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US3714566A
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Apparatus and methods for deriving in essentially real time continuous electrical representations of the fourier and inverse fourier transform
Assignee: Bunker Ramo Corp
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Filing: 1970-09-02
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Granted: 1973-01-30
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Expires: 1990-09-02
Abstract
Abstract Apparatus and methods for deriving in essentially real time unweighted and weighted continuous electrical representations of the Fourier transform and/or the inverse Fourier transform of a complex waveform. In performing the Fourier transform, the input waveform is sampled at the Nyquist sampling rate and the samples stored in respective sample-and-hold circuits. These samples are applied to signal generating circuitry for deriving harmonically related time-varying cosine and sine signals having peak values corresponding to weighted or unweighted values of respective ones of the sample-and-hold circuit outputs, and having a fundamental frequency which may be chosen independently of the frequency content of the input waveform. These cosine and sine signals are then respectively summed for producing resultant summed sine and cosine signals which respectively correspond to weighted or unweighted representations of the real and imaginary components of the Fourier transform of the input waveform with the frequency variable being simulated by time. In one embodiment, these summed sine and cosine signals are applied to a function generator for generating signals representative of the weighted or unweighted amplitude spectrum and/or phase spectrum of the input waveform for further application to appropriately calibrated and adjusted oscilloscopes for producing visual displays thereof. In another embodiment, these resultant summed sine and cosine signals are in turn sampled at the Nyquist sampling rate to provide samples which may conveniently be modified in accordance with desired criteria. The modified samples are then recombined using the inverse Fourier transform technique of the invention which employs circuitry basically similar to that used for the Fourier transform to produce an output signal representative of the original input signal and containing the modifications produced in accordance with the desired criteria.
Inventors
- 👤 G Kang
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-10-23 16:55
CPC Classifications
G; G06; G06G; G06G7/00; G06G7/12; G06G7/19; G06G7/1921; G01; G01R; G01R23/00
Claims Analysis
Total Claims: 59
Claim 1
Independent Claim
111 words
In apparatus for deriving an electrical signal representative of a Fourier-type mathematical transformation of an input signal, the combination of: sampling means including a plurality of sample-and-hold circuits for providing amplitude sampling of said input signal and for simultaneously storing the resulting amplitude samples of said input signal in respective ones of said sample-and-hold circuits, generating means responsive to the samples stored in said sample-and-hold circuits for simultaneously generating harmonically related time-varying cosine and sine signals having peak values proportional to respective ones of said samples, and means for simultaneously combining respective ones of said cosine and sine signals to produce resultant electrical signals representative of the desired Fourier-type mathematical transformation.
Claim 2
Dependent Claim
111 words
In apparatus for deriving an electrical signal representative of a Fourier-type mathematical transformation of an input signal, the combination of: sampling means including a plurality of sample-and-hold circuits for providing amplitude sampling of said input signal and for simultaneously storing the resulting amplitude samples of said input signal in respective ones of said sample-and-hold circuits, generating means responsive to the samples stored in said sample-and-hold circuits for simultaneously generating harmonically related time-varying cosine and sine signals having peak values proportional to respective ones of said samples, and means for simultaneously combining respective ones of said cosine and sine signals to produce resultant electrical signals representative of the desired Fourier-type mathematical transformation.
Claim 3
Dependent Claim
111 words
In apparatus for deriving an electrical signal representative of a Fourier-type mathematical transformation of an input signal, the combination of: sampling means including a plurality of sample-and-hold circuits for providing amplitude sampling of said input signal and for simultaneously storing the resulting amplitude samples of said input signal in respective ones of said sample-and-hold circuits, generating means responsive to the samples stored in said sample-and-hold circuits for simultaneously generating harmonically related time-varying cosine and sine signals having peak values proportional to respective ones of said samples, and means for simultaneously combining respective ones of said cosine and sine signals to produce resultant electrical signals representative of the desired Fourier-type mathematical transformation.
Claim 4
Dependent Claim
111 words
In apparatus for deriving an electrical signal representative of a Fourier-type mathematical transformation of an input signal, the combination of: sampling means including a plurality of sample-and-hold circuits for providing amplitude sampling of said input signal and for simultaneously storing the resulting amplitude samples of said input signal in respective ones of said sample-and-hold circuits, generating means responsive to the samples stored in said sample-and-hold circuits for simultaneously generating harmonically related time-varying cosine and sine signals having peak values proportional to respective ones of said samples, and means for simultaneously combining respective ones of said cosine and sine signals to produce resultant electrical signals representative of the desired Fourier-type mathematical transformation.
