Patent US2477701A successfully refreshed from Google Patents.
US3699318A
Expired / Lapsed
US
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Incremental slope method for optimum continuous digital linearization
Assignee: Leeds and Northrup Co
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Filing: 1970-08-19
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Granted: 1972-10-17
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Expires: 1990-08-19
Abstract
Abstract An incremental slope method for optimum continuous digital linearization is performed utilizing a programmed digital computer to determine the straight line segments best approximating a nonlinear function. By incrementing the slope of a straight line segment at each breakpoint on or near the curve of the nonlinear function, the difference between the value of the dependent variable on the function and the value of the dependent variable on the straight line segment for different slopes may be determined. By minimizing this difference and maximizing straight line segment length, the best approximating straight line segment is determined. In this manner, a linearized approximating function may be obtained for any set of data points stored in the computer corresponding to any nonlinear function such as a thermocouple curve. The straight line approximating segments with their corresponding preset values of slope and intercept are then utilized to linearize an analog-to-digital converter.
Inventors
- 👤 Victor S Underkoffler
- 👤 Richard B White
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-10-22 22:19
CPC Classifications
G; G06; G06F; G06F17/00; G06F17/10; G06F17/17; H; H03; H03M; H03M1/00; H03M1/12; H03M1/50; H03M1/52; H03M1/58
Claims Analysis
Total Claims: 52
Claim 1
Independent Claim
252 words
In the manufacture of a system for generating a dependent output variable which is a nonlinear function of an independent input variable, said function capable of approximation by a plurality of linear segments joining breakpoints near the curve representing said nonlinear function, each of the linear segments having characteristic slopes and intercepts, the method comprising the following step: 1. storing the values of variables corresponding to a plurality of points on said curve representing said nonlinear function in a programmed, automatic computing apparatus; the method also comprising the following programmed steps executed by said computing apparatus: 2. determining the difference between the value of one of the function variables on said curve and the approximated value of said one variable on a straight line segment having a particular slope and intercept for a particular value of the other of the function variables; 3. incrementing said other variable and repeating step 2 so long as the difference obtained from step 2 lies within a predetermined range of deviation thereby incrementing the length of the straight line segment; 4. incrementing the slope of the straight line segment when the difference of step 2 exceeds a predetermined range of deviation; 5. storing the length of the straight line segment before the slope is incremented; 6. determining the slope and intercept characteristic of the straight line segment having the longest length; the method further comprising the step of 7. identifying a circuit connection for said system corresponding to the straight line segment having the longest length.
Claim 2
Dependent Claim
252 words
In the manufacture of a system for generating a dependent output variable which is a nonlinear function of an independent input variable, said function capable of approximation by a plurality of linear segments joining breakpoints near the curve representing said nonlinear function, each of the linear segments having characteristic slopes and intercepts, the method comprising the following step: 1. storing the values of variables corresponding to a plurality of points on said curve representing said nonlinear function in a programmed, automatic computing apparatus; the method also comprising the following programmed steps executed by said computing apparatus: 2. determining the difference between the value of one of the function variables on said curve and the approximated value of said one variable on a straight line segment having a particular slope and intercept for a particular value of the other of the function variables; 3. incrementing said other variable and repeating step 2 so long as the difference obtained from step 2 lies within a predetermined range of deviation thereby incrementing the length of the straight line segment; 4. incrementing the slope of the straight line segment when the difference of step 2 exceeds a predetermined range of deviation; 5. storing the length of the straight line segment before the slope is incremented; 6. determining the slope and intercept characteristic of the straight line segment having the longest length; the method further comprising the step of 7. identifying a circuit connection for said system corresponding to the straight line segment having the longest length.
Claim 3
Dependent Claim
45 words
determining the difference between the value of one of the function variables on said curve and the approximated value of said one variable on a straight line segment having a particular slope and intercept for a particular value of the other of the function variables;
Claim 4
Dependent Claim
45 words
determining the difference between the value of one of the function variables on said curve and the approximated value of said one variable on a straight line segment having a particular slope and intercept for a particular value of the other of the function variables;
Claim 5
Dependent Claim
32 words
determining the maximum length for one straight line segment in said set such that said difference does not exceed a predetermined range of deviation and the other end terminates off the curve;
Claim 6
Dependent Claim
32 words
determining the maximum length for one straight line segment in said set such that said difference does not exceed a predetermined range of deviation and the other end terminates off the curve;
Claim 7
Dependent Claim
35 words
The method of claim 1 wherein one end of said line segment pivots about the breakpoint while the slope of the straight line segment is incremented and the value of said other variable is incremented.
