US3636338A
Expired / Lapsed
US
⏱️ 0.0 years remaining
Continuous function generation
Assignee: Reliance Electric Co
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Filing: 1969-07-31
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Granted: 1972-01-18
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Expires: 1989-07-31
Abstract
Abstract There is disclosed a method and apparatus for transforming an input signal Yin f(x) into an output signal Yout g(x) involving approximation of the input by a function having a plurality of terms which are functions of the independent variable, generating electrical signals representing each of the terms of the approximating function except for a designated remainder term, and subtracting the signals representing the generated terms from the input signal thereby yielding the designated remainder term, the latter being employed to generate the signals to be subtracted. In one embodiment, a circuit is provided to convert an input signal into a linear output signal in the form Yout mx+b. In another embodiment, a circuit is provided for converting an input signal into an output signal in power series forms. The circuits are closed loop signal processors in which the forward loop operates to subtract the terms of the approximating function from the input signal to yield the designated remaining term, and the feedback operates to convert the designated remaining term into the necessary signals for subtraction. A separate output path appropriately modifies some or all of the signals generated by the feedback and combines the modified signals to form the output.
Inventors
- 👤 Albert C Abnett
- 👤 Jack S Alexander
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-11-01 09:07
CPC Classifications
G; G06; G06G; G06G7/00; G06G7/12; G06G7/26
Claims Analysis
Total Claims: 18
Claim 1
Independent Claim
244 words
Apparatus for transforming an input signal Yin f(x) into an output signal Yout g(x), said input signal Yin being capable of approximation by a function f*(x) having at least two terms which are functions of said independent variable x comprising; input circuit means for receiving said input signal Yin; first and second signal processing means; said first signal processing means having a first input connected to said input circuit means; said first signal processing means having additional input means connected to respective output means of said second signal processing means; said second signal processing means having an input connected to an output of said first signal processing means; said second signal processing means including means responsive to a predetermined term of the independent variable x provided at said input to generate signals representing all of the terms of said function f*(x) including said independent variable except for a designated remaining term; said first signal processing means including signal source means to generate signals representing constant terms of said function f*(x), subtraction means coupled to said signal source means and to said additional input means to subtract said signals representing said constant terms, and said signals generated by said second processing means from the input signal Yin thereby yielding a signal representing said designated remaining term at the output of said first signal processing means; and further means coupled to the output of said first signal processing means to generate the desired output signal Yout.
Claim 2
Dependent Claim
244 words
Apparatus for transforming an input signal Yin f(x) into an output signal Yout g(x), said input signal Yin being capable of approximation by a function f*(x) having at least two terms which are functions of said independent variable x comprising; input circuit means for receiving said input signal Yin; first and second signal processing means; said first signal processing means having a first input connected to said input circuit means; said first signal processing means having additional input means connected to respective output means of said second signal processing means; said second signal processing means having an input connected to an output of said first signal processing means; said second signal processing means including means responsive to a predetermined term of the independent variable x provided at said input to generate signals representing all of the terms of said function f*(x) including said independent variable except for a designated remaining term; said first signal processing means including signal source means to generate signals representing constant terms of said function f*(x), subtraction means coupled to said signal source means and to said additional input means to subtract said signals representing said constant terms, and said signals generated by said second processing means from the input signal Yin thereby yielding a signal representing said designated remaining term at the output of said first signal processing means; and further means coupled to the output of said first signal processing means to generate the desired output signal Yout.
Claim 3
Dependent Claim
130 words
Apparatus as defined in claim 1 wherein said approximating function f*(x) is in the form: f*(x) AK x+Bx+ C wherein said designated remaining term is the exponential term AK x; wherein said signal source means includes means to generate a signal representing the constant C, for subtraction from the input signal Yin; and wherein said second signal processing means includes converter means responsive to a signal representing said exponential term AK x appearing at the output of said first signal processing means to generate a signal representing the linear term Bx; said first signal processing means further including means to subtract said signal representing the linear term Bx from said input signal Yin, whereby the output of said first signal processing means is representative of the exponential term AK x.
Claim 4
Dependent Claim
77 words
Apparatus as defined in claim 2 wherein said converter means comprises logarithmic circuit means responsive to an input signal v to generate an output signal representative of the quantity log10v/10 whereby the output of said logarithmic circuit means is a signal representative of the quantity: log10(AK x) log10A-Xlog10(K)-1 means connected to said logarithmic circuit means to generate an intermediate signal xlog10K, and means to adjust the numerical coefficient log10K of said intermediate signal to the value B.
Claim 5
Dependent Claim
56 words
Apparatus as defined in claim 3 wherein the desired output signal Yout is in the form: Yout mx+ b and wherein said means for generating said desired output signal comprises further means coupled said intermediate signal generating means to adjust the numerical coefficient of said intermediate signal to produce a signal representative of the quantity mx.
Claim 6
Dependent Claim
42 words
Apparatus as defined in claim 4 wherein said means for generating the desired output signal Yout further includes means coupled to said further adjusting means for adding a signal representative of the quantity b to the signal representative of the quantity mx.
Claim 7
Dependent Claim
131 words
Apparatus as defined in claim 1 wherein said function f*(x) is in the form: wherein said designated remainder term is a linear term A1x; wherein said signal source means includes means to generate a signal representative of the zero order term Aoxo Ao, for subtraction from the input signal Yin; and wherein said second signal processing means includes converter means responsive to a signal representing said linear term A1x appearing at the output of said first signal processing means to generate a plurality of signals, each representing one of the higher order terms Anxn for 2< n r; said first signal processing means further including means to subtract said sequence of signals from said input signal whereby the output of said signal processing means is representative of the linear term A1x.
