US3581199A
Expired / Lapsed
US
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Spectrum analyzer including sampling and scaling means
Assignee: Industrial Nucleonics Corp
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Filing: 1967-09-01
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Granted: 1971-05-25
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Expires: 1987-09-01
Abstract
Abstract Disclosed is a digital spectrum analyzer wherein the spectral content at a plurality of frequencies wm is computed in response to Fourier transforms at each frequency of an analyzed signal at a plurality of discrete time intervals. The Fourier transforms over each interval are combined to indicate the Fourier transform over the entire interval being considered. A further disclosed feature relates to determining with a specific degree of certainty whether a frequency component is periodic. The determination is made by multiplying average power spectrum density over all the frequencies by a predetermined factor, dependent upon the degree of certainty desired. If the spectral density at a particular frequency is greater than the product, it can be assumed, with the predetermined degree of certainty, that the frequency is periodic. Another disclosed feature concerns automatically scaling the amplitudes of the spectral responses at a plurality of predetermined frequencies, whereby no off-scale readings are obtained.
Inventors
- 👤 David A Spitz
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-10-29 02:39
CPC Classifications
G; G01; G01R; G01R23/00; G01R23/16
Claims Analysis
Total Claims: 34
Claim 1
Independent Claim
14 words
The analyzer of claim 1 wherein said means for computing comprises means for computing:
Claim 2
Dependent Claim
25 words
The analyzer of claiM 1 wherein g(t) at +b, where a and b are constants indicative of a sampled value of f(t) during Delta ti.
Claim 3
Dependent Claim
36 words
The analyzer of claim 3 wherein said computing means includes means for approximating g(t) as a predetermined function within the subinterval Delta ti in response to sampled values at the beginning and end of Delta ti.
Claim 4
Dependent Claim
70 words
The analyzer of claim 4 wherein each of said sampling subintervals is of the same duration, equal to Delta t, said means for computing including means for storing signals indicative of the values of functions proportional to: cos omega mn Delta t and sin omega mn Delta t, and means for combining said stored signals with signals indicative of the sampled values at the beginning and end of each subinterval.
Claim 5
Dependent Claim
36 words
The analyzer of claim 2 wherein said computing means includes means for approximating g(t) as a predetermined function within the subinterval Delta ti in response to sampled values at the beginning and end of Delta ti.
Claim 6
Dependent Claim
170 words
A spectrum analyzer for determining the power density at a plurality of frequencies of a signal f(t) within the time interval t1 t tN, said interval being divided into a multiplicity of subintervals Delta t1, Delta t2 ... Delta ti ... Delta tN 1, comprising means responsive to a multiplicity of discrete sampled values of f(t) within t1 t tN, one of said sampled values being taken during each of the subintervals, means responsive to said sampled values for computing the terms forming the real and imaginary power spectrum components of f(t) for each of said frequencies during the subinterval Delta ti from a predetermined continuous functional variation during Delta ti, a point on the functional variation during Delta ti including a sampled value during Delta ti, where i is successively every value between 1 and N-1, and means separately combining the computed components for each of said frequencies for deriving a plurality of signals, each indicative of the power density of f(t) at a different one of said frequencies.
Claim 7
Dependent Claim
44 words
The analyzer of claim 7 wherein said computing means includes means for computing: where: tn and tn 1 are the boundaries of the subinterval Delta ti; g(t) is said predetermined continuous functional variation, and omega m is selectively each of the plurality of frequencies.
Claim 8
Dependent Claim
65 words
The analyzer of claim 8 wherein each of said sampling subintervals is of the same duration equal to Delta t, said computing means including means for storing signals indicative of the values of functions proportional to: cos omega mn Delta t and sin omega mn Delta t, means for combining said stored signals with signals indicative of a sampled value within each of said intervals.
