US4047002A
Expired / Lapsed
US
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Laplace transform system
Assignee: TIME DATA CORP
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Filing: 1976-06-28
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Granted: 1977-09-06
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Expires: 1996-06-28
Abstract
Abstract A system for determining the location of poles in the complex s-plane and their residues from empirical data is disclosed. The system utilizes the impulse response or similar data of a specimen and through repeated differentiations of a frequency domain representation of this response locates the frequency of the poles. The results of any two consecutive differentiations are used to determine the location of the poles in the s-plane and their residues.
Inventors
- 👤 Edwin A. Sloane
- 👤 Bruce T. McKeever
- 👤 Eugene Wong
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-10-29 04:51
CPC Classifications
G; G06; G06F; G06F17/00; G06F17/10; G06F17/14; G01; G01R; G01R23/00
Claims Analysis
Total Claims: 43
Claim 1
Independent Claim
97 words
A system for determining the natural resonant frequencies associated with a specimen comprising: sensor means for sensing the response of the specimen to a predetermined excitation; converting means for converting the sensed response of said specimen to a frequency domain representative of said response coupled to said sensor means; differentiation means for differentiating said frequency domain representation, coupled to said converting means; and peak detection means for detecting the peaks of a signal coupled to said differentiation means; whereby the interaction of the poles are minimized through said differentiation such that said resonant frequencies may be determined.
Claim 2
Independent Claim
97 words
A system for determining the natural resonant frequencies associated with a specimen comprising: sensor means for sensing the response of the specimen to a predetermined excitation; converting means for converting the sensed response of said specimen to a frequency domain representative of said response coupled to said sensor means; differentiation means for differentiating said frequency domain representation, coupled to said converting means; and peak detection means for detecting the peaks of a signal coupled to said differentiation means; whereby the interaction of the poles are minimized through said differentiation such that said resonant frequencies may be determined.
Claim 3
Independent Claim
120 words
A system for determining the natural resonant frequencies associated with a specimen comprising: sensor means for sensing the response of said specimen to a known excitation; function generating means for generating a predetermined function; multiplication means for multiplying the sensed response of said specimen by said predetermining function coupled to said sensor means and said function generating means; converting means for converting the output of said multiplication means to a frequency domain representation coupled to said multiplication means; and peak direction means for detecting the peak of a signal coupled to said converting means; whereby the interaction of the peaks are minimized through said multiplication and the conversion to the frequency domain such that the resonant frequencies may be determined.
Claim 4
Independent Claim
120 words
A system for determining the natural resonant frequencies associated with a specimen comprising: sensor means for sensing the response of said specimen to a known excitation; function generating means for generating a predetermined function; multiplication means for multiplying the sensed response of said specimen by said predetermining function coupled to said sensor means and said function generating means; converting means for converting the output of said multiplication means to a frequency domain representation coupled to said multiplication means; and peak direction means for detecting the peak of a signal coupled to said converting means; whereby the interaction of the peaks are minimized through said multiplication and the conversion to the frequency domain such that the resonant frequencies may be determined.
Claim 5
Dependent Claim
22 words
The system defined in claim 2 wherein said multiplication means also multiplies said sensed response by the square of said predetermined function.
Claim 6
Dependent Claim
15 words
The system defined in claim 3 wherein said frequency domain representation is the Fourier transform.
Claim 7
Dependent Claim
14 words
The system defined in claim 4 wherein said predetermined function is a ramp function.
Claim 8
Dependent Claim
14 words
The system defined in claim 4 wherein said predetermined function is a sine function.
Claim 9
Dependent Claim
15 words
The system defined in claim 2 wherein said peak detection means includes a display means.
Claim 10
Independent Claim
81 words
A method for determining the natural resonant frequencies of a specimen including the steps of: determining the response of said specimen to excitation with a sensing means; converting said response of said specimen to said excitation to a frequency domain representation of said response with a computer means; differentiating said converted response with a differentiating means; and selected the peaks of said differentiated, converted response; whereby the location of said peaks is representative of the natural resonant frequencies of said specimen.
