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US4894795A
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High-resolution technique for time-frequency signal analysis using modified wigner-ville analysis
Assignee: United States Department of the Navy
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Filing: 1987-04-28
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Granted: 1990-01-16
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Expires: 2007-04-28
Abstract
Abstract An apparatus and method of improving the resolution of a linear FM signal s(t)=a(t)cos φ(t) where φ(t)=2π(s o t+αt 2 ) is provided by a modified computation of the Wigner-Ville Distribution. An analytical signal ##EQU1## is translated or calculated from the received linear FM signal r(t) so that a Wigner-Ville Kernel sequence ##EQU2## is formulated. An analysis of the frequency of the kernel sequence follows in accordance with a high resolution estimation technique that may include a kind of a least squares approximation fit or an eigenvector spectral estimator such as MUSIC OR ESPRIT to provide an improved time/frequency representation having a resolution of about an order of magnitude better as compared to a conventional discrete Fourier transform frequency analyze of the kernel sequence.
Inventors
- 👤 Harper J. Whitehouse
- 👤 Boualem Boashash
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-11-05 06:21
CPC Classifications
G; G06; G06E; G06E3/00; G06E3/001; G06F; G06F2218/00; G06F2218/22
Claims Analysis
Total Claims: 43
Claim 1
Independent Claim
139 words
A method of improving the resolution of a linear FM signal s(t)=a(t) cos Φ(t) where Φ(t)=2π(s o t+αt 2 ) and in which α is a chirp parameter comprising the steps of: translating in translating means received linear FM signals r(t)=Σ N i=1 a i s(t-τ i ) to an analytic signal of the form z(t)=Σ N i=1 a i jΦ(t-τ i ); formulating in formulating means the analytic signal form z(t) into a Wigner-Ville kernel sequence z(t+τ/2)z*(t-τ/2); analyzing in analyzing means the frequency of the kernel sequence z(t+τ/2)z*(t-τ/2) by a high resolution estimation technique to provide a signal having an improved time/frequency representation; and applying the improved time/frequency representation signal in an appropriate processing means to present a degree of resolution of an order of magnitude greater than a discrete Fourier transform implemented by a fast Fourier transform.
Claim 2
Independent Claim
139 words
A method of improving the resolution of a linear FM signal s(t)=a(t) cos Φ(t) where Φ(t)=2π(s o t+αt 2 ) and in which α is a chirp parameter comprising the steps of: translating in translating means received linear FM signals r(t)=Σ N i=1 a i s(t-τ i ) to an analytic signal of the form z(t)=Σ N i=1 a i jΦ(t-τ i ); formulating in formulating means the analytic signal form z(t) into a Wigner-Ville kernel sequence z(t+τ/2)z*(t-τ/2); analyzing in analyzing means the frequency of the kernel sequence z(t+τ/2)z*(t-τ/2) by a high resolution estimation technique to provide a signal having an improved time/frequency representation; and applying the improved time/frequency representation signal in an appropriate processing means to present a degree of resolution of an order of magnitude greater than a discrete Fourier transform implemented by a fast Fourier transform.
Claim 3
Dependent Claim
21 words
A method according to claim 1 in which the high resolution estimation technique is a form of least sequences approximation fit.
Claim 4
Dependent Claim
18 words
A method according to claim 1 in which the high resolution estimation technique is known as Prony's method.
Claim 5
Dependent Claim
20 words
A method according to claim 1 in which the high resolution estimation technique is known as the Maximum Entropy method.
Claim 6
Dependent Claim
21 words
A method according to claim 1 in which the high resolution estimation technique is known as Auto Regressive Moving Average method.
Claim 7
Dependent Claim
19 words
A method according to claim 1 in which the high resolution estimation technique is known as Maximum Likelihood method.
Claim 8
Dependent Claim
26 words
A method according to claim 1 in which the translating to the analytic signal includes computing in the time domain using finite impulse response (FIR) filters.
Claim 9
Dependent Claim
26 words
A method according to claim 7 in which the translating to the analytic signal includes computing in the Fourier domain using a fast Fourier transform (FFT).
Claim 10
Dependent Claim
24 words
A method according to claim 7 in which the translating to the analytic signal includes computing in the Fourier domain using a chirp-z-transform (CZT).
Claim 11
Dependent Claim
26 words
A method according to claim 1 in which the translating to the analytic signal includes computing in the time domain using infinite impulse response (IIR) filters.
Claim 12
Dependent Claim
19 words
A method according to claim 1 in which the formulating step is the analog computing optically using Bragg cells.
Claim 13
Dependent Claim
18 words
A method according to claim 1 in which the formulating step is the digital computing using semiconductor technology.
