US4654808A
Expired / Lapsed
US
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Noise corrected pole and zero analyzer
Assignee: Agilent Technologies Inc
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Filing: 1984-08-23
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Granted: 1987-03-31
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Expires: 2004-08-23
Abstract
Abstract A pole and zero analyzer determines the poles and zeroes of a device by applying a stimulus signal to the device, detecting the stimulus and response signals and computing the auto- and cross-spectra. An estimated transfer function is least squares fit to a measured transfer function obtained from the auto- and cross-spectra and the poles and zeroes are obtained as the roots of the estimated transfer function. A weighting function may be used to emphasize certain desired regions of the frequencies of interest in the determination of the least squares fit. The orders of the poles and zeroes are modified until an optimum fit is reached.
Inventors
- 👤 Ronald W. Potter
- 👤 James L. Adcock
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-11-05 00:22
CPC Classifications
G; G06; G06F; G06F17/00; G06F17/10
Claims Analysis
Total Claims: 27
Claim 1
Independent Claim
198 words
A method for determining poles and zeroes of an estimated transfer function of a device having a measured transfer function, comprising the steps of: stimulating the device with a stimulus signal and exciting a response signal; detecting the stimulus and response signals; computing from the stimulus and response signals the auto- and cross-spectra of the device at each of a plurality of frequencies of interest; measuring a noise level incident on the cross-spectrum at each of the frequencies of interest; generating the estimated transfer function; generating a weighting function to emphasize certain desired regions of the estimated transfer function; multiplying the estimated transfer function by the weighting function; determining an error, at each of the frequencies of interest, between the measured transfer function and the estimated transfer function multiplied by the weighting function; differentiating the error, at each of the frequencies of interest, with respect to the estimated transfer function; equating the differentiated error to zero at each of the frequencies of interest; determining coefficients of the estimated transfer function; determining the poles and zeroes of the estimated transfer function as roots of the estimated transfer function; and displaying the poles and zeroes of the estimated transfer function.
Claim 2
Independent Claim
198 words
A method for determining poles and zeroes of an estimated transfer function of a device having a measured transfer function, comprising the steps of: stimulating the device with a stimulus signal and exciting a response signal; detecting the stimulus and response signals; computing from the stimulus and response signals the auto- and cross-spectra of the device at each of a plurality of frequencies of interest; measuring a noise level incident on the cross-spectrum at each of the frequencies of interest; generating the estimated transfer function; generating a weighting function to emphasize certain desired regions of the estimated transfer function; multiplying the estimated transfer function by the weighting function; determining an error, at each of the frequencies of interest, between the measured transfer function and the estimated transfer function multiplied by the weighting function; differentiating the error, at each of the frequencies of interest, with respect to the estimated transfer function; equating the differentiated error to zero at each of the frequencies of interest; determining coefficients of the estimated transfer function; determining the poles and zeroes of the estimated transfer function as roots of the estimated transfer function; and displaying the poles and zeroes of the estimated transfer function.
Claim 3
Dependent Claim
32 words
A method as in claim 1, wherein the step of detecting the stimulus and response signals further comprises the step of transforming the detected stimulus and response signals to the frequency domain.
Claim 4
Dependent Claim
18 words
A method as in claim 2, wherein the stimulus signal comprises random noise over the frequencies of interest.
Claim 5
Dependent Claim
26 words
A method as in claim 3, wherein matrix techniques are used to perform the steps of differentiating the error, equating the differentiated error and determining coefficients.
Claim 6
Dependent Claim
73 words
A method as in claim 4, wherein the step of generating a weighting function comprises: differentiating, with respect to frequency, the phase of the measured transfer function at each of the frequencies of interest; converting the differentiated phase to absolute magnitude at each of the frequencies of interest; deemphasizing any frequency of interest at which the measured noise on the cross-spectrum is high; and normalizing to one the result of the previous step.
Claim 7
Dependent Claim
22 words
A method as in claim 5, further comprising after the step of differentiating the phase, the step of smoothing the phase derivative.
Claim 8
Dependent Claim
23 words
A method as in claim 6, further comprising after the step of converting the differentiated phase, the step of smoothing the absolute magnitude.
Claim 9
Dependent Claim
43 words
A method as in claim 7, further comprising after the step of converting to absolute magnitude and before the step of smoothing the phase derivative, the step of forming the square root of the absolute magnitude at each of the frequencies of interest.
Claim 10
Dependent Claim
31 words
A method as in claim 8, wherein the noise level incident on the cross-spectrum is measured as a coherence over a plurality of measurements at each of the frequencies of interest.
Claim 11
Dependent Claim
40 words
A method as in claim 4, wherein the step of generating a weighting function comprises: detecting peaks in the measured transfer function; forming a surface at each of the detected peaks; and summing the surfaces across the frequencies of interest.
Claim 12
Dependent Claim
28 words
A method as in claim 10, further comprising after the step of summing the surfaces the step of normalizing the summation of surfaces to a maximum surface value.
Claim 13
Dependent Claim
12 words
A method as in claim 11, wherein each surface comprises a parabola.
Claim 14
Dependent Claim
20 words
A method as in claim 12, wherein each parabola is centered at a detected peak in the measured transfer function.
Claim 15
Dependent Claim
16 words
A method as in claim 13, wherein each of the parabolas contains a substantially equal area.
Claim 16
Dependent Claim
28 words
A method as in claim 14, wherein each particular parabola has a width which is proportional to a width of the detected peak associated with that particular parabola.