Claim 11
Independent Claim
81 words
A method for determining the natural resonant frequencies of a specimen including the steps of: determining the response of said specimen to excitation with a sensing means; converting said response of said specimen to said excitation to a frequency domain representation of said response with a computer means; differentiating said converted response with a differentiating means; and selected the peaks of said differentiated, converted response; whereby the location of said peaks is representative of the natural resonant frequencies of said specimen.
Claim 12
Dependent Claim
22 words
The method defined in claim 8 wherein at least two successive differentiations are performed prior to the selection of the said peaks.
Claim 13
Independent Claim
87 words
A method for determining the natural resonant frequencies of a specimen including the steps of: determining the response of said specimen to an excitation; generating a predetermined function with a generating means; combining said predetermined function with said response of said specimen to said excitation with an electrical means; converting the results of said combining steps to a frequency domain representation with a computer means; and, selecting the peaks of said frequency domain representation; whereby the peaks are representative of the natural resonant frequencies of said specimen.
Claim 14
Independent Claim
87 words
A method for determining the natural resonant frequencies of a specimen including the steps of: determining the response of said specimen to an excitation; generating a predetermined function with a generating means; combining said predetermined function with said response of said specimen to said excitation with an electrical means; converting the results of said combining steps to a frequency domain representation with a computer means; and, selecting the peaks of said frequency domain representation; whereby the peaks are representative of the natural resonant frequencies of said specimen.
Claim 15
Independent Claim
124 words
A system for determining the location of poles and their residues in a complex s-plane of a specimen comprising; sensing means for sensing the response of said specimen to an excitation; converting means for converting the sensed reponse of said impulse to a frequency domain representation of said response, coupled to said sensing means; differentiation means for differentiating said frequency domain representation, coupled to said converting means; peak detection means for detecting the peaks of a signal, coupled to said differentiation means; and, arithmetic means coupled to said peak detection means and differentiation means for performing arithmetic computations; wherein said arithmetic means may compute the location of the poles and their residues from the information supplied from said differentiation means and peak detection means.
Claim 16
Independent Claim
124 words
A system for determining the location of poles and their residues in a complex s-plane of a specimen comprising; sensing means for sensing the response of said specimen to an excitation; converting means for converting the sensed reponse of said impulse to a frequency domain representation of said response, coupled to said sensing means; differentiation means for differentiating said frequency domain representation, coupled to said converting means; peak detection means for detecting the peaks of a signal, coupled to said differentiation means; and, arithmetic means coupled to said peak detection means and differentiation means for performing arithmetic computations; wherein said arithmetic means may compute the location of the poles and their residues from the information supplied from said differentiation means and peak detection means.
Claim 17
Dependent Claim
41 words
The system defined in claim 11 wherein said differentiation means generates two successive derivatives of said frequency domain representation and where said two successive derivatives are utilized by said arithmetic means for computing the location of the poles and their residues.
Claim 18
Dependent Claim
15 words
The system defined in claim 12 wherein said frequency domain representation is the Fourier transform.
Claim 19
Independent Claim
144 words
A system for determining the location of poles in a complex s-plane and their residue of a specimen comprising: sensing means for sensing the response of said specimen to a predetermined excitation; function generation means for generating a predetermined function; combining means for combining the sensed response of said specimen with said predetermined function, coupled to said sensing means and said function generation means; converting means for converting the output of said combining means to a frequency domain representation, coupled to said combining means; peak detection means for detecting the peaks of a signal, coupled to said converting means; and, arithmetic means for performing arithmetic computations coupled to said converting means and to said peak detection means; whereby said arithmetic means from the data furnished it by said converting means and peak detection means may compute the location of the poles and their residues.
Claim 20
Independent Claim
144 words
A system for determining the location of poles in a complex s-plane and their residue of a specimen comprising: sensing means for sensing the response of said specimen to a predetermined excitation; function generation means for generating a predetermined function; combining means for combining the sensed response of said specimen with said predetermined function, coupled to said sensing means and said function generation means; converting means for converting the output of said combining means to a frequency domain representation, coupled to said combining means; peak detection means for detecting the peaks of a signal, coupled to said converting means; and, arithmetic means for performing arithmetic computations coupled to said converting means and to said peak detection means; whereby said arithmetic means from the data furnished it by said converting means and peak detection means may compute the location of the poles and their residues.