Claim 14
Independent Claim
140 words
A method of improving the resolution of a linear FM signal s(t)=a(t) cos Φ(t) where Φ(t)=2π(s o t+αt 2 ) and in which α is a chirp parameter comprising the steps of: translating in translating means received linear FM signals r(t)=Σ N i=1 a i s(t-τ i ) to an analytic signal of the form z(t)=Σ N i=1 a 1 jΦ(t-τ i ); formulating in formulating means the analytic signal form z(t) into a Wigner-Ville kernel sequence z(t+τ/2)z*(t-τ/2); analyzing in analyzing means the frequency of the kernel sequence z(t+τ/2)z*(t-τ/2) by a high resolution eigenvector spectral estimator to provide a signal having an improved time/frequency representation; and applying the improved time/frequency representation signal in an appropriate processing means to present a degree of resolution of an order of magnitude greater than a discrete Fourier transform implemented by a fast Fourier transform.
Claim 15
Independent Claim
140 words
A method of improving the resolution of a linear FM signal s(t)=a(t) cos Φ(t) where Φ(t)=2π(s o t+αt 2 ) and in which α is a chirp parameter comprising the steps of: translating in translating means received linear FM signals r(t)=Σ N i=1 a i s(t-τ i ) to an analytic signal of the form z(t)=Σ N i=1 a 1 jΦ(t-τ i ); formulating in formulating means the analytic signal form z(t) into a Wigner-Ville kernel sequence z(t+τ/2)z*(t-τ/2); analyzing in analyzing means the frequency of the kernel sequence z(t+τ/2)z*(t-τ/2) by a high resolution eigenvector spectral estimator to provide a signal having an improved time/frequency representation; and applying the improved time/frequency representation signal in an appropriate processing means to present a degree of resolution of an order of magnitude greater than a discrete Fourier transform implemented by a fast Fourier transform.
Claim 16
Dependent Claim
20 words
A method according to claim 13 in which the high resolution estimation technique is known as multiple signal classification (MUSIC).
Claim 17
Dependent Claim
21 words
A method according to claim 13 in which the high resolution estimation technique is known as eigenvector signal parameter technique (ESPRIT).
Claim 18
Dependent Claim
18 words
A method according to claim 13 in which the high resolution estimation technique is known as Pisarenko's method.
Claim 19
Dependent Claim
27 words
A method according to claim 13 in which the translating to an analytic signal step includes computing in the time domain using finite impulse response (FIR) filters.
Claim 20
Dependent Claim
24 words
A method according to claim 17 in which the translating step includes a computing in the Fourier domain using a fast Fourier transform (FFT).
Claim 21
Dependent Claim
22 words
A method according to claim 17 in which the translating step includes a computing in the Fourier domain using a chirp-z-transform (CZT).
Claim 22
Dependent Claim
27 words
A method according to claim 13 in which the translating to an analytic signal step includes computing in the time domain using infinite impulse response (IIR) filters.
Claim 23
Dependent Claim
19 words
A method according to claim 13 in which the formulating step is the analog computing optically using Bragg cells.
Claim 24
Dependent Claim
18 words
A method according to claim 13 in which the formulating step is the digital computing using semiconductor technology.
Claim 25
Independent Claim
126 words
An apparatus for improving the resolution of a linear FM signal s(t)=a(t) cos Φ(t) where Φ(t)=2π(s o t+αt 2 ) and in which α is a chirp parameter comprising: means for translating received linear FM signals (r(t)=Σ N i=1 a i s(t-τ i ) to an analytic signal of the form z(t)=Σ N i=1 a i jΦ(t-96 i ); means for formulating the analytic signal form z(t) into a Wigner-Ville kernel sequence z(t+τ/2)z*(t-τ/2); and means for analyzing the frequency of the kernel sequence z(t+τ/2)z*(t-τ/2) by a high resolution estimator technique to provide a signal having an improved time/frequency representation to achieve a degree of resolution in associated processing means of an order of magnitude greater than a discrete Fourier transform implemented by a fast Fourier transform.
Claim 26
Independent Claim
126 words
An apparatus for improving the resolution of a linear FM signal s(t)=a(t) cos Φ(t) where Φ(t)=2π(s o t+αt 2 ) and in which α is a chirp parameter comprising: means for translating received linear FM signals (r(t)=Σ N i=1 a i s(t-τ i ) to an analytic signal of the form z(t)=Σ N i=1 a i jΦ(t-96 i ); means for formulating the analytic signal form z(t) into a Wigner-Ville kernel sequence z(t+τ/2)z*(t-τ/2); and means for analyzing the frequency of the kernel sequence z(t+τ/2)z*(t-τ/2) by a high resolution estimator technique to provide a signal having an improved time/frequency representation to achieve a degree of resolution in associated processing means of an order of magnitude greater than a discrete Fourier transform implemented by a fast Fourier transform.