Claim 5
Dependent Claim
53 words
The invention in accordance with claim 1, wherein said desired Fourier-type transform is the Fourier transform of the input signal, and wherein said sampling means operates to sample said input signal at least at a Nyquist sampling rate to provide amplitude samples thereof which are stored in respective ones of said sample-and-hold circuits.
Claim 6
Dependent Claim
94 words
The invention in accordance with claim 2 wherein said time-varying harmonically related cosine and sine signals are expressable as e1cosw1t, e2cosw2t, ... encoswnt and e1sinw1t, e2sinw2t . . . encoswnt, where e1, e2, . . . en correspond to said samples, n is the number of samples, t is the time variable, and w is frequency in radians per second, and wherein the frequencies w1 to wn and the fundamental frequency wo thereof satisfy the relationships w1 (b 1)wo, w2 (b+2)wo, . . . wn (b+n)wo, where b is an integer and includes zero.
Claim 7
Dependent Claim
35 words
The invention in accordance with claim 3, wherein said input signal comprises a plurality of pulses, and wherein the fundamental frequency wo is chosen to provide an analysis time less than the time between pulses.
Claim 8
Dependent Claim
30 words
The invention in accordance with claim 3 wherein the fundamental frequency wo of said cosine and sine signals may be chosen independently of the frequency content of said input signal.
Claim 9
Dependent Claim
177 words
The invention in accordance with claim 1, wherein said desired Fourier-type transform is the inverse Fourier transform of the input signal, wherein said input signal is provided in the form of two time-simulated signals corresponding to its real and imaginary components, wherein a separate set of sample-and-hold circuits is provided for the amplitude samples of each of said time-simulated signals, wherein said sampling means operates to sample each of said time-simulated signals at least at a Nyquist sampling rate to provide amplitude samples thereof which are stored in respective ones of the respective sets of sample-and-hold circuits, and wherein said generating means responds to said amplitude samples in a manner so that the harmonically related time-varying cosine signals have peak values proportional to respective ones of the amplitude samples obtained from the time-simulated signal corresponding to the real component of the input signal and so that the harmonically related time-varying sine signals have peak values proportional to respective ones of the amplitude samples obtained from the time-simulated signal corresponding to the imaginary component of the input signal.
Claim 10
Dependent Claim
95 words
The invention in accordance with claim 6 wherein said time-varying harmonically related cosine and sine signals are expressable as e1cosw1t, e2cosw2t, . . . encoswnt and e1sinw1t, e2sinw2t . . . encoswnt, where e1, e2, . . . en correspond to said samples, n is the number of samples, t is the time variable, and w is frequency in radians per second, and wherein the frequencies w1 to wn and the fundamental frequency wo thereof satisfy the relationships w1 (b+1)wo, w2 (b+2)wo, . . . wn (b+n)wo, where b is an integer and includes zero.
Claim 11
Dependent Claim
30 words
The invention in accordance with claim 7 wherein the fundamental frequency wo of said cosine and sine signals may be chosen independently of the frequency content of said input signal.
Claim 12
Dependent Claim
113 words
In apparatus for performing Fourier-type mathematical manipulations of electrical signals in essentially real-time, the combination of: means for deriving time-simulated electrical signals representative of the real and imaginary components of the Fourier transform of an input signal, means for providing separate Nyquist sampling of each of the real and imaginary component signals and for simultaneously providing fixed amplitude samples thereof, means for modifying said amplitude samples in accordance with desired criteria, and generating means responsive to the modified samples for performing an inverse Fourier transformation to produce essentially real-time resultant electrical signals representative of the real and imaginary components of said input signal but containing the modifications introduced by said means for modifying.
Claim 13
Dependent Claim
113 words
In apparatus for performing Fourier-type mathematical manipulations of electrical signals in essentially real-time, the combination of: means for deriving time-simulated electrical signals representative of the real and imaginary components of the Fourier transform of an input signal, means for providing separate Nyquist sampling of each of the real and imaginary component signals and for simultaneously providing fixed amplitude samples thereof, means for modifying said amplitude samples in accordance with desired criteria, and generating means responsive to the modified samples for performing an inverse Fourier transformation to produce essentially real-time resultant electrical signals representative of the real and imaginary components of said input signal but containing the modifications introduced by said means for modifying.
Claim 14
Dependent Claim
53 words
The invention in accordance with claim 9 wherein said generating means includes: means for simultaneously generating time-varying harmonically related cosine and sine signals having peak values proportional to respective ones of said modified samples, and means for simultaneously summing respective ones of said cosine and sine signals to produce said resultant electrical signals.