Claim 8
Dependent Claim
208 words
Apparatus as defined in claim 6 wherein said converter means comprises means responsive to the signal representing said linear term A1x to generate a signal representing the quantity x and to present the same on a signal distribution path; a series (r- 2) multipliers each having an input and an output, said multipliers being arranged in series relationship with the output of one multiplier being connected to the input of the next multiplier, and with the input of said first multiplier being connected to said signal distribution path; each of said multipliers having a further input connected in common to said signal distribution path whereby the output of the first multiplier is a signal representing the quantity x2, the output of the second multiplier is a signal representing the quantity x3, etc., the output of the last multiplier being a signal representative of the quantity xr; a series of (r- 2) further signal processing means each connected to the output of one of said multipliers to generate the respective coefficient An for each of the terms xn, for 2 n r; and means for connecting said further signal processing means to said first signal processing means for subtraction of said sequence of signals from said input signal Yin.
Claim 9
Dependent Claim
29 words
Apparatus as defined in claim 7 wherein said further signal processing means comprise means to adjust the amplitude of said signals corresponding to the quantities xn, 2 n r.
Claim 10
Dependent Claim
77 words
Apparatus as defined in claim 8 wherein the desired output signal Yout is in the form and wherein said means for generating said output signal comprises a series of (p) additional signal processors, connected to at least some of the multipliers to adjust the amplitudes of the signals representing the quantities xn, 2 n r in accordance with the respective coefficient Bn; and means coupling outputs of the additional signal processors together to produce the signal Yout.
Claim 11
Dependent Claim
20 words
Apparatus as defined in claim 9 wherein one of said additional signal processors is connected to the signal distribution path.
Claim 12
Dependent Claim
28 words
Apparatus as defined in claim 10 further including means connected to said output coupling means to add a constant level to said output signal representing a quantity Boxo.
Claim 13
Independent Claim
149 words
A method for transforming an electrical input signal Yin f(x) into an electrical output signal Yout g(x), said input signal Yin being capable of approximation by a function f*(x) having at least two terms which are functions of said independent variable x comprising: generating a first electrical signal representative of any constant term in said function f*(x); subtracting said constant term signal from said input signal Yin; generating a further signal for each of the terms of said function f*(x) including the independent variable except for a designated remaining term; subtracting said one or more further signals from said input signal, to produce a signal representing said designated remaining term; the latter being employed in generating said one or more further signals by conversion thereof into said signals representing the required functions of said independent variable, and electrically processing said further signals to generate the desired output signal Yout.
Claim 14
Independent Claim
149 words
A method for transforming an electrical input signal Yin f(x) into an electrical output signal Yout g(x), said input signal Yin being capable of approximation by a function f*(x) having at least two terms which are functions of said independent variable x comprising: generating a first electrical signal representative of any constant term in said function f*(x); subtracting said constant term signal from said input signal Yin; generating a further signal for each of the terms of said function f*(x) including the independent variable except for a designated remaining term; subtracting said one or more further signals from said input signal, to produce a signal representing said designated remaining term; the latter being employed in generating said one or more further signals by conversion thereof into said signals representing the required functions of said independent variable, and electrically processing said further signals to generate the desired output signal Yout.
Claim 15
Dependent Claim
104 words
A method as set forth in claim 12 wherein said further f*(x) is in the form f*(x) AK x+Bx+ C; wherein said designated remaining term is the exponential term AK x; and wherein the step of conversion of the signal representing said remaining term comprises processing said signal by means of a logarithmic circuit element to produce a first intermediate signal in the form: log10(A)-xlog10(K)-1; subtracting from said first intermediate signal another signal in the form log10(A)-1, thereby yielding a second intermediate signal in the form xlog10(K); and adjusting the amplitude of said second intermediate signal to produce a signal representing the quantity Bx.
Claim 16
Dependent Claim
68 words
A method as set forth in claim 13 wherein said output signal is in the form Yout mx+ b; b o and wherein said step of electrically processing said further signals comprises adjusting the amplitude of said second intermediate signal to produce a signal representing the quantity mx; and further including the step of adding a signal representing the quantity b to the signal representing the quantity mx.
Claim 17
Dependent Claim
98 words
A method as set forth in claim 12 wherein said function f*(x) is in the form wherein said designated remaining term is the linear term A1x; and wherein the step of conversion of the signal representing said remaining term comprises adjusting the amplitude of said linear term to produce a first intermediate signal representing the quantity x; processing said first intermediate signal to generate a sequence of further intermediate signals x2, x3,...xr; and adjusting the n each of said further intermediate signals according to the Ycoefficients A2, A3,...Ar to generate said further signals representing the quantities A2x2, A3x3...Arxr.
Claim 18
Dependent Claim
71 words
A method as set forth in claim 15 wherein said output signal is in the form: and wherein said step of electrically processing said further signals comprises adjusting the amplitude of said first intermediate signal and said further intermediate signals to produce signals representing the quantities Bnxn, 1 n p; generating a signal representing the quantity Boxo; and combining said signals representing the quantities Bnxno np to generate the signal Yout.
References Cited (Backward Citations)
No citation records indexed.
USPTO Annuity & Maintenance Windows
| Annuity Stage | Window Opens | Payment Deadline | Surcharge Period Until | Estimated Fee | Status |
|---|---|---|---|---|---|
| 3.5 Years (Year 4) | 1975-01-17 | 1975-07-19 | 1976-01-18 | $2000.00 | Window Closed / Lapsed |
| 7.5 Years (Year 8) | 1979-01-17 | 1979-07-19 | 1980-01-18 | $3760.00 | Window Closed / Lapsed |
| 11.5 Years (Year 12) | 1983-01-17 | 1983-07-19 | 1984-01-18 | $7700.00 | Window Closed / Lapsed |