Claim 21
Dependent Claim
15 words
The system defined by claim 14 wherein said frequency domain representation is a Fourier transform.
Claim 22
Dependent Claim
14 words
The system defined by claim 15 wherein said function generator generates a sine function.
Claim 23
Dependent Claim
24 words
The system defined by claim 16 wherein a storage means is coupled between said arithmetic means and said converting means and peak detection means.
Claim 24
Dependent Claim
25 words
The system defined in claim 14 wherein said arithmetic means employs finite differencing in the computation of the location of the poles and their residues.
Claim 25
Dependent Claim
27 words
The system defined by claim 18 wherein at least the square of said predetermined function is combined with the response of said specimen to said predetermined excitation.
Claim 26
Dependent Claim
36 words
The system defined by claim 14 wherein two consecutive powers of said predetermined function are combined by said combining means and utilized by said arithmetic means for determining said location of the poles and their residues.
Claim 27
Dependent Claim
15 words
The system defined by claim 14 including means for generating powers of said predetermined function.
Claim 28
Dependent Claim
28 words
The system defined by claim 11 wherein said sensing means includes data conditioner means for converting a frequency domain representation of a response to a time domain representation.
Claim 29
Dependent Claim
28 words
The system defined by claim 14 wherein said sensing means includes data conditioner means for converting a frequency domain representation of a response to a time domain representation.
Claim 30
Dependent Claim
13 words
The system defined in claim 1 wherein said differentiation means employs finite differencing.
Claim 31
Independent Claim
125 words
A system for determining the location of poles in a complex s-plane and their residues of an input signal comprising: function generating means for generating a predetermined function; combining means for combining said input signal with said predetermined function, coupled to said function generation means; converting means for converting the output of said combining means to a frequency domain representation, coupled to said combining means; peak detection means for detecting the peaks of a signal, coupled to said converting means; and, arithmetic means for performing arithmetic computations coupled to said converting means and to said peak detection means; whereby said arithmetic means from the data furnished it by said converting means and peak detection means may compute the location of the poles and their residues.
Claim 32
Independent Claim
125 words
A system for determining the location of poles in a complex s-plane and their residues of an input signal comprising: function generating means for generating a predetermined function; combining means for combining said input signal with said predetermined function, coupled to said function generation means; converting means for converting the output of said combining means to a frequency domain representation, coupled to said combining means; peak detection means for detecting the peaks of a signal, coupled to said converting means; and, arithmetic means for performing arithmetic computations coupled to said converting means and to said peak detection means; whereby said arithmetic means from the data furnished it by said converting means and peak detection means may compute the location of the poles and their residues.
Claim 33
Dependent Claim
13 words
The system defined by claim 25 wherein said arithmetic means employs finite differencing.
Claim 34
Independent Claim
106 words
A system for determining the location of poles and their residues in a complex s-plane of an input signal comprising: converting means for converting said input signal to a frequency domain representation of said input signal; differentiation means for differentiating said frequency domain representation, coupled to said converting means; peak detection means for detecting the peaks of a signal, coupled to said differentiation means; and, arithmetic means coupled to said peak detection means and differentiation means for performing arithmetic computations; whereby said arithmetic means may compute the location of the poles and their residues from the information supplied from said differentiation means and peak detection means.
Claim 35
Independent Claim
106 words
A system for determining the location of poles and their residues in a complex s-plane of an input signal comprising: converting means for converting said input signal to a frequency domain representation of said input signal; differentiation means for differentiating said frequency domain representation, coupled to said converting means; peak detection means for detecting the peaks of a signal, coupled to said differentiation means; and, arithmetic means coupled to said peak detection means and differentiation means for performing arithmetic computations; whereby said arithmetic means may compute the location of the poles and their residues from the information supplied from said differentiation means and peak detection means.