Claim 15
Dependent Claim
224 words
In apparatus for performing Fourier-type mathematical manipulations on electrical signals, the combination of: first sampling means including a first plurality of sample-and-hold circuits for sampling an input signal and for storing amplitude samples representative thereof in respective ones of said first plurality of sample-and-hold circuits, first generating means responsive to said sampling means for generating a first series of harmonically related time-varying cosine and sine signals having peak values proportional to respective ones of said samples, first combining means for respectively summing and first series of cosine and sine signals to produce time-simulated electrical signals representative of the real and imaginary components of the Fourier transform of said input signal, second sampling means including second and third pluralities of sample-and-hold circuits for separately sampling each of the real and imaginary component signals and for storing amplitude samples representative thereof in respective ones of said second and third pluralities of sample-and-hold circuits, means for modifying the samples stored in said second and third pluralities of sample-and-hold circuits in accordance with desired criteria, second generating means responsive to the modified samples for generating a second series of harmonically related time-varying cosine and sine signals having peak values proportional to respective ones of the modified samples derived from said real component signal, and second combining means for respectively summing the second series of cosine and sine signals.
Claim 16
Dependent Claim
224 words
In apparatus for performing Fourier-type mathematical manipulations on electrical signals, the combination of: first sampling means including a first plurality of sample-and-hold circuits for sampling an input signal and for storing amplitude samples representative thereof in respective ones of said first plurality of sample-and-hold circuits, first generating means responsive to said sampling means for generating a first series of harmonically related time-varying cosine and sine signals having peak values proportional to respective ones of said samples, first combining means for respectively summing and first series of cosine and sine signals to produce time-simulated electrical signals representative of the real and imaginary components of the Fourier transform of said input signal, second sampling means including second and third pluralities of sample-and-hold circuits for separately sampling each of the real and imaginary component signals and for storing amplitude samples representative thereof in respective ones of said second and third pluralities of sample-and-hold circuits, means for modifying the samples stored in said second and third pluralities of sample-and-hold circuits in accordance with desired criteria, second generating means responsive to the modified samples for generating a second series of harmonically related time-varying cosine and sine signals having peak values proportional to respective ones of the modified samples derived from said real component signal, and second combining means for respectively summing the second series of cosine and sine signals.
Claim 17
Dependent Claim
45 words
The invention in accordance with claim 11, wherein said means for modifying includes means for comparing the samples stored in said second and third pluralities of sample-and-hold circuits with predetermined reference values and for modifying sand samples in response to the results of the comparison.
Claim 18
Dependent Claim
46 words
The invention in accordance with claim 11, wherein said apparatus includes third combining means for combining the respectively summed second series of cosine and sine signals to produce an electrical signal representative of said input signal but containing the modifications introduced by said means for modifying.
Claim 19
Dependent Claim
125 words
In apparatus for analyzing a waveform, means for simultaneously providing amplitude samples of said waveform at intervals of ts < or = 1/2W, where ts is the interval between samples and W is the highest frequency content of said waveform, means for simultaneously producing time-varying harmonically related cosine and sine signals having peak values respectively proportional to said samples and having a fundamental frequency which is independent of the frequency content of said waveform, and means for simultaneously combining respective ones of said cosine and sine signals to produce a time-varying spectrum signal having a time variable simulating the frequency variable of the spectrum of said waveform and having a period equal to the fundamental frequency of said time-varying harmonically related cosine and sine signals.
Claim 20
Dependent Claim
125 words
In apparatus for analyzing a waveform, means for simultaneously providing amplitude samples of said waveform at intervals of ts < or = 1/2W, where ts is the interval between samples and W is the highest frequency content of said waveform, means for simultaneously producing time-varying harmonically related cosine and sine signals having peak values respectively proportional to said samples and having a fundamental frequency which is independent of the frequency content of said waveform, and means for simultaneously combining respective ones of said cosine and sine signals to produce a time-varying spectrum signal having a time variable simulating the frequency variable of the spectrum of said waveform and having a period equal to the fundamental frequency of said time-varying harmonically related cosine and sine signals.
Claim 21
Dependent Claim
95 words
The invention in accordance with claim 14, wherein said time-varying harmonically related cosine and sine signals are expressable as e1cosw1t, e2cosw2t, . . . encoswnt and e1sinw1t, e2sinw2t . . . encoswnt, where e1, e2, . . . en correspond to said samples, n is the number of samples, t is the time variable, and w is frequency in radians per second, and wherein the frequencies w1 to wn and the fundamental frequency wo thereof satisfy the relatiOnships w1 (b+1)wo, w2 (b+2)wo, . . . wn (b+n)wo, where b is an integer and includes zero.
