US5574639A
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System and method for constructing filters for detecting signals whose frequency content varies with time
Assignee: National Instruments Corp
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Filing: 1994-10-12
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Granted: 1996-11-12
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Expires: 2014-10-12
Abstract
Abstract A system and method for constructing a bank of filters which detect the presence of signals whose frequency content varies with time. The present invention includes a novel system and method for developing one or more time templates designed to match the received signals of interest and the bank of matched filters use the one or more time templates to detect the received signals. Each matched filter compares the received signal x(t) with a respective, unique time template that has been designed to approximate a form of the signals of interest. The robust time domain template is assumed to be of the order of w(t)=A(t)cos{2πφ(t)} and the present invention uses the trajectory of a joint time-frequency representation of x(t) as an approximation of the instantaneous frequency function {φ'(t). First, numerous data samples of the received signal x(t) are collected. A joint time frequency representation is then applied to represent the signal, preferably using the time frequency distribution series (also known as the Gabor spectrogram). The joint time-frequency transformation represents the analyzed signal energy at time t and frequency ƒ, P(t,f), which is a three-dimensional plot of time vs. frequency vs. signal energy. Then P(t,f) is reduced to a multivalued function f(t), a two dimensional plot of time vs. frequency, using a thresholding process. Curve fitting steps are then performed on the time/frequency plot, preferably using Levenberg-Marquardt curve fitting techniques, to derive a general instantaneous frequency function φ'(t) which best fits the multivalued function f(t), a trajectory of the joint time-frequency domain representation of x(t). Integrating φ'(t) along t yields φ(t), which is then inserted into the form of the time template equation. A suitable amplitude A(t) is also preferably determined. Once the time template has been determined, one or more filters are developed which each use a version or form of the time template.
Inventors
- 👤 Shie Qian
- 👤 Mark E. Dunham
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-11-09 15:21
CPC Classifications
G; G06; G06F; G06F18/00; G06F2218/00; G06F2218/12
Claims Analysis
Total Claims: 37
Claim 1
Independent Claim
106 words
A method for constructing one or more filters to detect signals having a frequency content which varies with time, comprising the steps of: collecting data regarding the signals: computing a joint time-frequency representation of the signals; mapping the joint time-frequency representation to a multi-valued function; curve-fitting the multi-valued function to derive an instantaneous frequency function φ'(t); integrating the instantaneous frequency function φ'(t) to obtain φ(t); determining a time template equation using said function φ(t); constructing one or more filters which receive the signals and compare the signals with one or more terms of said time template equation, wherein said one or more filters detect the signals.
Claim 2
Independent Claim
106 words
A method for constructing one or more filters to detect signals having a frequency content which varies with time, comprising the steps of: collecting data regarding the signals: computing a joint time-frequency representation of the signals; mapping the joint time-frequency representation to a multi-valued function; curve-fitting the multi-valued function to derive an instantaneous frequency function φ'(t); integrating the instantaneous frequency function φ'(t) to obtain φ(t); determining a time template equation using said function φ(t); constructing one or more filters which receive the signals and compare the signals with one or more terms of said time template equation, wherein said one or more filters detect the signals.
Claim 3
Dependent Claim
27 words
The method of claim 1, wherein said step of computing a joint time-frequency representation of the signals comprises computing a joint time-frequency distribution series of the signals.
Claim 4
Dependent Claim
28 words
The method of claim 1, wherein said step of computing a joint time-frequency representation of the signals comprises computing a Short Time Fourier Transform (STFT) of the signals.
Claim 5
Dependent Claim
32 words
The method of claim 1, wherein said step of computing a joint time-frequency representation of the signals comprises computing a 3-dimensional representation of the signals of time vs. frequency vs. signal energy.
Claim 6
Dependent Claim
32 words
The method of claim 4, wherein said step of mapping the joint time-frequency representation to a multi-valued function comprises mapping the joint time-frequency to a 2-dimensional multi-valued function of time vs. frequency.
Claim 7
Dependent Claim
36 words
The method of claim 1, wherein said step of mapping comprises applying a thresholding process to said joint time-frequency representation of the signals to map said joint time-frequency representation of the signals to the multi-valued function.
Claim 8
Dependent Claim
62 words
The method of claim 1, wherein said step of mapping comprises determining the relative energy of each sample of said joint time-frequency representation above a threshold value; wherein said step of curve-fitting uses said relative energy of each sample to set the appropriate weights in a non-linear curve fitting algorithm; and wherein said step of curve-fitting uses said non-linear curve fitting algorithm.
Claim 9
Dependent Claim
14 words
The method of claim 1, wherein said step of curve-fitting uses Levenberg-Marquardt curve-fitting techniques.
Claim 10
Dependent Claim
25 words
The method of claim 1, wherein said step of curve-fitting uses one or more techniques from the group consisting of Simplex, Levenberg-Marquardt, and Conjugate Gradient.
Claim 11
Dependent Claim
14 words
The method of claim 1, wherein said time template equation is: A(t) cos {2πφ(t)}.
Claim 12
Dependent Claim
24 words
The method of claim 1, further comprising the steps of: determining an amplitude A(t); and incorporating said amplitude A(t) into said time template equation.
Claim 13
Dependent Claim
14 words
The method of claim 11, wherein said amplitude A(t) comprises a unit step function.
Claim 14
Dependent Claim
48 words
The method of claim 1, wherein said step of constructing one or more filters comprises constructing a bank comprising a plurality N of filters, wherein each of said plurality N of filters compares the signals with a respective form of said time template equation to detect the signals.
