Data processing: speech signal processing – linguistics – language – Speech signal processing
Reexamination Certificate
1999-08-20
2002-08-06
Banks-Harold, Marsha D. (Department: 2654)
Data processing: speech signal processing, linguistics, language
Speech signal processing
C704S233000, C375S340000
Reexamination Certificate
active
06430528
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates generally to estimating multiple electrical or acoustic source signals from only mixtures of these signals, and more specifically to obtaining in real-time estimates of the mixing parameters of such signals. Furthermore, in the present invention a demixing (or separation) of a mixture of the signals is accomplished by using estimated mixing parameters to partition a time-frequency representation of one of the mixture signals into estimates of its source signals.
2. Description of the Prior Art
Blind source separation (BSS) is a class of methods that are used extensively in areas where one needs to estimate individual original signals from a linear mixture of the individual signals. One area where these methods are important is in the electromagnetic (EM) domain, such as in wired or wireless communications, where nodes or receiving antennas typically receive a linear mixture of delayed and attenuated EM signals from a plurality of signal sources. A further area where these methods are important is in the acoustic domain where it is desirable to separate one voice or other useful signal being received from background noise being received by one or more receivers, such as microphones in a telephone or hearing aid (where the mixtures of acoustic signals are received by one or more microphones and the mixtures often contain undesirable signals such as other voices or environmental noise). Even further areas of application of BSS techniques of the present invention are in surface acoustic waves processing, signal processing and radar signal processing.
The difficulty in separating the individual original signals from their linear mixtures is that in many practical applications little is known about the original signals or the way they are mixed. An exception, however, is in wireless communications where training sequences of signals known ahead of time are transmitted intermixed with the useful data signals, thereby allowing for transmission channel estimation. These training sequences typically take a large portion of the available channel capacity and therefore this technique is undesirable.
In order to do demixing blindly some assumptions on the statistical nature of signals are typically made. Some solutions to BSS are known in the art for the limited case of instantaneous mixing, i.e., when the signals arrive at the receivers without delay in propagation, and are non-degenerately mixed, that is, when the number of signal emitters is less than or equal to the number of signal receivers. Such solutions are typically cumbersome since they involve computation of statistical quantities of signals that are third or higher order moments of signal probability distributions. The demixing is most often done under the assumption of statistical independence of signals, which implies that all moments of the signals factorize. One useful feature of the present invention is that a considerably weaker assumption on the nature of the signals is used, namely, W-disjoint orthogonality. We assume that our sources are deterministic functions for which the Fourier transform is well defined and that W(t) is a function that is localized in time. Then we call two sources, s
i
(t) and s
k
(t), W-disjoint orthogonal if the supports of the Fourier transform of the W-windowed sources, denoted ŝ
i
W
(&ohgr;,t) and ŝ
k
W
(&ohgr;,t), are disjoint for all t, where,
ŝ
i
W
(&ohgr;,
t
)=∫
−∞
∞
W
(&tgr;−
t
)
s
i
(&tgr;)
e
−j&ohgr;&tgr;
d&tgr;.
(1)
In other words, let us denote the support of ŝ
i
W
(&ohgr;, t) with &OHgr;
i
. Then s
i
(t) and s
k
(t) are W-disjoint orthogonal if,
&OHgr;
i
∩&OHgr;
k
=∅. (2)
Note, the above definition is valid if the Fourier transform of the signals are distributions.
A special case is if we choose W to be constant. Then two functions are W-disjoint orthogonal if their Fourier transforms have disjoint support. In this case, we will call them globally disjoint orthogonal, or simply, disjoint orthogonal. Two time dependent signals s
i
(t), s
k
(t) are disjoint orthogonal if,
∫
s
i
(
t
)·
{overscore (s)}
k
(
t
+&tgr;)·dt=0
∀&tgr;i,k
=1, . . . , N.
In practice condition (2) does not have to hold exactly. It is sufficient for the present invention if the sources are weakly W-disjoint orthogonal which we is defined formally as,
|
ŝ
i
W
(&ohgr;,
t
)|>>1
→|ŝ
k
W
(&ohgr;,
t
)<<1
,∀k≠i,∀t,∀&ohgr;.
(
3)
In order to differentiate (2) from (3), (2) is sometimes referred to as strong W-disjoint orthogonality. While we have used the Fourier transform in (1), it is important to note that any appropriate transform can be used (e.g., wavelet transforms) as long as condition (2) or (3) is satisfied.
It is generally believed in the art that computation of third and higher degree moments is necessary to demix signals in convolutive non-degenerate mixtures. In fact it has been proved by Weinstein et al., in his article entitled “Multi-channel Signal Separation by Decorrelation”, IEEE Transaction on Speech and Audio Processing, Vol. 1, No. 4, October 1993, that signals cannot be recovered from mixtures of statistically stationary and orthogonal signals for an arbitrary convolutive mixture. One useful feature of the present invention is that it presents a practical method to obviate the restriction in Weinstein et al., and establishes a practical method to demix signals mixtures from convolutive mixtures. In the present invention, the restriction is voided by reducing the class of signals to those that satisfy strong or weak W-disjoint orthogonality and by requiring the mixing of the signals to either have a parametric form or the corresponding mixing filters in convolutive mixing be sufficiently smooth in the frequency domain to allow extrapolation from the set of points on which the support of signals is non-zero. In practice weak W-disjoint orthogonality of signals is very frequently observed, as in the examples of speech and environmental acoustic noise, or can be imposed, such as on the waveform of an emitted EM signal in the case of wireless communications.
Although a number of methods are known in the state of the art for blind demixing of signal mixtures, as noted above most of them use higher order statistics to effect the demixing, such as taught by Bell et al. in their article entitled “An information-maximization approach to blind separation and blind deconvolution”, Neural Computation, vol. 7 pp. 1129-1159, 1995. The least computationally intensive methods known in the state of the art use second order statistics. They typically work by simplifying the demixing problem to an optimization problem so that the optimization objective function is a function of signal auto- and cross-correlations such as taught by Weinstein et al. in their forenoted article. However, even these methods are known to place an exceptional demand on computational resources, especially when there is need for real-time or on-line implementations. A useful feature of the present invention is that the necessary computations involve only first order moments, i.e., the signal values themselves, and no complicated computations of signal statistics is needed. This is particularly advantageous since computation of statistical properties of signals is typically prone to large measurement and estimation errors.
Yet another useful feature of the present invention is that instead of statistical orthogonality most commonly used in second order statistical methods, e.g., as assumed in the forenoted article by Weinstein et al., the present invention uses a deterministic definition of orthogonality. The use of W-disjoint orthogonality condition among other things is advantageous because it is much simpler test than one for statistical orthogonality. To test for statistical orthogonality one needs to create a statistical ensemble of si
Jourjine Alexander
Rickard Scott T.
Yilmaz Ozgur
Abebe Daniel
Banks-Harold Marsha D.
Paschburg Donald B.
Siemens Corporate Research Inc.
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