Claim 27
Dependent Claim
24 words
An apparatus according to claim 23 in which the means for analyzing includes a means for implementing a form of least squares approximation fit.
Claim 28
Dependent Claim
30 words
An apparatus according to claim 23 in which the means for translating to the analytic signal includes means for computing in the time domain using finite impulse response (FIR) filters.
Claim 29
Dependent Claim
30 words
An apparatus according to claim 23 in which the means for translating to the analytic signal includes means for computing in the time domain using infinite impulse response (IIR) filters.
Claim 30
Dependent Claim
30 words
An apparatus according to claim 23 in which the means for translating to the analytic signal includes means for computing in the Fourier domain using a fast Fourier transform (FFT).
Claim 31
Dependent Claim
28 words
An apparatus according to claim 23 in which the means for translating to the analytic signal includes means for computing in the Fourier domain using a chirp-z-transform (CZT).
Claim 32
Dependent Claim
27 words
An apparatus accordin to claim 23 in which the means for formulating further includes a means for optically implementing in analog using an array of Bragg cells.
Claim 33
Dependent Claim
23 words
An apparatus according to claim 23 in which the means for formulating further includes a means for digitally implementing using conventional semiconductor technology.
Claim 34
Independent Claim
127 words
An apparatus for improving the resolution of a linear FM signal s(t)=a(t) cos Φ(t) where Φ(t)=2π(s o t+αt 2 ) and in which α is a chirp parameter comprising: means for translating received linear FM signals r(t)=Σ N i=1 a i s(t-τ i ) to an analytic signal of the form z(t)=Σ N i=1 a i jΦ(t-τ i ); means for formulating the analytic signal form z(t) into a Wigner-Ville kernel sequence z(t+τ/2)z*(t-τ/2); and means for analyzing the frequency of the kernel sequence z(t+τ/2)z*(t-τ/2) by a high resolution eigenvector spectral estimator to provide a signal having an improved time/frequency representation to achieve a degree of resolution in associated processing means of an order of magnitude greater than a discrete Fourier transform implemented by a fast Fourier transform.
Claim 35
Independent Claim
127 words
An apparatus for improving the resolution of a linear FM signal s(t)=a(t) cos Φ(t) where Φ(t)=2π(s o t+αt 2 ) and in which α is a chirp parameter comprising: means for translating received linear FM signals r(t)=Σ N i=1 a i s(t-τ i ) to an analytic signal of the form z(t)=Σ N i=1 a i jΦ(t-τ i ); means for formulating the analytic signal form z(t) into a Wigner-Ville kernel sequence z(t+τ/2)z*(t-τ/2); and means for analyzing the frequency of the kernel sequence z(t+τ/2)z*(t-τ/2) by a high resolution eigenvector spectral estimator to provide a signal having an improved time/frequency representation to achieve a degree of resolution in associated processing means of an order of magnitude greater than a discrete Fourier transform implemented by a fast Fourier transform.
Claim 36
Dependent Claim
20 words
An apparatus according to claim 31 in which the eigenvector spectral estimation technique is known as multiple signal classification (MUSIC).
Claim 37
Dependent Claim
21 words
An apparatus according to claim 31 in which the eigenvector spectral estimation technique is known as eigenvector signal parameter technique (ESPRIT).
Claim 38
Dependent Claim
31 words
An apparatus according to claim 31 in which the means for translating to the analytic signal further includes means for computing in the time domain using finite impulse response (FIR) filters.
Claim 39
Dependent Claim
31 words
An apparatus according to claim 34 in which the means for translating to the analytic signal further includes means for computing in the Fourier domain using a fast Fourier transform (FFT).
Claim 40
Dependent Claim
29 words
An apparatus according to claim 34 in which the means for translating to the analytic signal further includes means for computing in the Fourier domain using a chirp-z-transform (CZT).
Claim 41
Dependent Claim
29 words
An apparatus according to claim 31 in which the means for translating analytic signal further includes means for computing in the time domain using infinite impulse response (IIR) filters.
Claim 42
Dependent Claim
27 words
An apparatus according to claim 31 in which the means for formulating further includes a means for optically implementing in analog using an array of Bragg cells.
Claim 43
Dependent Claim
23 words
An apparatus according to claim 31 in which the means for formulating further includes a means for digitally implementing using conventional semiconductor technology.
References Cited (Backward Citations)
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