US3626384A
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Method for representing measured data values by coefficient values
Assignee: International Business Machines Corp
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Filing: 1969-12-23
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Granted: 1971-12-07
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Expires: 1989-12-23
Abstract
Abstract A method is provided for reducing measured data to representative coefficient values. The data relates to physical energy collected and measured by a physical sensor, and therefore, the measured data includes noise. In the method which may be carried out by programming a general purpose digital computer, the measured data values are first processed to remove the linear trend. The resultant values are then processed to provide the maximum number of coefficient values which represent the measured data values. A certain number of the set of coefficient values represent the portion of the measurements which is substantially noise, and may be eliminated. The method therefore includes a process for determining a number of coefficients of the total set which represent the measured data with minimum error where minimum error is defined as minimum stochastic uncertainty.
Inventors
- 👤 Jonathan B Davis
- 👤 Nathen P Edwards
- 👤 Harold H Herd
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-10-26 18:22
CPC Classifications
G; G01; G01R; G01R17/00
Claims Analysis
Total Claims: 10
Claim 1
Independent Claim
244 words
A method of representing by coefficients a physical variable from which measured data values were obtained where said data is obtained by a series of measurements of a dependent physical variable at equally spaced intervals of an independent variable with a sensor to produce a set of measured values of said physical variable designated Y(1), Y(2), Y(3)....Y(N), and wherein said set of N measured values includes nonlinear components, and linear components referred to as the linear trend, comprising the steps of: Step 1-storing said N discrete measured values in the memory unit of a computer, said measured values being indexed in the order obtained by said sensor by the index values one through N. Step 2-programming the computer to calculate the incremental slope of the linear trend of said set of N measured values, said incremental slope being designated Y''. Step 3-programming the computer to calculate a new set of N values designated H(1), H(2), H(3)....H(N), said set of N calculated values being representative of said set of N measured values with the lineaR trend removed. Step 4-and programming the computer to calculate an orthogonal polynomial approximating function of said new set of N values of step 3 to produce a number of coefficients equal to N minus 2 minus index (N-2-index) which are representative of said physical variable, said coefficients being designated B(1), B(2), B(3)....B(N 2 index) where N-2-index is the number of coefficients which represent the N measured values with minimum error.
Claim 2
Independent Claim
244 words
A method of representing by coefficients a physical variable from which measured data values were obtained where said data is obtained by a series of measurements of a dependent physical variable at equally spaced intervals of an independent variable with a sensor to produce a set of measured values of said physical variable designated Y(1), Y(2), Y(3)....Y(N), and wherein said set of N measured values includes nonlinear components, and linear components referred to as the linear trend, comprising the steps of: Step 1-storing said N discrete measured values in the memory unit of a computer, said measured values being indexed in the order obtained by said sensor by the index values one through N. Step 2-programming the computer to calculate the incremental slope of the linear trend of said set of N measured values, said incremental slope being designated Y''. Step 3-programming the computer to calculate a new set of N values designated H(1), H(2), H(3)....H(N), said set of N calculated values being representative of said set of N measured values with the lineaR trend removed. Step 4-and programming the computer to calculate an orthogonal polynomial approximating function of said new set of N values of step 3 to produce a number of coefficients equal to N minus 2 minus index (N-2-index) which are representative of said physical variable, said coefficients being designated B(1), B(2), B(3)....B(N 2 index) where N-2-index is the number of coefficients which represent the N measured values with minimum error.
Claim 3
Independent Claim
309 words
A method of representing by coefficients a physical variable from which measured data values were obtained where said data is obtained by a series of measurements of a dependent physical variable at equally spaced intervals of an independent variable with a sensor to produce a set of N discrete measured values of said physical variable designated Y(1), Y(2), Y(3)....Y(N) and wherein said set of N measured values includes nonlinear components, and linear components referred to as the linear trend, comprising the steps of: Step 1-storing said N discrete measured values in the memory unit of a computer, said measured values being indexed in the order obtained by said sensor by index values designated (j 1), (j 2), (j 3)....(j N), where (j 1) is the index of the first measured value Y(1) and (j N) is the index for the last measured value Y(N). Step 2-programming the computer to calculate the difference between the first and last measured values (Y(N)-Y(1)) and dividing the difference by the value (N-1) to provide the incremental slope Y'' of the linear trend of the set of N measured values. Step 3-programming the computer to calculate a new set of N values by subtracting from each one of said N stored measured values a quantity equal to the first measured value Y1 plus the product of the slope Y'' and one less than the index of each measured value wherein said new set of calculated values is designated H(1), H(2), H(3)....H(N). Step 4-and programming the computer to calculate the sine Fourier transform of said new set of N values of step 3 to produce a number of harmonic coefficients equal to N-2-index which are representative of said N measured values, said harmonic coefficients being designated B(1), B(2), B(3)....B(N 2 index)where N-2-index is the number of coefficients which represent the physical variable with minimum error.
