Data processing: speech signal processing – linguistics – language – Speech signal processing – Recognition
Reexamination Certificate
1999-04-01
2001-06-19
{haeck over (S)}mits, T{overscore (a)}livaldis I. (Department: 2641)
Data processing: speech signal processing, linguistics, language
Speech signal processing
Recognition
C704S219000, C704S220000, C379S386000
Reexamination Certificate
active
06249762
ABSTRACT:
BACKGROUND OF THE INVENTION
(1) Field of the Invention
The present invention relates to a method for detecting signals in noise. More specifically, the present invention relates to the separation of known or unknown time series data into its narrowband and broadband components.
(2) Description of the Prior Art
Many applications require the identification of a desired signal within undesired random signals (noise) which is received with, and often interferes with, the desired signal. For example, in sonar systems randomly generated sounds from both natural and man-made sources give rise to a noise that interferes with desired acoustic signals. The detection and identification of a specific target, such as an underwater vehicle, requires a system which can detect a signal corresponding to the target within received data containing both the signal and noise.
Underwater acoustic signals are often complicated, consisting of a superposition:
x
(
t
)
=
∑
k
=
1
p
n
k
(
t
)
+
b
(
t
)
t
o
≤
t
≤
t
o
+
T
(
1
)
of non-stationary narrowband (hereinafter designated as NB) n
k
(t) and broadband (hereinafter designated as BB) b(t) components. Such signals arise from a variety of sources, such as ship machinery, marine mammals, drilling platforms, and active sonars.
FIG. 1
illustrates what a typical underwater acoustic spectrum might look like, consisting of a superposition of narrowband line-like components plus a broadband component. The BB component itself can be colored, with many local spectral peaks and valleys.
There is a need for the separation of the signal x(t) into the constituent NB:n
k
(t)=S
p
k=1
n
k
(t) and BB:b(t) time series components when little or nothing is known about the NB and BB components and only a short data record is available. This is of great importance in sonar, especially passive sonar, where the desirable signal (for detection, classification, and localization) is often either the NB or BB component and the other is regarded as interference.
Existing approaches primarily deal with power spectrum estimation of the composite data, rather than recovering the constituent narrowband and broadband time series. Having the separated narrowband and broadband time series available is very useful since it allows many additional forms of processing (processing which is impossible or difficult to do using only the power spectrum), such as extraction of time series statistics, improved wavelet and Wigner analysis, pattern recognition, and parametric modeling.
The separation of the time series data into the NB and BB time series components is difficult. Wiener filtering (see S. Haykin, “Adaptive Filter Theory, Third Edition”, Prentice Hall, 1996) is not practical since the covariance or spectral densities of the NB and BB components are not known. Parametric methods, e.g., MA (Moving Average), AR (Auto Regressive), ARMA (Auto Regressive Moving Average) modeling (see P. Stoica et al., “Introduction to Spectral Analysis”, Prentice Hall, 1997), require choosing a model type for the underlying broadband component and for each of the NB components present. This is difficult since nothing is known about the NB and BB components. Adaptive methods applied directly to the time series, such as adaptive notch filters and line enhancers (see S. Haykin, supra) and Principal Component Inverse (PCI) method (see D. Tufts et al., “Data Adaptive Estimation by Singular-Value Decomposition of a Data Matrix” Proc. IEEE, Vol. 7, pp. 684-685, 1982; I. P. Kirsteins et al., “Adaptive Detection Using Low Rank Approximation to a Data Matrix” IEEE, Trans. Aerospace and Elect. Sys., Vol. 30, No. 1, pp. 55-57, 1994), tend to perform poorly when the broadband spectrum has a large dynamic range. That is, if a weak NB component is present in a “valley” of the BB spectrum, the notch filter tracker or PCI method might lock onto a nearby peak of the BB spectrum and filter it as the NB component, rather than the true NB component.
