sub.estimated =.tau..sub.true. Although there are many possible choices of measure functions for the misclassification measure, the following Equation (4) is preferably provided as the simplest definition: ##EQU3##

The function "argmax" in the right side of the second equation of the Equation (4) is a value of argument .tau. at which the discriminant function value Ry.sub.1 y.sub.2 (.tau.) becomes a maximum when .tau..noteq..tau..sub.true, and is a function that represents a maximum .tau..sub.max of the argument .tau.. In order to minimize the number of estimation errors, the respective transfer functions H.sub.1 (.omega.) and H.sub.2 (.omega.) of the FIR filters 11 and 12 are adjusted so as to minimize the misclassification measure dx.sub.1,x.sub.2 (H.sub.1 (.omega.), H.sub.2 (.omega.)). This adjustment can be achieved by the gradient descent method in the present preferred embodiment, although any suitable optimization technique such as a simulated annealing could be used theoretically. The cross correlation value is typically expressed in a general form of the cross correlation function, which changes in real time and is a function of time, as shown by the following Equation (5): ##EQU4## where w(.) is a window function that has previously been suitably chosen. For example, one possible, preferable choice for the window function w(.) is an exponential function expressed by the following Equation (6):

w(t)=e.sup.-(t/Tc), t.gtoreq.0w(t)=0, t<0 (6)

where T.sub.c is a predetermined window time constant and Tc>0. One simple way of applying such an exponentially decaying window function as shown in the Equation (6) to a discriminant function can be expressed by the following Equation (7):

Ry.sub.1 y.sub.2 (.tau., t)=(1-.alpha.)Ry.sub.1 y.sub.2 (.tau., t-1)+.alpha.y.sub.1 (t)y.sub.2 (t-.tau.), 0.ltoreq..alpha..ltoreq.1 (7)

where .alpha. is a forgetting factor, which is directly proportional to the inverse of the window time constant Tc. The time-varying equivalent of the misclassification measure defined in the Equation (4) is expressed by the following Equation (8): ##EQU5## where "argmax" in the right side of the second equation of the Equation (8) is a value of argument .tau. at which the discriminant function value Ry.sub.1 y.sub.2 (.tau., t) becomes a maximum when .tau..noteq..tau..sub.true, and is a function that represents the maximum .tau..sub.max of the argument .tau.. The transfer functions H.sub.t-1,1 (.omega.) and H.sub.t-1,2 (.omega.) of the filters 11 and 12 in the Equation (8) are updated at each time "t" using the gradient descent method expressed by the following Equation (9), respectively: ##EQU6## where the case of j=1 applies to the FIR filter 11, the case of j=2 applies to the FIR filter 12, and .eta. is a training constant that has previously been suitably chosen. In the present preferred embodiment, it is an essential requirement that the misclassification measure dx.sub.1,x.sub.2 (H.sub.t-1,1 (.omega.), H.sub.t-1,2 (.omega.)) can be linearly partially differentiated with the transfer function H.sub.t-1,j (.omega.), and the only assumptions made concerning the signal and noise statistics are:

(a) the inputted signals x.sub.1 (t) and x.sub.2 (t) as well as noise inputted along with the inputted signals x.sub.1 (t) and x.sub.2 (t) are long term stationary over a time period of the training and detection modes; and

(b) the inputted signals x.sub.1 (t) and x.sub.2 (t) as well as a noise signal inputted along with the inputted signals arrive from different spatial locations as seen from the input end of the adaptive cross correlator apparatus 100.

It is noted that the adaptive cross correlator apparatus 100 of the present preferred embodiment is unable to separate a signal and a noise which have been arrived from the same spatial location. Unlike the conventional generalized cross correlator apparatus, neither the evaluation of error-prone coherence nor the computation of error-prone signal-t