Claim 4
Independent Claim
309 words
A method of representing by coefficients a physical variable from which measured data values were obtained where said data is obtained by a series of measurements of a dependent physical variable at equally spaced intervals of an independent variable with a sensor to produce a set of N discrete measured values of said physical variable designated Y(1), Y(2), Y(3)....Y(N) and wherein said set of N measured values includes nonlinear components, and linear components referred to as the linear trend, comprising the steps of: Step 1-storing said N discrete measured values in the memory unit of a computer, said measured values being indexed in the order obtained by said sensor by index values designated (j 1), (j 2), (j 3)....(j N), where (j 1) is the index of the first measured value Y(1) and (j N) is the index for the last measured value Y(N). Step 2-programming the computer to calculate the difference between the first and last measured values (Y(N)-Y(1)) and dividing the difference by the value (N-1) to provide the incremental slope Y'' of the linear trend of the set of N measured values. Step 3-programming the computer to calculate a new set of N values by subtracting from each one of said N stored measured values a quantity equal to the first measured value Y1 plus the product of the slope Y'' and one less than the index of each measured value wherein said new set of calculated values is designated H(1), H(2), H(3)....H(N). Step 4-and programming the computer to calculate the sine Fourier transform of said new set of N values of step 3 to produce a number of harmonic coefficients equal to N-2-index which are representative of said N measured values, said harmonic coefficients being designated B(1), B(2), B(3)....B(N 2 index)where N-2-index is the number of coefficients which represent the physical variable with minimum error.
Claim 5
Dependent Claim
98 words
A method according to claim 2 wherein said step 4 of programming the computer to calculate the sine Fourier transform of said set of N values H(1) through H(N) includes the steps for calculating the coefficients B(1) through B(n 2 index) according to the relationship as follows: Step 4-1 calculate the product where k is equal to 1. Step 4-2 for j 1 calculate the product of step 4- 1 by (j-1). Step 4-3 calculate the trigonometric sine of the result of step 4-2. Step 4-4 multiply the result of step 4-3 by H(j) for j equal to
Claim 6
Independent Claim
321 words
A method of representing by coefficients a physical variable from which measured data values were obtained where said data is obtained by a series of measurements of a dependent physical variable at equally spaced intervals of an independent variable with a sensor to produce a set of N discrete measured values of said physical variable designated Y(1), Y(2), Y(3)....Y(N), and wherein said set of N measured values includes nonlinear components, and linear components referred to as the linear trend comprising the steps of: Step 1-storing said N discrete measured values in the memory unit of a computer, said measured values being indexed in the order obtained by said sensor by index value designated (j 1), (j 2), (j 3)....(j N) where (j 1) is the index of the first measured value Y(1) and (j N) is the index for the last measured value Y(N). Step 2-programming the computer to calculate the incremental slope Y'' of the linear trend of the set of N measured values. Step 3-programming the computer to calculate a new set of N values designated H(1), H(2), H(3)....H(N), said set of N calculated values being representative of said set of N measured values with the linear trend removed. Step 4-programming the computer to calculate an orthogonal polynomial approximating function of said new set of N values of step 3 to produce a number of coefficients equal to N-1 which are representative of said set of N measured values, said coefficients being designated B(1), B(2), B(3)....B(N 1). Step 5-programming the computer to calculate for each coefficient B(1) through B(N 1) the standard error of estimate of mean uncertainty and to store the index number of the coefficient producing the minimum value of error. Step 6-programming the computer to calculate the number N-2 minus the index number obtained in step 5 and to provide the coefficients B(1) through B(N 2 index), said coefficients representing the physical variable with minimum error.
