US3831016A
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Function interpolator
Assignee: Individual
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Filing: 1972-07-05
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Granted: 1974-08-20
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Expires: 1992-07-05
Abstract
Abstract Methods and apparatus are disclosed for producing an output signal by interpolation from a finite plurality of samples representing values of a function at sample points thereof. The output signal is produced as the sum of reconstruction functions having similar shape, one each associated with each sample point and so chosen as to ensure a frequency spectrum that is substantially band-limited and an output signal that is substantially continuous when the samples are updated and to produce a constant output signal when the accepted samples are all equal.
Inventors
- 👤 A Nathan
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-10-29 09:07
CPC Classifications
G; G06; G06G; G06G7/00; G06G7/12; G06G7/30
Claims Analysis
Total Claims: 22
Claim 1
Independent Claim
174 words
A function interpolator producing an output Signal in accordance with a desired function of an independent variable from a plurality (M) of samples of a function of said variable at corresponding sampling points comprising: First circuit means for the production of at least one analog input signal representing a predetermined function of said variable; Second circuit means for storing a plurality (M) of signals respresenting said plural samples, respectively; Nonlinear circuit means connected to said first circuit means for producing a plurality of second output signals each representing the value of a reconstruction function for the instantaneous value of said input signal, wherein each of said reconstruction functions represents a predetermined nonlinear function of said variable; a plurality of multiplier means each having input means for receiving one of said second output signals and at least one of said sample respresentative signals and output means for producing thereat a third output signal; summing circuit means connected to said plural multiplier output means summing said plural third output signals for producing said generator output signal.
Claim 2
Dependent Claim
174 words
A function interpolator producing an output Signal in accordance with a desired function of an independent variable from a plurality (M) of samples of a function of said variable at corresponding sampling points comprising: First circuit means for the production of at least one analog input signal representing a predetermined function of said variable; Second circuit means for storing a plurality (M) of signals respresenting said plural samples, respectively; Nonlinear circuit means connected to said first circuit means for producing a plurality of second output signals each representing the value of a reconstruction function for the instantaneous value of said input signal, wherein each of said reconstruction functions represents a predetermined nonlinear function of said variable; a plurality of multiplier means each having input means for receiving one of said second output signals and at least one of said sample respresentative signals and output means for producing thereat a third output signal; summing circuit means connected to said plural multiplier output means summing said plural third output signals for producing said generator output signal.
Claim 3
Dependent Claim
40 words
The interpolator as defined in claim 1 wherein said predetermined nonlinear function represents a linear combination of (k) sinusoidal functions of said variable of predetermined relative phase, (k) being the greatest integer that is not greater than ( 1/2 M).
Claim 4
Dependent Claim
62 words
The interpolator as defined in claim 2 wherein (M) is an even positive integer, (N) is defined as ( 1/2 M), and said nonlinear function corresponds to 1/2N ( 1 + 2 cos ( pi x /N) + 2 cos (2 pi x/N) + . . . + 2 cos (N -1) pi x/N + cos pi x), (x) representing said variable.
Claim 5
Dependent Claim
54 words
The interpolator as defined in claim 2 wherein (M) is an odd integer greater than two and said nonlinear function corresponds to 1/M ( 1 + 2 cos (2 pi x/M) + 2 cos (4 pi x /M) + . . . + 2 cos (M- 1) pi x/M ), (x) representing said variable.
Claim 6
Dependent Claim
40 words
The interpolator as defined in claim 1 wherein said second circuit means include digital circuit means and said sample representative signals are stored therein in digital form; and wherein said multiplier means receive said sample representative signals in digital form.
Claim 7
Dependent Claim
41 words
The interpolator as defined in claim 5 further comprising: Digital control means responsive to a signal representing a predetermined function of said independent variable for updating said plural stored sample signals whenever said independent variable traverses one of said sampling points
Claim 8
Dependent Claim
29 words
The interpolator as defined in claim 5 wherein said second output signals are produced in analog form and said multiplier means are comprised of multiplying analog-to-digital converter (MDAC) means.
Claim 9
Dependent Claim
30 words
The interpolator as defined in claim 1 wherein said one analog signal produced in said first circuit means is in the form of a sinusoidal function of said independent variable.
Claim 10
Dependent Claim
23 words
The interpolator as defined in claim 8 wherein said nonlinear circuit means include analog multiplier means for the provision of the nonlinearity thereof.
Claim 11
Dependent Claim
50 words
The interpolator as defined in claim 8 wherein said second circuit means comprise digitally controlled means for storing said plural stored signals in analog form and updating said stored signals whenever said independent variable traverses a sampling point; each of said plural multiplier means being comprised of analog multiplier means.
Claim 12
Dependent Claim
35 words
The interpolator as defined in claim 1 wherein said nonlinear circuit means include linear circuit means receiving all but one of said plural second output signals for the production of a further second output signal.