Claim 9
Dependent Claim
83 words
The analyzer of claim 8 further including readout means responsive to the power density signal for each frequency for simultaneously displaying the power density amplitude of a plurality of said frequencies as a displacement, said readout means having a predetermined full scale response, and means responsive to the largest amplitude power density signal for scaling the amplitudes of all of the power density signals displayed by the same factor to prevent the largest power density amplitude displayed from exceeding said full scale response.
Claim 10
Dependent Claim
103 words
The analyzer of claim 7 further including readout means responsive to the power density signal for each frequency for simultaneously displaying the power density amplitude of a plurality of said frequencies as a displacement, said readout means having a predetermined full scale response, and means responsive to the largest amplitude power density signal for scaling the amplitude of all of the power density signals displayed by the same factor to prevent the largest power density amplitude displayed from exceeding said full scale response and enable the largest power density amplitude displayed to be greater than a predetermined percentage of said full scale response.
Claim 11
Dependent Claim
138 words
In an analyzer for determining the spectral content at a frequency omega m of a signal f(t) within the time interval t1 t tN, said interval being divided into a multiplicity of subintervals Delta t1, Delta t2 ... Delta ti ... Delta tN 1, comprising means responsive to a multiplicity of discrete sampled values of f(t) within t1 t tN, one of said sampled values being taken during each of the subintervals, means responsive to said sampled values for computing terms forming the power spectrum coefficients of f(t) at omega m during the subinterval Delta ti from a predetermined continuous functional variation during Delta ti, a point on the functional variation during Delta ti including a sampled value during Delta ti, where i is successively every value between 1 and N-1, and means for combining said computed components.
Claim 12
Dependent Claim
30 words
The analyzer of claim 12 wherein said predetermined continuous functional variation is f(t) at + b, where a and b are constants indicative of a sampled value during Delta ti.
Claim 13
Dependent Claim
37 words
The analyzer of claim 13 wherein said computing means including includes means for approximately g(t) as a predetermined function within the subinterval Delta ti in response to sampled values at the beginning and end of Delta ti.
Claim 14
Independent Claim
165 words
A method of analyzing the spectral content at a frequency omega m of a function f(t) within the time interval t1 t tN with a processor including a memory and calculating means, said interval being divided into a multiplicity of subintervals Delta t1 ... Delta ti ... Delta tN 1, comprising the steps of: (a) storing in the memory first signals indicative of a discrete sampled amplitude of f(t) during each of the subintervals, (b) feeding the stored first signals from the memory to the calculating means, (c) in the calculating means operating on the first signals to derive a second signal for each subinterval indicative of the power spectrum components at omega m of a predetermined continuous functional variation including a stored signal indicative of f(t) for the subinterval, and (d) accumulating in the calculating means second signals indicative of the power spectrum components at omega m of the different subintervals to derive an indication of the power density of f(t) at omega m.
Claim 15
Dependent Claim
48 words
The method of claim 15 wherein the spectral content of f(t) is analyzed for a gamut of frequencies omega 1, omega 2 ... omega m ... omega M and further including the steps of repeating steps (b), (c) and (d) for each of the frequencies in the gamut.
Claim 16
Dependent Claim
129 words
The method of claim 16 further including the steps of operating on the accumulated indication of the power density of f(t) for each frequency of the gamut in the calculating means to derive an indication of the average power density of f(t) over the gamut, and in the calculating means comparing the power spectral density of f(t) for each of the frequencies in the gamut with the average power spectral density of f(t) over the gamut, in the calculating means Modifying the magnitude of one of the compared quantities by a predetermined factor prior to the comparison step, said factor changing the relative amplitudes of the compared quantities for each frequency in accordance with a statistical function related to the probability of each frequency in the gamut being periodic.
Claim 17
Dependent Claim
67 words
The method of claim 45 wherein the spectral content is analyzed for a gamut of frequencies omega 1, omega 2 ... omega m ... omega M, further including the steps of repeating steps (b), (c) and (d) for each of the frequencies in the gamut, and displaying the indication of the power density of f(t) for each of the frequencies of the gamut versus the gamut frequencies.