Claim 22
Dependent Claim
23 words
The invention in accordance with claim 14, wherein said spectrum signal corresponds to the amplitude spectrum of said waveform and is expressable as
Claim 23
Dependent Claim
23 words
The invention in accordance with claim 15, wherein said spectrum signal corresponds to the phase spectrum of said waveform and is expressable as
Claim 24
Dependent Claim
34 words
The invention in accordance with claim 15, wherein said means for combining said cosine and sine signals produces a time-varying amplitude spectrum signal A'' and a time-varying phase spectrum signal phi '' expressable as
Claim 25
Dependent Claim
28 words
The invention in accordance with claim 28, wherein said apparatus additionally includes output means to which said spectrum signal is applied for providing a manifestation of said waveform.
Claim 26
Dependent Claim
34 words
The invention in accordance with claim 19 wherein said output means includes cathode ray tube means for producing a display of at least one of the amplitude and phase spectra of said input waveform.
Claim 27
Dependent Claim
34 words
The invention in accordance with claim 14 wherein said waveform comprises a plurality of pulses, and wherein said fundamental frequency is chosen to provide an analysis time less than the time between said pulses.
Claim 28
Dependent Claim
105 words
The invention in accordance with claim 14, wherein said means for producing time-varying harmonically related cosine and sine signals includes means for producing a first group of time-varying harmonically related cosine and sine signals having peak values respectively corresponding to a first plurality of said samples, means for producing a second group of time-varying harmonically related cosine and sine signals of like frequencies of those of said first group and having amplitudes corresponding to a second plurality of samples, and means for converting the frequencies of the second group of cosine and sine signals to frequencies which continue the harmonic relation of the first group.
Claim 29
Dependent Claim
73 words
The invention in accordance with claim 18, wherein said means for combining includes: means for producing time-varying cosine and sine signals of like frequency, means for multiplying the signal Ec'' by one of the cosine and sine signals of like frequency and for multiplying the signal Es'' by the other, means for summing the thus multiplied signals, and envelope detector means for producing the amplitude spectrum signal A'' from the summed multiplied signals.
Claim 30
Dependent Claim
63 words
The invention in accordance with claim 19, wherein said means for combining additionally includes: phase detector means to which the summed multiplied signals are applied along with one of said cosine and sine signals of like frequency for detecting the phase difference phi o'' therebetween, and means for subtracting the term (bts)t from phi o'' for producing the phase spectrum signal phi ''.
Claim 31
Dependent Claim
199 words
In apparatus for analyzing a waveform, a basic unit for providing a plurality of samples of said waveform at intervals satisfying the Nyquist sampling theorem and for producing time-varying harmonically related cosine and sine signals having peak values respectively proportional to said samples, at least one add-on unit for providing an additional plurality of samples of said waveform at Nyquist sampling intervals and for producing time-varying harmonically related cosine and sine signals having peak values respectively proportional to the additional plurality of samples and with like frequencies as those produced by said basic unit, said add-on unit also including means for up-converting the frequencies of the cosine and sine signals produced thereby to frequencies such that the cosine and sine signals of the add-on unit will continue the harmonic relation of the cosine and sine signals of the basic unit, and means for combining all of said cosine and sine signals to produce a time-varying spectrum signal of said waveform with the time variable of said spectrum signal simulating the frequency variable of the spectrum of said waveform and said spectrum signal having a period equal to the fundamental frequency of the time-varying harmonically related sine and cosine signals.
Claim 32
Dependent Claim
199 words
In apparatus for analyzing a waveform, a basic unit for providing a plurality of samples of said waveform at intervals satisfying the Nyquist sampling theorem and for producing time-varying harmonically related cosine and sine signals having peak values respectively proportional to said samples, at least one add-on unit for providing an additional plurality of samples of said waveform at Nyquist sampling intervals and for producing time-varying harmonically related cosine and sine signals having peak values respectively proportional to the additional plurality of samples and with like frequencies as those produced by said basic unit, said add-on unit also including means for up-converting the frequencies of the cosine and sine signals produced thereby to frequencies such that the cosine and sine signals of the add-on unit will continue the harmonic relation of the cosine and sine signals of the basic unit, and means for combining all of said cosine and sine signals to produce a time-varying spectrum signal of said waveform with the time variable of said spectrum signal simulating the frequency variable of the spectrum of said waveform and said spectrum signal having a period equal to the fundamental frequency of the time-varying harmonically related sine and cosine signals.