Claim 13
Dependent Claim
78 words
The interpolator as defined in claim 1 wherein said one analog signal produced in said first cirCuit means is in the form of a sawtooth function, changing linearly as a function of said variable from a first preassigned constant value at any one sampling point to a second preassigned constant value at the adjacent sampling point and changing in value from one to the other of said first and second constant values on traversal of a sampling point.
Claim 14
Dependent Claim
59 words
The interpolator as defined in claim 1 wherein said one analog signal produced in said first circuit means is in the form of a continuous triangular wave function of said variable, being a linear function of said variable between any two adjacent sampling points and alternately assuming one and another of two preassigned constant values at adjacent sampling points.
Claim 15
Dependent Claim
43 words
The interpolator as defined in claim 13 wherein said first circuit means comprise means for the production of a second triangular input signal such that the sum of said first and second triangular signals is substantially independent of the value of said variable.
Claim 16
Dependent Claim
143 words
A nonlinear function generator responsive to a digital signal for the production of an analog output signal as a digitally controlled nonlinear function of an analog input signal comprising: Nonlinear circuit means having input means for receiving the analog input signal and output means for producing thereat a plurality of analog reconstruction signals each characterised by a nowhere linear function of said input signal; Digitally controlled storage circuit means for receiving the digital signal, storing a plurality of signals representing function values, and issuing selected stored signals; Multiplier means connected to said nonlinear circuit means and said storage circuit means for receiving and multiplying each of said plural reconstruction signals and a respective stored and issued signal for producing a plurality of product signals; Summing circuit means connected to said multiplier means summing said plural product signals to produce said analog output signal.
Claim 17
Dependent Claim
143 words
A nonlinear function generator responsive to a digital signal for the production of an analog output signal as a digitally controlled nonlinear function of an analog input signal comprising: Nonlinear circuit means having input means for receiving the analog input signal and output means for producing thereat a plurality of analog reconstruction signals each characterised by a nowhere linear function of said input signal; Digitally controlled storage circuit means for receiving the digital signal, storing a plurality of signals representing function values, and issuing selected stored signals; Multiplier means connected to said nonlinear circuit means and said storage circuit means for receiving and multiplying each of said plural reconstruction signals and a respective stored and issued signal for producing a plurality of product signals; Summing circuit means connected to said multiplier means summing said plural product signals to produce said analog output signal.
Claim 18
Dependent Claim
136 words
A nonlinear function interpolator responsive to a sample signal sequence for the production of an analog output signal representing an interpolation function to the sample sequence comprising: Digitally controlled storage circuit means for storing and sequentially issuing said sample signals; Signal generator means having output means for producing thereat, as a function of time, a plurality of reconstruction function signals, wherein said reconstruction functions are periodic in time and any one thereof represents any other thereof shifted by a predetermined time interval; Multiplier means connected to said signal generator output means and said storage circuit means for receiving said plural reconstruction function signals and said issued signals for the production of a plurality of analog product signals; Summing circuit means connected to said multiplier means summing said plural product signals to produce said analog output signal.
Claim 19
Dependent Claim
136 words
A nonlinear function interpolator responsive to a sample signal sequence for the production of an analog output signal representing an interpolation function to the sample sequence comprising: Digitally controlled storage circuit means for storing and sequentially issuing said sample signals; Signal generator means having output means for producing thereat, as a function of time, a plurality of reconstruction function signals, wherein said reconstruction functions are periodic in time and any one thereof represents any other thereof shifted by a predetermined time interval; Multiplier means connected to said signal generator output means and said storage circuit means for receiving said plural reconstruction function signals and said issued signals for the production of a plurality of analog product signals; Summing circuit means connected to said multiplier means summing said plural product signals to produce said analog output signal.
Claim 20
Dependent Claim
35 words
The interpolator as defined in claim 16 wherein said signal generator means include delay circuit means receiving one of said reconstruction function signals for the production of at least one further said reconstruction function signal.
Claim 21
Dependent Claim
38 words
The interpolator as defined in claim 16 wherein said signal generator means include means for the production of a sinusoidal signal and nonlinear circuit means receiving said sinusoidal signal for the production of said plural reconstruction function signals.
Claim 22
Dependent Claim
22 words
The interpolator as defined in claim 18 wherein said nonlinear means are comprised of linear circuit means and plural analog multiplier means.
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) | 1977-08-19 | 1978-02-18 | 1978-08-20 | $2000.00 | Window Closed / Lapsed |
| 7.5 Years (Year 8) | 1981-08-19 | 1982-02-18 | 1982-08-20 | $3760.00 | Window Closed / Lapsed |
| 11.5 Years (Year 12) | 1985-08-19 | 1986-02-18 | 1986-08-20 | $7700.00 | Window Closed / Lapsed |