Claim 8
Dependent Claim
33 words
incrementing said other variable and repeating step 1 so long as the difference obtained from step 1 lies within a predetermined range of deviation thereby incrementing the length of the straight line segment;
Claim 9
Dependent Claim
33 words
incrementing said other variable and repeating step 1 so long as the difference obtained from step 1 lies within a predetermined range of deviation thereby incrementing the length of the straight line segment;
Claim 10
Dependent Claim
39 words
repeatedly applying a scanning function with respect to said straight line segment to identify a plurality of straight line segments having different lengths and extending from said breakpoint in different angular directions with respect to said one terminal breakpoint;
Claim 11
Dependent Claim
39 words
repeatedly applying a scanning function with respect to said straight line segment to identify a plurality of straight line segments having different lengths and extending from said breakpoint in different angular directions with respect to said one terminal breakpoint;
Claim 12
Dependent Claim
128 words
identifying the one of said straight line segments representing a line having the maximum length, originating at said breakpoint, and terminating at its opposite end at another breakpoint near said curve, the deviation of said straight line throughout its length from said curve not exceeding said predetermined limit, repeating the foregoing steps utilizing each last-named breakpoint for scanning until there has been identified that plurality of straight line segments coextensive with and approximating said curve and none of which throughout the respective lengths thereof deviates from said curve beyond said predetermined limit; determining the slopes and intercepts of each of said straight lines approximating said curve; and applying said slopes and intercepts to a system for generation of said linearized digital output for said dual slope analog-to-digital converter.
Claim 13
Dependent Claim
128 words
identifying the one of said straight line segments representing a line having the maximum length, originating at said breakpoint, and terminating at its opposite end at another breakpoint near said curve, the deviation of said straight line throughout its length from said curve not exceeding said predetermined limit, repeating the foregoing steps utilizing each last-named breakpoint for scanning until there has been identified that plurality of straight line segments coextensive with and approximating said curve and none of which throughout the respective lengths thereof deviates from said curve beyond said predetermined limit; determining the slopes and intercepts of each of said straight lines approximating said curve; and applying said slopes and intercepts to a system for generation of said linearized digital output for said dual slope analog-to-digital converter.
Claim 14
Dependent Claim
20 words
incrementing the slope of the straight line segment when the difference of step 1 exceeds a predetermined range of deviation;
Claim 15
Dependent Claim
20 words
incrementing the slope of the straight line segment when the difference of step 1 exceeds a predetermined range of deviation;
Claim 16
Dependent Claim
36 words
The method of claim 2 wherein steps 1-7 are repeated using the other end of said straight line segment having the longest length as the next breakpoint until all of said plurality of segments are determined.
Claim 17
Dependent Claim
18 words
repeating the foregoing steps utilizing the other end of said one straight line segment as another breakpoint; and
Claim 18
Dependent Claim
18 words
repeating the foregoing steps utilizing the other end of said one straight line segment as another breakpoint; and
Claim 19
Dependent Claim
33 words
incrementing said other variable and repeating step 2 so long as the difference obtained from step 2 lies within a predetermined range of deviation thereby incrementing the length of the straight line segment;
Claim 20
Dependent Claim
33 words
incrementing said other variable and repeating step 2 so long as the difference obtained from step 2 lies within a predetermined range of deviation thereby incrementing the length of the straight line segment;
Claim 21
Dependent Claim
20 words
incrementing the slope of the straight line segment when the difference of step 2 exceeds a predetermined range of deviation;
Claim 22
Dependent Claim
20 words
incrementing the slope of the straight line segment when the difference of step 2 exceeds a predetermined range of deviation;
Claim 23
Dependent Claim
23 words
determining slopes and intercepts on the dependent variable coordinate axis for each determined straight line segment joining breakpoints on or near said curve.
Claim 24
Dependent Claim
23 words
determining slopes and intercepts on the dependent variable coordinate axis for each determined straight line segment joining breakpoints on or near said curve.
Claim 25
Dependent Claim
31 words
The method of claim 3 wherein the incrementing of the slope in step 4 continues until the length of the straight line segment characterized by the incremented slope begins to decrease.
Claim 26
Dependent Claim
14 words
storing the length of the straight line segment before the slope is incremented; and
Claim 27
Dependent Claim
14 words
storing the length of the straight line segment before the slope is incremented; and
Claim 28
Dependent Claim
17 words
determining the increment of slope and intercept characteristic of the straight line segment having the longest length.
Claim 29
Dependent Claim
17 words
determining the increment of slope and intercept characteristic of the straight line segment having the longest length.
Claim 30
Dependent Claim
48 words
The method of claim 4 wherein the increment of the slope characteristic of the straight line segment having the longest length is determined in step 6 by counting the number of incremented values of said other variable for each straight line segment characterized by a particular slope increment.
Claim 31
Dependent Claim
13 words
storing the length of the straight line segment before the slope is incremented;
Claim 32
Dependent Claim
13 words
storing the length of the straight line segment before the slope is incremented;
Claim 33
Dependent Claim
22 words
determining the slope and intercept characteristic of the straight line segment having the longest length; the method further comprising the step of
Claim 34
Dependent Claim
22 words
determining the slope and intercept characteristic of the straight line segment having the longest length; the method further comprising the step of
Claim 35
Dependent Claim
24 words
The method of claim 5 including the step of computing each straight line segment terminating at each breakpoint for each characteristic increment of slope.