Claim 33
Dependent Claim
249 words
The invention in accordance with claim 25, wherein the cosine and sine signals produced by said basic unit are expressable as e1cosw1t, e2cosw2t . . . encoswnt and e1sinw1t, e2sinw2t . . . ensinwnt, where e1, e2, . . . en are the samples provided by said basic unit, w1 to wn are the harmonically related frequencies of the cosine and sine signals, and n is the number of samples provided by the basic unit, wherein the cosine and sine signals produced by said add-on unit prior to application to said means for up-converting are expressable as en 1cosw1t, en 2cosw2t, . . . en mcoswnt and en 1sinw1t, en 2sinw2t . . . en msinwnt, where en 1, en 2 . . . en m are the samples provided by said add-on units, w1 to wn are as defined above, and m is the number of samples provided by the add-on unit, wherein the cosine and sine signals provided by said add-on unit after application to said means for up-converting are expressable as en 1coswn 1t, en 2coswn 2t . . . en mcoswn mt, and en 1sinwn 1t, en 2sinwn 2t . . . en msinwn mt, and wherein the frequencies w1 to wn and wn 1 to wn m and the fundamental frequencies wo thereof satisfy the relationships w1 (b+1)wo, w2 (b+2)wo . . . wn (b+n)wo, wn 1 (b+n+1)wo, wn 2 (b+n+2)wo . . . wn m (b+n+m)wo, where b is an integer including zero.
Claim 34
Dependent Claim
187 words
In a method of analyzing the spectrum of a waveform in essentially real-time, the steps of: amplitude sampling said waveform at intervals of ts < or = 1/2W, where ts is the interval between samples and W is the highest frequency content of said waveform, simultaneously generating time-varying harmonically related cosine and sine signals having peak values respectively proportional to said samples and expressable as e1cosw1t, e2cosw2t . . . encoswnt and e1sinw1t, e2sinw2t . . . ensinwnt, where e1, e2 . . . en correspond to said samples, n is the number of samples, t is the time variable and w is frequency in radians per second, and the frequencies w1 to wn and the fundamental frequency wo thereof satisfy the relationships w1 (b+1)wo, w2 (b+2)wo . . . wn (b+n)wo, where b is an integer and includes zero, and simultaneously combining the generated cosine and sine signals to produce a time-varying spectrum signal such that the time variable of said spectrum signal simulates the frequency variable of the spectrum of said waveform and said spectrum signal has a period equal to the fundamental frequency wo.
Claim 35
Dependent Claim
187 words
In a method of analyzing the spectrum of a waveform in essentially real-time, the steps of: amplitude sampling said waveform at intervals of ts < or = 1/2W, where ts is the interval between samples and W is the highest frequency content of said waveform, simultaneously generating time-varying harmonically related cosine and sine signals having peak values respectively proportional to said samples and expressable as e1cosw1t, e2cosw2t . . . encoswnt and e1sinw1t, e2sinw2t . . . ensinwnt, where e1, e2 . . . en correspond to said samples, n is the number of samples, t is the time variable and w is frequency in radians per second, and the frequencies w1 to wn and the fundamental frequency wo thereof satisfy the relationships w1 (b+1)wo, w2 (b+2)wo . . . wn (b+n)wo, where b is an integer and includes zero, and simultaneously combining the generated cosine and sine signals to produce a time-varying spectrum signal such that the time variable of said spectrum signal simulates the frequency variable of the spectrum of said waveform and said spectrum signal has a period equal to the fundamental frequency wo.
Claim 36
Dependent Claim
27 words
The invention in accordance with claim 27, wherein the step of combining produces an amplitude spectrum signal A'' and a phase spectrum signal phi '' expressable as
Claim 37
Dependent Claim
48 words
The invention in accordance with claim 27, wherein the step of generating is performed by steps including generating pulse trains having harmonically related frequencies with amplitudes proportional to said samples, and filtering the resultant signals over narrow frequency bands corresponding to the respective frequencies of said pulse trains.
Claim 38
Dependent Claim
97 words
The invention in accordance with claim 27, wherein said steps of sampling and generating are performed by steps including generating a first group of time-varying harmonically related cosine and sine signals having amplitudes proportional to a first plurality of said samples, generating a second group of time-varying harmonically related cosine and sine signals of like frequencies as those of said first group and having amplitudes proportional to a second plurality of said samples, and converting the frequencies of the second group of cosine and sine signals to frequencies which continue the harmonic relation of the first group.
Claim 39
Dependent Claim
77 words
In a method of deriving an essentially real-time electrical signal representative of a desired Fourier-type mathematical transformation of an input signal, the steps of: sampling said input signal to provide fixed value amplitude samples representative thereof, simultaneously generating harmonically related time-varying cosine and sine signals having peak values proportional to respective ones of said samples, and simultaneously combining said cosine and sine signals to produce essentially real-time resultant electrical signals representative of the desired Fourier-type mathematical transformation.