Claim 15
Dependent Claim
77 words
The method of claim 13, wherein said step of constructing one or more filters comprises constructing a bank comprising a plurality N of filters, wherein each of said plurality N of filters compares the signals with a unique form of said time template equation that varies according to one or more parameters; wherein said plurality N of filters each compare the signals with one of a corresponding plurality N of different forms of said time template equation.
Claim 16
Dependent Claim
27 words
The method of claim 14, wherein said plurality N of different forms of said time template equation are designed to match various possible forms of the signals.
Claim 17
Dependent Claim
21 words
The method of claim 1, wherein said step of constructing one or more filters comprises constructing a bank of transversal filters.
Claim 18
Dependent Claim
21 words
The method of claim 1, wherein said step of constructing one or more filters comprises constructing a bank of matched filters.
Claim 19
Independent Claim
100 words
A method for constructing one or more filters to detect signals having a frequency content which varies with time, comprising the steps of: collecting data regarding the signals; computing a joint time-frequency representation of the signals; calculating an instantaneous frequency function φ'(t) using said joint time-frequency representation of the signals; integrating the instantaneous frequency function φ'(t) to obtain φ(t); determining a time template equation using said function φ(t); constructing one or more filters which receive the signals and compare the signals with one or more forms of said time template equation, wherein said one or more filters detect the signals.
Claim 20
Independent Claim
100 words
A method for constructing one or more filters to detect signals having a frequency content which varies with time, comprising the steps of: collecting data regarding the signals; computing a joint time-frequency representation of the signals; calculating an instantaneous frequency function φ'(t) using said joint time-frequency representation of the signals; integrating the instantaneous frequency function φ'(t) to obtain φ(t); determining a time template equation using said function φ(t); constructing one or more filters which receive the signals and compare the signals with one or more forms of said time template equation, wherein said one or more filters detect the signals.
Claim 21
Dependent Claim
27 words
The method of claim 18, wherein said step of computing a joint time-frequency representation of the signals comprises computing a joint time-frequency distribution series of the signals.
Claim 22
Dependent Claim
28 words
The method of claim 18, wherein said step of computing a joint time-frequency representation of the signals comprises computing a Short Time Fourier Transform (STFT) of the signals.
Claim 23
Dependent Claim
32 words
The method of claim 18, wherein said step of computing a joint time-frequency representation of the signals comprises computing a 3-dimensional representation of the signals of time vs. frequency vs. signal energy.
Claim 24
Dependent Claim
44 words
The method of claim 18, wherein said step of calculating comprises determining the frequency mean values at each time sample of said joint time-frequency representation with all energy values below a certain minimal value set to zero to calculate said instantaneous frequency function φ'(t).
Claim 25
Dependent Claim
71 words
The method of claim 18, wherein said joint time-frequency representation includes many frequency values at each time sample with significant signal energy; and wherein said step of calculating comprises finding the point of maximum energy change with respect to frequency on either side of the frequency value at each time sample having maximum energy, and then assigning the mean of these two values as the instantaneous frequency value at this location.
Claim 26
Dependent Claim
36 words
The method of claim 18, wherein said step of calculating an instantaneous frequency function comprises: mapping the joint time-frequency representation to a multi-valued function; and curve-fitting the multi-valued function to derive an instantaneous frequency function φ'(t).
Claim 27
Dependent Claim
32 words
The method of claim 24, wherein said step of mapping the joint time-frequency representation to a multi-valued function comprises mapping the joint time-frequency to a 2-dimensional multi-valued function of time vs. frequency.
Claim 28
Dependent Claim
36 words
The method of claim 24, wherein said step of mapping comprises applying a thresholding process to said joint time-frequency representation of the signals to map said joint time-frequency representation of the signals to the multi-valued function.
Claim 29
Dependent Claim
14 words
The method of claim 24, wherein said step of curve-fitting uses Levenberg-Marquardt curve-fitting techniques.
Claim 30
Dependent Claim
14 words
The method of claim 18, wherein said time template equation is: A(t) cos {2πφ(t)}.
Claim 31
Dependent Claim
24 words
The method of claim 18, further comprising the steps of: determining an amplitude A(t); and incorporating said amplitude A(t) into said time template equation.
Claim 32
Dependent Claim
14 words
The method of claim 29, wherein said amplitude A(t) comprises a unit step function.
Claim 33
Dependent Claim
48 words
The method of claim 18, wherein said step of constructing one or more filters comprises constructing a bank comprising a plurality N of filters, wherein each of said plurality N of filters compares the signals with a respective form of said time template equation to detect the signals.
Claim 34
Dependent Claim
77 words
The method of claim 31, wherein said step of constructing one or more filters comprises constructing a bank comprising a plurality N of filters, wherein each of said plurality N of filters compares the signals with a unique form of said time template equation that varies according to one or more parameters; wherein said plurality N of filters, each compare the signals with one of a corresponding plurality N of different forms of said time template equation.
Claim 35
Dependent Claim
27 words
The method of claim 18, wherein said plurality N of different forms of said time template equation are designed to match various possible forms of the signals.
Claim 36
Dependent Claim
21 words
The method of claim 18, wherein said step of constructing one or more filters comprises constructing a bank of transversal filters.
Claim 37
Dependent Claim
21 words
The method of claim 18, wherein said step of constructing one or more filters comprises constructing a bank of matched filters.
References Cited (Backward Citations)
US4633426A
Cited
US4493080A
Cited
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