Data processing: measuring – calibrating – or testing – Measurement system – Measured signal processing
Reexamination Certificate
2001-02-09
2004-02-10
Hoff, Marc S. (Department: 2857)
Data processing: measuring, calibrating, or testing
Measurement system
Measured signal processing
C702S039000, C702S054000, C702S074000, C702S190000, C702S197000, C700S028000, C700S044000, C700S073000, C700S173000, C381S094100, C381S099000, C379S390020, C379S390030, C379S386000, C379S388060, C367S043000, C367S045000, C367S056000, C367S129000
Reexamination Certificate
active
06691073
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention pertains to systems for recovering original signal information or content by processing multiple measurements of a set of mixed signals. More specifically the invention pertains to adaptive systems for recovering several original signals from received measurements of their mixtures. In order to understand the problem solved by the invention, and the approach of the prior art to solve this problem, the following problem statement is helpful: With reference to
FIG. 1
of the attached drawings, consider N independent signals s
1
(t), . . . , and S
N
(t). These signals may represent any of, or a combination of, independent speakers or speeches, sounds, music, radio-based or light based wireless transmissions, electronic or optic communication signals, still images, videos, etc. These signals may be delayed and superimposed with one another by means of natural or synthetic mixing in the medium or environment through which they propagate. One consequently desires an architecture, framework, or device
20
that, upon receiving the delayed and superimposed signals, works to successfully separate the independent signal sources using a set of appropriate algorithms and procedures for their applications.
2. Discussion of Related Art
The recovery and separation of independent sources is a classic but difficult signal processing problem. The problem is complicated by the fact that in many practical situations, many relevant characteristics of both the signal sources and the mixing media are unknown.
Two main categories of methods are used:
1. Neurally inspired adaptive algorithms (e.g., U.S. Pat. Nos. 5,383,164 and 5.315,532), and
2. Conventional discrete signal processing (e.g., U.S. Pat. Nos. 5,208,786 and 5.539,832).
Neurally inspired adaptive arhitectures and algorithms follow a method originally proposed by J. Herault and C. Jutten, now called the Herault-Jutten (or HJ) algorithm. The suitability of this set of methods for CMOS integration have been recognized. However, the standard HJ algorithm is at best heuristic with suggested adaptation laws that have been shown to work mainly in special circumstances. The theory and analysis of prior work pertaining to the HJ algorithm are still not sufficient to support or guarantee the success encountered in experimental simulations. Herault and Jutten recognize these analytical deficiencies and they describe additional problems to be solved. Their proposed algorithm assumes a linear medium and filtering or no delays. Specifically, the original signals are assumed to be transferred by the medium via a matrix of unknown but constant coefficients. To summarize, the Herault-Jutten method (i) is restricted to the full rank and linear static mixing environments, (ii) requires matrix inversion operations, and (iii) does not take into account the presence of signal delays. In many practical applications, however, filtering and relative delays do occur. Accordingly, previous work fails to successfully separate signals in many practical situations and real world applications.
Conventional signal processing approaches to signal separation originate mostly in the discrete domain in the spirit of traditional digital signal processing methods and use the statistical properties of signals. Such signal separation methods employ computations that involve mostly discrete signal transforms and filter/transform function inversion. Statistical properties of the signals in the form of a set of cumulants are used to achieve separation of mixed signals where these cumulants are mathematically forced to approach zero. This constitutes the crux of the family of algorithms that search for the parameters of transfer functions that recover and separate the signals from one another. Calculating all possible cumulants, on the other hand, would be impractical and too time consuming for real time implementation.
The specifics of these methods are elaborated in these categories below.
1. Neurally Inspired Architectures and Algorithms for Signal Separation
These set of neurally inspired adaptive approaches to signal separation assume that the “statistically independent” signal vector S(t)=[s
1
(t), . . . , and s
N
(t)]
T
is mixed to produce the signal vector M(t). The vector M(t) is received by the sensors (e.g, microphones, antenna, etc.).
Let the mixing environment be represented by the general (static or dynamic) operator ℑ. Then,
M
(
t
)=ℑ(
S
(
t
)) Equation (1)
There are several formulations that can be used to invert the mixing process, i.e., operator ℑ in a “blind” fashion where no apriori knowledge exists as to the nature or content of the mixing operator ℑ or the original sources S(t). We group these into two categories, static and dynamic. Additional distinctions can be made as to the nature of the employed adaptation criteria, e.g., information maximization, minimization of high order cumulants, etc.
1.1. The Static Case
The static case is limited to mixing by a constant nonsingular matrix. Let us assume that the “statistically independent” signal vector S(t)=[s
1
(t), . . . , and s
N
(t)]
T
is mixed to produce the signal vector M(t). Specifically, let the mixing operator ℑ be represented by a constant matrix A, namely
M
(
t
)=
AS
(
t
) Equation (2)
In
FIG. 2
, two architectures that outline the modeling of the mixing and the separation environments and processes are shown. The architecture in FIG.
2
(
a
) necessarily computes the inverse of the constant mixing matrix A, which requires that A is invertible, i.e., A
−1
exists.
The alternate architecture in FIG.
2
(
b
) does not impose this restriction in that upon convergence the off diagonal elements of the matrix D are exactly those of the off diagonal elements of the matrix A. In this case, however, diagonal elements of the matrix A are restricted to equal “1.0.” By setting the diagonal elements of D to zero, one essentially concludes that the mixing process is invertible even if the mixing matrix is not.
In both cases, S(t) is the set of unknown sources, M(t) is the set of mixtures, U(t) is the set of separated signals that estimate S(t), and Y(t) is the set of control signals used to update the parameters of the unmixing process. As shown in
FIG. 2
, the weight update utilizes a function of the output U(t).
In the first case, we labeled the unmixing matrix W, and in the second case we labeled it D. Note that D has zero diagonal entries. The update of the entries of these two matrices is defined by the criteria used for signal separation, discrimination or recovery, e.g., information maximization, minimization of higher order cumulants, etc.
As an example, one possible weight update rule for the case where
U
(
t
)=
WM
(
t
) Equation (3)
could be
{dot over (w)}
ij
=&eegr;[W
−T
+g
″(
u
)/
g
′(
u
)
M
T
]
ij
Equation (4)
where &eegr; is sufficiently small, g is an odd function, and M is the set of mixtures, U is the set of outputs which estimate the source signals, subscript T denotes transpose, and −T denotes inverse of transpose. Note that the function g( ) plays an additional role in the update which can be related to the above diagram as
Y
(
t
)=
g
(
U
(
t
)) Equation (5)
One uses Equation (4) to update the entries of W in Equation (3). Through this is an iterative update procedure, the entries of W converge so that the product WA is nearly equal to the identity matrix or a permutation of the identity matrix.
On the other hand, in the second case, one potentially useful rule for the update of the D matrix entries d
ij
is generically described as
{dot over (d)}
ij
=&eegr;f
(
u
i
(
t
))
g
(
u
j
(
t
)) Equation (6)
where &eegr; is sufficiently small. In practice some useful functions for f(·) include a cubic function, and for g(·) include a hyperbolic tangent function. When using this procedure, one computationally solves fo
Erten Gamze
Salam Fathi M.
Brooks & Kushman P.C.
Clarity Technologies Inc.
Desta Elias
Hoff Marc S.
LandOfFree
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