Claim 36
Independent Claim
139 words
A system for determining the location of poles and their residues in a complex s-plane of an input signal comprising: converting means for converting said input signal to a frequency domain representation of said input signal; differentiation means coupled to said converting means for differentiating said frequency domain representation, coupled to said converting means, said differentiation means generating two successive derivatives of said frequency domain representation by use of finite differencing employing the same differencing distance in deriving both of said derivatives; peak detection means for detecting the peaks of a signal, coupled to said differentiation means; and, arithmetic means coupled to said peak detection means and differentiation means for performing arithmetic computations; whereby said arithmetic means may compute the location of said poles and their residues from the information supplied from said differentiation means and peak detection means.
Claim 37
Independent Claim
139 words
A system for determining the location of poles and their residues in a complex s-plane of an input signal comprising: converting means for converting said input signal to a frequency domain representation of said input signal; differentiation means coupled to said converting means for differentiating said frequency domain representation, coupled to said converting means, said differentiation means generating two successive derivatives of said frequency domain representation by use of finite differencing employing the same differencing distance in deriving both of said derivatives; peak detection means for detecting the peaks of a signal, coupled to said differentiation means; and, arithmetic means coupled to said peak detection means and differentiation means for performing arithmetic computations; whereby said arithmetic means may compute the location of said poles and their residues from the information supplied from said differentiation means and peak detection means.
Claim 38
Dependent Claim
47 words
The system of claim 28 wherein said differentiation means includes means for producing frequency domain representations at a preselected frequency and at frequencies higher and lower than said preselected frequency by a preselected amount; and means for differencing said frequency domain representations to obtain said successive derivatives.
Claim 39
Dependent Claim
42 words
The system of claim 29 wherein said means for obtaining said successive derivatives includes means for producing said frequency domain representation at said higher frequency and shift register means for producing frequency domain representations at said preselected frequency and said lower frequency.
Claim 40
Dependent Claim
34 words
The system of claim 28 wherein said arithmetic means includes means for computing the complex ratio of said successive derivatives, the real part thereof being proportional to the damping factor associated with said poles.
Claim 41
Dependent Claim
117 words
In a system for determining the location of poles and their residues in a complex s-plane of an input signal the improvement comprising: converting means for converting said input signal to a frequency domain representation of said input signal; differentiation means coupled to said converting means for differentiating said frequency domain representation, coupled to said converting means; said differentiation means generating two successive derivatives of said frequency domain representation by use of finite differencing employing the same differencing distance in deriving both of said derivatives; arithmetic means coupled to said differentiation means for performing arithmetic computations; whereby said arithmetic means may compute the damping factor associated with said poles from the information supplied from said differentiation means.
Claim 42
Dependent Claim
117 words
In a system for determining the location of poles and their residues in a complex s-plane of an input signal the improvement comprising: converting means for converting said input signal to a frequency domain representation of said input signal; differentiation means coupled to said converting means for differentiating said frequency domain representation, coupled to said converting means; said differentiation means generating two successive derivatives of said frequency domain representation by use of finite differencing employing the same differencing distance in deriving both of said derivatives; arithmetic means coupled to said differentiation means for performing arithmetic computations; whereby said arithmetic means may compute the damping factor associated with said poles from the information supplied from said differentiation means.
Claim 43
Dependent Claim
34 words
The system of claim 32 wherein said arithmetic means includes means for computing the complex ratio of said successive derivatives, the real part thereof being proportioned to the damping factor associated with said poles.
References Cited (Backward Citations)
USPTO Annuity & Maintenance Windows
| Annuity Stage | Window Opens | Payment Deadline | Surcharge Period Until | Estimated Fee | Status |
|---|---|---|---|---|---|
| 3.5 Years (Year 4) | 1980-09-05 | 1981-03-07 | 1981-09-06 | $2000.00 | Window Closed / Lapsed |
| 7.5 Years (Year 8) | 1984-09-05 | 1985-03-07 | 1985-09-06 | $3760.00 | Window Closed / Lapsed |
| 11.5 Years (Year 12) | 1988-09-05 | 1989-03-07 | 1989-09-06 | $7700.00 | Window Closed / Lapsed |