Claim 18
Independent Claim
206 words
A method of determining if a frequency component omega m in a function f(t) analyzed by digital computer means exists with a predetermined probability, said computer means including a memory and calculating means comprising in said calculating means analyzing the function in response to discrete sampled values of f(t) at a gamut of frequencies omega 1 ... omega k ... omega M to derive indications of the power spectral density of f(t) for each of the frequencies of the gamut, where k is successively 1 ... m ... M, feeding a functional indication of power spectral density for each value of k to the memory, calculating in the calculating means the average power spectral density of f(t) for all of the frequencies in the gamut, comparing in the calculating means functions of the relative magnitudes of the power spectral density of f(t) for each omega k stored in the memory means and the computed average power spectral density, and prior to comparing the relative magnitudes changing one of the compared magnitudes by a predetermined factor in the calculating means, said fourth factor changing the relative amplitudes of the compared magnitudes in accordance with a statistical function related to the probability of omega m existing in f(t).
Claim 19
Independent Claim
140 words
A method of determining if a frequency component omega m in a function f(t) analyzed by digital computer means exists with a predetermined probability, said computer means including a memory and calculating means, comprising in said calculating means analyzing the function in response to discrete sampled values of f(t) to derive an indication of the power spectral density of f(t) for omega m, in the calculating means calculating an indication of the average power spectral density of f(t) over a multifrequency range including omega m, storing a function of at least one of the indications in the storage means, and thereafter in the calculating means responding to the storage means to compare the relative magnitudes of a function of the power spectral density of f(t) at omega m with a function of the calculated average power spectral density of f(t).
Claim 20
Dependent Claim
129 words
Apparatus for determining if a function f(t) that includes frequency components in a spectrum omega 1 omega omega M is periodic with a predetermined probability at one of the frequencies, omega m, in the spectrum during a time interval t1 t tN comprising digital computer means responsive to discrete samples of f(t) for computing a first signal commensurate with a power spectral density indication of f(t) at omega m during said interval, means responsive to f(t) for deriving a second signal indicative of the average power density of f(t) within said spectrum during said interval, and means responsive to said computing and deriving means for comparing the relative amplitudes of the computed signal of power spectral density of f(t) at omega m with the derived average power density signal.
Claim 21
Dependent Claim
46 words
The apparatus of claim 21 wherein said means for deriving includes means for deriving a signal magnitude directly proportional to the average power density of f(t) within said interval and spectrum, and means for multiplying said signal magnitude by a factor determined by said predetermined probability.
Claim 22
Dependent Claim
44 words
The apparatus of claim 21 wherein said means for deriving the signal indicative of average power spectral density of f(t) at omega m includes means for deriving the Fourier transform of f(t) at a plurality of discrete frequencies, including omega m, within said spectrum.
Claim 23
Dependent Claim
46 words
The apparatus of claim 23 wherein said Fourier transform deriving means includes means for each of said plurality of discrete frequencies for deriving the Fourier transform of f(t) for a multiplicity of discrete continuous time intervals together covering the entire time interval of t1 t tN.
Claim 24
Dependent Claim
47 words
The apparatus of claim 21 further including means responsive to said computing means for displaying the power spectrum of f(t) at each of said wm, said displaying means being responsive to said comparing means for indicating what values of wm, if any, are periodic with said probability.
Claim 25
Independent Claim
124 words
A system for displaying the amplitudes of a signal comprising readout means responsive to the signal for simultaneously displaying a plurality of the amplitudes of the signal as displacements, said readout means having a predetermined full scale response, and means responsive to the largest amplitude of the signal for scaling all the displayed amplitudes of the signal by the same factor to prevent the largest displayed signal amplitude from exceeding said full scale response, said scaling means including means for storing all of the amplitudes, means for successively comparing each of said amplitudes with the full scale response, and means for dividing all of the stored amplitudes by a predetermined factor in response to said comparing means indicating that an amplitude exceeds full scale.