Claim 40
Dependent Claim
77 words
In a method of deriving an essentially real-time electrical signal representative of a desired Fourier-type mathematical transformation of an input signal, the steps of: sampling said input signal to provide fixed value amplitude samples representative thereof, simultaneously generating harmonically related time-varying cosine and sine signals having peak values proportional to respective ones of said samples, and simultaneously combining said cosine and sine signals to produce essentially real-time resultant electrical signals representative of the desired Fourier-type mathematical transformation.
Claim 41
Dependent Claim
80 words
The invention in accordance with claim 31, wherein said desired Fourier-type mathematical transformation is the Fourier transform of the input signal, wherein said sampling is such as to sample said input waveform in a manner so that said samples are amplitude samples of said input signal taken at intervals satisfying the Nyquist sampling rate, and wherein said resultant electrical signals comprise two time-simulated electrical signals representative of the real and imaginary components of the Fourier transform of the input signal.
Claim 42
Dependent Claim
86 words
The invention in accordance with claim 31, wherein said desired Fourier-type mathematical transformation is the inverse Fourier transform of the input signal, wherein said input signal is provided in the forms of time-simulated signals corresponding to its real and imaginary components, and wherein said sampling is such as to separately sample each of said time-simulated signals in a manner so that said samples are amplitude samples thereof taken at sufficiently closely spaced intervals so that said resultant electrical signals are representative of the inverse Fourier transform.
Claim 43
Dependent Claim
76 words
The invention in accordance with claim 33, wherein said generating is such that the harmonically related time-varying cosine signals having peak values proportional to respective ones of the amplitude samples obtained from the time-simulated signal corresponding to the real component of the input signal and the harmonically related time-varying sine signals have peak values corresponding to respective ones of the amplitude samples obtained from the time-simulated signal corresponding to the imaginary component of the input signal.
Claim 44
Dependent Claim
158 words
In a method of performing Fourier-type mathematical manipulations on electrical signals, the steps of: sampling an input signal at least at a Nyquist sampling rate to provide fixed value amplitude samples representative thereof, generating a first series of harmonically related time-varying cosine and sine signals having peak values proportional to respective ones of said samples, combining said cosine and sine signaLs to produce time-simulated electrical signals representative of the real and imaginary components of the Fourier transform of said input signal, sampling each of the real and imaginary component signals at least at a Nyquist sampling rate to provide fixed value amplitude samples thereof, modifying the fixed value amplitude samples obtained from sampling the real and imaginary component signals in accordance with desired criteria, generating a second series of harmonically related time-varying cosine and sine signals having peak values proportional to respective ones of the modified samples, and respectively summing the second series of cosine and sine signals.
Claim 45
Dependent Claim
158 words
In a method of performing Fourier-type mathematical manipulations on electrical signals, the steps of: sampling an input signal at least at a Nyquist sampling rate to provide fixed value amplitude samples representative thereof, generating a first series of harmonically related time-varying cosine and sine signals having peak values proportional to respective ones of said samples, combining said cosine and sine signaLs to produce time-simulated electrical signals representative of the real and imaginary components of the Fourier transform of said input signal, sampling each of the real and imaginary component signals at least at a Nyquist sampling rate to provide fixed value amplitude samples thereof, modifying the fixed value amplitude samples obtained from sampling the real and imaginary component signals in accordance with desired criteria, generating a second series of harmonically related time-varying cosine and sine signals having peak values proportional to respective ones of the modified samples, and respectively summing the second series of cosine and sine signals.
Claim 46
Dependent Claim
63 words
The invention in accordance with claim 35, wherein said method includes the step of comparing the fixed value amplitude samples obtained from sampling the real and imaginary component signals with predetermined reference values, and wherein the step of modifying modifies the amplitude samples obtained from sampling the real and imaginary component signals in response to the results obtained during the step of comparing.
Claim 47
Dependent Claim
46 words
The invention in accordance with claim 35, wherein said method includes the step of combining the respectively summed second series of cosine and sine signals to produce a resultant electrical signal representative of said input signal but containing the modifications introduced by the step of modifying.
Claim 48
Dependent Claim
187 words
In apparatus for deriving an electrical signal representative of a Fourier-type mathematical transformation of an input signal, the combination of: sampling means including a plurality of sample and hold circuits for sampling said input signal and for storing samples representative thereof in respective ones of said sample-and-hold circuits, generating means responsive to the samples stored in said sample-and-hold circuits for generating harmonically related time-varying cosine and sine signals having peak values proportional to respective ones of said samples, said generating means including: means for producing a first group of time-varying harmonically related cosine and sine signals having peak values respectively corresponding to a first plurality of said samples, means for producing a second group of time-varying harmonically related cosine and sine signals of like frequencies of those of said first group and having amplitudes corresponding to a second plurality of samples, means for converting the frequencies of the second group of cosine and sine signals to frequencies which continue the harmonic relation of the first group, and means for combining said cosine and sine signals to produce resultant electrical signals representative of the desired Fourier-type mathematical transformation.