Claim 36
Dependent Claim
79 words
The method of claim 4 wherein the incrementing of the slope in step 4 comprises the steps of incrementing the slope with coarser or larger increments initially so as to roughly determine the characteristic slope of the straight line segment having the longest length and incrementing the slope with finer or smaller increments subsequently in the vicinity of the roughly determined characteristic slope to more precisely determine the characteristic slope of the straight line segment having the longest length.
Claim 37
Dependent Claim
17 words
identifying a circuit connection for said system corresponding to the straight line segment having the longest length.
Claim 38
Dependent Claim
17 words
identifying a circuit connection for said system corresponding to the straight line segment having the longest length.
Claim 39
Dependent Claim
33 words
The method of claim 7 wherein the slope is increased and decreased by incrementing with the finer or smaller increment in the vicinity of the roughly determined characteristic slope of the line segment.
Claim 40
Dependent Claim
51 words
The method of claim 8 wherein the slope is incremented utilizing increments having at least three degrees of coarseness, said slope being incremented with a finer increment on both sides of a coarser increment to determine the appropriate direction of incrementation to locate the straight line segment having the longest length.
Claim 41
Dependent Claim
24 words
The method of claim 4 wherein the identification of the circuit connection of step 7 comprises the marking of the connection in said system.
Claim 42
Dependent Claim
25 words
The method of claim 4 wherein the identification of the circuit connection in step 7 comprises the wiring of the circuit connection in said system.
Claim 43
Dependent Claim
79 words
In the manufacture of a system including a analog-to-digital converter for generating a linearized digital output as a dependent variable which is a nonlinear function of an input as an independent variable, said function being approximated by a plurality of continuous linear segments joining breakpoints on or near a curve plotted with respect to a pair of Cartesian coordinate axes and representing said nonlinear function, the method including the following steps each executed by a programmed, automatic computing apparatus:
Claim 44
Dependent Claim
79 words
In the manufacture of a system including a analog-to-digital converter for generating a linearized digital output as a dependent variable which is a nonlinear function of an input as an independent variable, said function being approximated by a plurality of continuous linear segments joining breakpoints on or near a curve plotted with respect to a pair of Cartesian coordinate axes and representing said nonlinear function, the method including the following steps each executed by a programmed, automatic computing apparatus:
Claim 45
Dependent Claim
27 words
The method of claim 12 further including the step of identifying circuit connections for said system in response to and corresponding to said determined slopes and intercepts.
Claim 46
Independent Claim
36 words
The method of approximating a nonlinear function by a plurality of straight line segments joining breakpoints near a curve representing said nonlinear function, the method comprising the following programmed steps executed by a programmed computing apparatus:
Claim 47
Independent Claim
36 words
The method of approximating a nonlinear function by a plurality of straight line segments joining breakpoints near a curve representing said nonlinear function, the method comprising the following programmed steps executed by a programmed computing apparatus:
Claim 48
Dependent Claim
35 words
The method of claim 14 wherein one end of said line segment pivots about the breakpoint while the slope of the straight line segment is incremented and the value of said other variable is incremented.
Claim 49
Dependent Claim
36 words
The method of claim 15 wherein steps 1-7 are repeated using the other end of said straight line segment having the longest length as the next breakpoint until all of said plurality of segments are determined.
Claim 50
Dependent Claim
38 words
The method of claim 16 wherein the slope is incremented in a direction so as to increase or decrease in a direction determined by the sign of said difference at the breakpoint of the previous straight line segment.
Claim 51
Independent Claim
61 words
A method of establishing a linearized digital output from a dual slope analog-to-digital converter approximating a nonlinear function characterized by a curve having an independent variable plotted along one Cartesian coordinate axis and a dependent variable plotted along the other coordinate axis, the method comprising The operation of an automatic programmed computing system in the performance of the following programmed steps:
Claim 52
Independent Claim
61 words
A method of establishing a linearized digital output from a dual slope analog-to-digital converter approximating a nonlinear function characterized by a curve having an independent variable plotted along one Cartesian coordinate axis and a dependent variable plotted along the other coordinate axis, the method comprising The operation of an automatic programmed computing system in the performance of the following programmed steps:
References Cited (Backward Citations)
US3513301A
Cited
US3557347A
Cited
USPTO Annuity & Maintenance Windows
| Annuity Stage | Window Opens | Payment Deadline | Surcharge Period Until | Estimated Fee | Status |
|---|---|---|---|---|---|
| 3.5 Years (Year 4) | 1975-10-17 | 1976-04-17 | 1976-10-17 | $2000.00 | Window Closed / Lapsed |
| 7.5 Years (Year 8) | 1979-10-17 | 1980-04-17 | 1980-10-17 | $3760.00 | Window Closed / Lapsed |
| 11.5 Years (Year 12) | 1983-10-17 | 1984-04-17 | 1984-10-17 | $7700.00 | Window Closed / Lapsed |