SUMMARY OF THE INVENTION
Accordingly, an object of the subject invention is to provide a new method, based on Thomson's multiple taper spectral estimation (hereinafter designated as MTSE) technique (see D. J. Thompson “Spectral Estimation and Harmonic Analysis”, Proc. of IEEE, Vol. 70, No. 9, pp. 1055-1096, 1992; “An Overview of Multi-Window and Quadratic-Inverse Spectrum Estimation Method” (ICASSP-94, Vol. VI, pp. 185-194, 1994; P. Stoica, supra), and PCI method (see D. Tufts, supra; I. P. Kirsteins, supra), which alleviates the problems of false tracking inherent in adaptive notch filters and adaptation to the background BB and NB components.
Thomson proposed Multiple Taper Spectral Estimation (MTSE) (see D. J. Thompson, infra; P. Stoica, supra) for spectral analysis of complicated non-stationary data consisting of lines plus a background component with continuous spectrum in which the physical processes generating the data were poorly understood. A multiple taper spectral estimate, as shown in
FIG. 2
, is given by:
|
X
_
(
f
k
)
2
=
1
K
&LeftDoubleBracketingBar;
U
H
D
(
f
k
)
x
&RightDoubleBracketingBar;
2
F
(
2
)
where U is a N×K matrix whose K columns are the principal Discrete Prolate Spherioidal Sequence's (DPSS's) u
k
n
(N,W), which are the eigenvectors of the N×N matrix,
[
R
]
m
,
n
=
sin
2
π
W
(
n
-
m
)
π
(
n
-
m
)
,
(
3
)
arranged to correspond to the eigenvalues in descending order, D(f)=diag(1, e
−i2xf
, . . . , e
−i(N−1)2xf
), W is the analysis bandwidth parameter, and K
~
2NW.
The matrix U in equation 2 acts as a lowpass filter with bandwidth W. Thus, the projection of the data vector x onto V
k
=D(f
k
)U
H
becomes a bandpass filtering of the data to [f
k
−W, f
k
+W]. X (f) is approximately the average energy in the band [f
k
−W, f
k
+W]. For a given set of frequency points, f
1
, . . , f
M
, the spectrum estimate of equation 2 is analogous to filtering x into the subbands {[f
0
−W, f
0
+W], [f
1
−W], f
1
+W, . . . , [f
M
−W, f
M
+W]}, as shown in
FIG. 2
, and then calculating the average energy in each band.
The multiple taper method provides a simple and effective way of locating and removing tonals from the underlying continuous BB spectrum component. To avoid mistaking local BB spectral peaks as NB components and for avoiding interference from adjacent tonals, Thomson proposed that the estimation and removal of tonals be done separately within each subband, as depicted in FIG.
2
. The main idea is that the projection of x onto V
k
effectively isolates the frequency band [f
k
−W, f
k
+W] from out of band tonals, and if W is properly chosen, the background noise spectrum is approximately locally flat or white. Thus, effects from out of band tonals and problems of locking onto local spectral peaks of the broadband component are minimized.
An object of the invention is to use the methodology of MTSE to recover the NB:n(t)=&Sgr;
p
k=1
n
k
(t) and BB:b(t) time series components. In concatenation of the matrix filter banks V
k
into matrix [V
1
|V
2
| . . . |V
h
], the total filter bank output can be written as z=V
H
x
. If rank [V]=N (where N is the number of time series samples in x), then×can be reconstructed from z using x=(V
H
)#z, where operator # means pseudo-inverse. This suggests that an estimate of the broadband time series might be x
BB
=(V
H
)#
Zclean
where
Z
clean
T
=[clean(V
1
H
x)
T
|clean(V
2
H
x)
T
. . . |clean(V
m
H
x)
T
] (4)
and the operator “clean” depicts the tonal removal procedure depicted in
FIG. 2
, applied to the subbands where tonals are present.
Two problems with the above procedure are: (1) the NB components may not necessarily be pure tones (they c
Fay John W.
Kirsteins Ivars P.
Mehta Sanjay K.
Lall Prithvi C.
McGowan Michael J.
Oglo Michael F.
The United States of America as represented by the Secretary of
{haeck over (S)}mits T{overscore (a)}livaldis I.
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