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US 4,047,002 AGranted
Laplace transform system
AssigneeTime/Data Corporation
InventorsEdwin A. Sloane, Bruce T. McKeever, Eugene Wong
Life of this patent
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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.
Claims33
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.
3 more elements
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.
4 more elements
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.
3 more elements
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.
4 more elements
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.
4 more elements
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.
5 more elements
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.
3 more elements
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.
3 more elements
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.
3 more elements
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.
2 more elements
Dependencies are inferred from the claim text.