Claim 26
Dependent Claim
38 words
The system of claim 26 wherein said scaling means includes means responsive to the largest amplitude of the signal for enabling the largest displayed signal amplitude to be greater than a predetermined percentage of said full scale response.
Claim 27
Independent Claim
105 words
A system for displaying the power spectrums of a signal at a plurality of frequencies, comprising means responsive to the signal for deriving a plurality of indications, each being proportional to the power density of the signal at a different frequency, readout means responsive to the indications for simultaneously displaying the amplitudes of a plurality of the indications as displacements, said readout means having a predetermined full scale response, and means responsive to the largest amplitude of the indications for scaling all the amplitudes of the displayed indications by the same factor to prevent the largest displayed indication amplitude from exceeding said full scale response.
Claim 28
Dependent Claim
41 words
The system of claim 28 wherein said power density indication deriving means includes digital computer means and further including means responsive to the derived power density indication for deriving an indication with a predetermined probability which frequencies exist in the signal.
Claim 29
Dependent Claim
66 words
The system of claim 29 wherein said power density indication deriving means includes digital computer means and said displaying means comprises a digital X-Y recorder for recording amplitude versus frequency, said recorder including means responsive to the periodic indication for marking frequency values having probable periodicity and means responsive to the scaling means for indicating the amount by which all of the displayed amplitudes are scaled.
Claim 30
Dependent Claim
58 words
A spectrum analyzer for a signal comprising digital computer means responsive to discrete samples of the signal for computing indications of spectral amplitude versus a spectrum of frequencies, and means respOnsive to the computed spectral amplitude indications for indicating with a predetermined probability which of the amplitude indications, if any, are associated with actual frequencies of the signal.
Claim 31
Dependent Claim
58 words
The analyzer of claim 31 further including means responsive to the computer for plotting spectral amplitude versus frequency, said plotting means having a predetermined full scale amplitude response, and means responsive to the maximum spectral amplitude for similarly scaling all of said amplitude indications to prevent a full scale amplitude response from being derived by said plotting means.
Claim 32
Dependent Claim
29 words
The analyzer of claim 32 further including separate means for activating said plotting means to indicate which of the amplitude variations is associated with actual frequencies of the signal.
Claim 33
Dependent Claim
31 words
The analyzer of claim 31 further including means for plotting spectral amplitude versus frequency, said plotting means including means for visually identifying which of said frequencies are periodic with said probability.
Claim 34
Dependent Claim
181 words
Apparatus for determining if a function f(t) that may include frequency components in a spectrum omega 1 omega omega M contains an actual periodic component with a predetermined probability at one of the frequencies, omega m, in the spectrum during a time interval t1 t tN comprising digital computer means responsive to discrete samples of f(t) for computing a first signal commensurate with a power spectral density indication of f(t) at omega m during said interval, means responsive to f(t) for deriving a second signal proportional to the average power density of f(t) within said spectrum during said interval, means responsive to said computing and deriving means for comparing the relative amplitudes of the computed signal value of power spectral density of f(t) at omega m with the derived average power density signal, and means for changing the amplitude of one of the signals fed to the comparing means by a predetermined factor, said factor changing the relative amplitudes of the compared signals in accordance with a statistical function related to the probability of each frequency in the gamut being periodic.
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) | 1974-05-24 | 1974-11-23 | 1975-05-25 | $2000.00 | Window Closed / Lapsed |
| 7.5 Years (Year 8) | 1978-05-24 | 1978-11-23 | 1979-05-25 | $3760.00 | Window Closed / Lapsed |
| 11.5 Years (Year 12) | 1982-05-24 | 1982-11-23 | 1983-05-25 | $7700.00 | Window Closed / Lapsed |