Claim 49
Dependent Claim
187 words
In apparatus for deriving an electrical signal representative of a Fourier-type mathematical transformation of an input signal, the combination of: sampling means including a plurality of sample and hold circuits for sampling said input signal and for storing samples representative thereof in respective ones of said sample-and-hold circuits, generating means responsive to the samples stored in said sample-and-hold circuits for generating harmonically related time-varying cosine and sine signals having peak values proportional to respective ones of said samples, said generating means including: means for producing a first group of time-varying harmonically related cosine and sine signals having peak values respectively corresponding to a first plurality of said samples, means for producing a second group of time-varying harmonically related cosine and sine signals of like frequencies of those of said first group and having amplitudes corresponding to a second plurality of samples, means for converting the frequencies of the second group of cosine and sine signals to frequencies which continue the harmonic relation of the first group, and means for combining said cosine and sine signals to produce resultant electrical signals representative of the desired Fourier-type mathematical transformation.
Claim 50
Dependent Claim
249 words
In apparatus for deriving an electrical signal representative of a Fourier transform of an input signal, the combination of: sampling means including a plurality of sample-and-hold circuits for sampling said input signal at least at a Nyquist rate and for storing amplitude samples representative thereof in respective ones of said sample-and-hold circuits, generating means responsive to the samples stored in said sample-and-hold circuits for generating harmonically related time-varying cosine and sine signals having peak values proportional to respective ones of said samples, said time-varying harmonically related cosine and sine signals being expressable as e1cosw1t, e2cosw2t, . . . encoswnt and e1sinw1t, e2sinw2t . . . encoswnt, where e1, e2, . . . en correspond to said samples, n is the number of samples, t is the time variable, and w is frequency in radians per second, and where the frequencies w1 to wn and the fundamental frequency wo thereof satisfy the relationships w1 (b+1)wo, w2 (b+2)wo, . . . wn (b+n)wo, wherein b is an integer and includes zero, and where the fundamental frequency wo of said cosine and sine signals may be chosen independently of the frequency content of said input signal, and means for combining said cosine and sine signals to produce resultant electrical signals representative of the desired Fourier-type mathematical transformation, said combining means operating to respectively sum said cosine and sine signals so that said resultant signals comprise two signals corresponding to the real and imaginary components of the Fourier transform of the input signal.
Claim 51
Dependent Claim
249 words
In apparatus for deriving an electrical signal representative of a Fourier transform of an input signal, the combination of: sampling means including a plurality of sample-and-hold circuits for sampling said input signal at least at a Nyquist rate and for storing amplitude samples representative thereof in respective ones of said sample-and-hold circuits, generating means responsive to the samples stored in said sample-and-hold circuits for generating harmonically related time-varying cosine and sine signals having peak values proportional to respective ones of said samples, said time-varying harmonically related cosine and sine signals being expressable as e1cosw1t, e2cosw2t, . . . encoswnt and e1sinw1t, e2sinw2t . . . encoswnt, where e1, e2, . . . en correspond to said samples, n is the number of samples, t is the time variable, and w is frequency in radians per second, and where the frequencies w1 to wn and the fundamental frequency wo thereof satisfy the relationships w1 (b+1)wo, w2 (b+2)wo, . . . wn (b+n)wo, wherein b is an integer and includes zero, and where the fundamental frequency wo of said cosine and sine signals may be chosen independently of the frequency content of said input signal, and means for combining said cosine and sine signals to produce resultant electrical signals representative of the desired Fourier-type mathematical transformation, said combining means operating to respectively sum said cosine and sine signals so that said resultant signals comprise two signals corresponding to the real and imaginary components of the Fourier transform of the input signal.
Claim 52
Dependent Claim
24 words
The invention in accordance with claim 39, wherein said generating means includes means for weighting the peak values of said cosine and sine signals.
Claim 53
Dependent Claim
57 words
The invention in accordance with claim 39, wherein said combining means includes means for combining said resultant signals to provide a time-varying spectrum signal representative of the amplitued spectrum of the input signal with the time variable simulating the frequency variable and having a period equal to the fundamental frequency wo of said cosine and sine signals.