Claim 17
Dependent Claim
19 words
A method as in claim 15, wherein each parabola has a height which is inversely proportional to its width.
Claim 18
Dependent Claim
63 words
A method as in claim 16, further comprising: determining a mean squared value of the measured transfer function; computing an absolute magnitude squared of the measured transfer function at each of the frequencies of interest; dividing the absolute magnitude squared by the mean squared value at each frequency of interest; and combining the divided absolute magnitude squared with the normalized summation of parabolas.
Claim 19
Independent Claim
139 words
A method for determining poles and zeroes of an estimated transfer function of a device, comprising: stimulating the device with a stimulus signal and exciting a response signal; detecting the stimulus and response signals; determining from the stimulus and response signals a measured transfer function of the device; selecting an initial number of poles and an initial number of zeroes for the estimated transfer function; determining the estimated transfer function from the initial numbers of poles and zeroes; comparing the measured and estimated transfer functions and determining a fit from the comparison; incrementing the numbers of poles and zeroes of the estimated transfer function until a best fit is obtained; decrementing the number of zeroes until an optimal fit is obtained; calculating the poles and zeroes as roots of the estimated transfer function; and displaying the poles and zeroes.
Claim 20
Independent Claim
139 words
A method for determining poles and zeroes of an estimated transfer function of a device, comprising: stimulating the device with a stimulus signal and exciting a response signal; detecting the stimulus and response signals; determining from the stimulus and response signals a measured transfer function of the device; selecting an initial number of poles and an initial number of zeroes for the estimated transfer function; determining the estimated transfer function from the initial numbers of poles and zeroes; comparing the measured and estimated transfer functions and determining a fit from the comparison; incrementing the numbers of poles and zeroes of the estimated transfer function until a best fit is obtained; decrementing the number of zeroes until an optimal fit is obtained; calculating the poles and zeroes as roots of the estimated transfer function; and displaying the poles and zeroes.
Claim 21
Dependent Claim
17 words
A method as in claim 18, wherein the initial number of poles and zeroes is each one.
Claim 22
Dependent Claim
74 words
A method as in claim 19, wherein the step of comparing the estimated and measured transfer functions comprises: determining an error limit at each of the frequencies of interest; subtracting the measured transfer function from the estimated transfer function at each of the frequencies of interest; comparing the result of the subtraction to the error limit at each of the frequncies of interest; and counting a number of results which exceed the error limit.
Claim 23
Dependent Claim
47 words
A method as in claim 20, wherein the step of comparing the estimated and measured transfer functions further comprises: recording the number of results exceeding the error limit; and determining that a good fit is obtained if the recorded number is less than a predetermined acceptance number.
Claim 24
Dependent Claim
29 words
A method as in claim 21, wherein the optimal fit is obtained if a subsequent two decrementations of the number of zeroes result in fits that are not good.
Claim 25
Independent Claim
153 words
A method for determining poles and zeroes of an estimated transfer function of a device, comprising: stimulating the device with a stimulus signal and exciting a response signal; detecting the stimulus and response signals; determining from the stimulus and response signals a measured transfer function of the device; selecting an initial number of poles and an initial number of zeroes of the estimated transfer function; determining the estimated transfer function having the initial number of poles and zeroes; measuring an error to signal ratio of the estimated and measured transfer functions; incrementing the numbers of poles and zeroes of the estimated transfer function if the error to signal ratio is greater than a noise to signal ratio of the measured transfer function; determining the estimated transfer function with the incremented numbers of poles and zeroes; calculating the poles and zeroes as roots of the estimated transfer function; and displaying the poles and zeroes.
Claim 26
Independent Claim
153 words
A method for determining poles and zeroes of an estimated transfer function of a device, comprising: stimulating the device with a stimulus signal and exciting a response signal; detecting the stimulus and response signals; determining from the stimulus and response signals a measured transfer function of the device; selecting an initial number of poles and an initial number of zeroes of the estimated transfer function; determining the estimated transfer function having the initial number of poles and zeroes; measuring an error to signal ratio of the estimated and measured transfer functions; incrementing the numbers of poles and zeroes of the estimated transfer function if the error to signal ratio is greater than a noise to signal ratio of the measured transfer function; determining the estimated transfer function with the incremented numbers of poles and zeroes; calculating the poles and zeroes as roots of the estimated transfer function; and displaying the poles and zeroes.
Claim 27
Dependent Claim
70 words
A method as in claim 23, further comprising, after the step of determining the estimated transfer function with the incremented numbers of poles and zeroes, the steps of: determining an effect of higher order coefficients of the estimated transfer function; decrementing the number of zeroes of the estimated transfer function if the effect is below a predetermined level; and redetermining the estimated transfer functon with the decremented number of zeroes.
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USPTO Annuity & Maintenance Windows
| Annuity Stage | Window Opens | Payment Deadline | Surcharge Period Until | Estimated Fee | Status |
|---|---|---|---|---|---|
| 3.5 Years (Year 4) | 1990-03-30 | 1990-09-29 | 1991-03-31 | $2000.00 | Window Closed / Lapsed |
| 7.5 Years (Year 8) | 1994-03-30 | 1994-09-29 | 1995-03-31 | $3760.00 | Window Closed / Lapsed |
| 11.5 Years (Year 12) | 1998-03-30 | 1998-09-29 | 1999-03-31 | $7700.00 | Window Closed / Lapsed |