Claim 54
Dependent Claim
63 words
The invention in accordance with claim 41, wherein said combining means additionally includes means for combining said resultant signals to provide a continuous time-varying spectrum signal representative of the phase spectrum of the input signal with the time variable simulating the frequency variable of the phase spectrum and having a period equal to the fundamental frequency wo of said cosine and sine signals.
Claim 55
Dependent Claim
24 words
The invention in accordance with claim 42, wherein said apparatus includes means for displaying at least one of the amplitude and phase spectra signals.
Claim 56
Dependent Claim
284 words
In apparatus for deriving an electrical signal representative of an inverse Fourier transform of an input signal provided in the form of two time-simulated signals corresponding to its real and imaginary components, the combination of: sampling means including a plurality of sample-and-hold circuits for sampling said time-simulated signals at least at a Nyquist rate and for storing amplitude samples representative thereof in respective ones of said sample-and-hold circuits, a separate set of sample-and-hold circuits being provided for the amplitude samples of each of said time-simulated signals, generating means responsive to the samples stored in said sample-and-hold circuits for generating harmonically related time-varying cosine and sine signals having peak values proportional to respective ones of said samples, said time-varying harmonically related cosine and sine signals being expressable as e1cosw1t, e2cosw2t, . . . encoswnt and e1sinw1t, e2sinw2t . . . encoswnt, where e1, e2, . . . en correspond to said samples, n is the number of samples, t is the time variable, and w is frequency in radians per second, and where the frequencies w1 to wn and the fundamental frequency wo thereof satisfy the relationships w1 (b+1)wo, w2 (b+2)wo, . . . wn (b+n)wo, where b is an integer and includes zero, and where the fundamental frequency wo of said cosine and sine signals may be chosen independently of the frequency content of said input signal, and means for combining said cosine and sine signals to produce resultant electrical signals representative of the desired Fourier-type mathematical transformation, said combining means operating to respectively sum said cosine and sine signals so that said resultant signals comprise two signals corresponding to the real and imaginary components of the inverse Fourier transform of the input signal.
Claim 57
Dependent Claim
284 words
In apparatus for deriving an electrical signal representative of an inverse Fourier transform of an input signal provided in the form of two time-simulated signals corresponding to its real and imaginary components, the combination of: sampling means including a plurality of sample-and-hold circuits for sampling said time-simulated signals at least at a Nyquist rate and for storing amplitude samples representative thereof in respective ones of said sample-and-hold circuits, a separate set of sample-and-hold circuits being provided for the amplitude samples of each of said time-simulated signals, generating means responsive to the samples stored in said sample-and-hold circuits for generating harmonically related time-varying cosine and sine signals having peak values proportional to respective ones of said samples, said time-varying harmonically related cosine and sine signals being expressable as e1cosw1t, e2cosw2t, . . . encoswnt and e1sinw1t, e2sinw2t . . . encoswnt, where e1, e2, . . . en correspond to said samples, n is the number of samples, t is the time variable, and w is frequency in radians per second, and where the frequencies w1 to wn and the fundamental frequency wo thereof satisfy the relationships w1 (b+1)wo, w2 (b+2)wo, . . . wn (b+n)wo, where b is an integer and includes zero, and where the fundamental frequency wo of said cosine and sine signals may be chosen independently of the frequency content of said input signal, and means for combining said cosine and sine signals to produce resultant electrical signals representative of the desired Fourier-type mathematical transformation, said combining means operating to respectively sum said cosine and sine signals so that said resultant signals comprise two signals corresponding to the real and imaginary components of the inverse Fourier transform of the input signal.
Claim 58
Dependent Claim
24 words
The invention in accordance with claim 44, wherein said generating means includes means for weighting the peak values of said cosine and sine signals.
Claim 59
Dependent Claim
35 words
The invention in accordance with claim 45, wherein said combining means includes means for combining said resultant signals to provide a single continuous time-varying signal representative of the inverse Fourier transform of the input signal.
References Cited (Backward Citations)
US3209250A
Cited
FR1452084A
Cited
USPTO Annuity & Maintenance Windows
| Annuity Stage | Window Opens | Payment Deadline | Surcharge Period Until | Estimated Fee | Status |
|---|---|---|---|---|---|
| 3.5 Years (Year 4) | 1976-01-30 | 1976-07-31 | 1977-01-30 | $2000.00 | Window Closed / Lapsed |
| 7.5 Years (Year 8) | 1980-01-30 | 1980-07-31 | 1981-01-30 | $3760.00 | Window Closed / Lapsed |
| 11.5 Years (Year 12) | 1984-01-30 | 1984-07-31 | 1985-01-30 | $7700.00 | Window Closed / Lapsed |