Claim 7
Independent Claim
321 words
A method of representing by coefficients a physical variable from which measured data values were obtained where said data is obtained by a series of measurements of a dependent physical variable at equally spaced intervals of an independent variable with a sensor to produce a set of N discrete measured values of said physical variable designated Y(1), Y(2), Y(3)....Y(N), and wherein said set of N measured values includes nonlinear components, and linear components referred to as the linear trend comprising the steps of: Step 1-storing said N discrete measured values in the memory unit of a computer, said measured values being indexed in the order obtained by said sensor by index value designated (j 1), (j 2), (j 3)....(j N) where (j 1) is the index of the first measured value Y(1) and (j N) is the index for the last measured value Y(N). Step 2-programming the computer to calculate the incremental slope Y'' of the linear trend of the set of N measured values. Step 3-programming the computer to calculate a new set of N values designated H(1), H(2), H(3)....H(N), said set of N calculated values being representative of said set of N measured values with the linear trend removed. Step 4-programming the computer to calculate an orthogonal polynomial approximating function of said new set of N values of step 3 to produce a number of coefficients equal to N-1 which are representative of said set of N measured values, said coefficients being designated B(1), B(2), B(3)....B(N 1). Step 5-programming the computer to calculate for each coefficient B(1) through B(N 1) the standard error of estimate of mean uncertainty and to store the index number of the coefficient producing the minimum value of error. Step 6-programming the computer to calculate the number N-2 minus the index number obtained in step 5 and to provide the coefficients B(1) through B(N 2 index), said coefficients representing the physical variable with minimum error.
Claim 8
Dependent Claim
184 words
A method according to claim 4 wherein said step 4 of programming the computer to calculate an orthogonal polynomial approximating function of said set of N values H(1) through H(N) includes the steps for calculating by a sine Fourier transform the coefficients B(1) through B(N 2 index) according to the relationship as follows: Step 4- 1 calculate the product where k is equal to 1. Step 4- 2 for j 1 calculate the product of step 4- 1 by (j-1). Step 4- 3 calculate the trigonometric sine of the result of step 4- 2. Step 4- 4 multiply the result of step 4- 3 by H(j) for j equal to 1. Step 4- 5 repeat steps 4- 2, 4- 3 and 4- 4 for values of j equal to 2 through N and accumulate all the resultant values. Step 4- 6 multiply the accumulated value of step 4- 5 by the value 2/(N-1) and store as B(1). Step 4- 7 repeat steps 4- 1 through 4- 6 for values of k equal to 2 through (N-2-index) and store as B(2) through B(N 2 index).
Claim 9
Dependent Claim
223 words
A method according to claim 4 wherein step 5 of programming the computer to calculate the standard error of estimate of mean uncertainty for The coefficients B(1) through B(N 1) includes the steps as follows: Step 5- 1 storing an index m of value of one and program the computer to calculate and store an error value E'' where E'' is a function of B(N 1) and a distribution value T(m). Step 5- 2 programming the computer to increment the index value m by one and calculate a new error value E'' as a function of B(N 2) and T(m) and comparing the new error value with the previous error value and storing the lesser error value and the value of m associated with the lesser error value. Step 5- 3 programming the computer to separately calculate in sequence new error values as a function of each of the coefficients B(N 3) through B(1) and T(m) where m is incremented by one for each calculation and comparing each new error value with the previously calculated error value and storing the lesser error value and the index value m associated with the lesser error value. Step 5- 4 programming the computer to calculate the value MAX equal to N minus 2 minus index where index is the value finally stored in step 5- 3.
Claim 10
Dependent Claim
266 words
A method according to claim 4 wherein step 5 of programming the computer to calculate the standard error of estimate of mean uncertainty for each coefficient B(1) through B(N 1) includes the steps as follows: Step 5- 1 storing in the computer memory an initial value of error. Step 5- 2 programming the computer to calculate an initial value S2 which is a function of B2(N 1). Step 5- 3 programming the computer to calculate a value which is a function of B2(N 2) and adding the value to the value of S2 to form a new value S2. Step 5- 4 programming the computer to calculate the value E equal to S2/m2 where S2 is obtained in step 5- 3 and m is the degree of freedom for the coefficient B(N 2). Step 5- 5 programming the computer to multiply 5-value E of step 5- 4 by a distribution value T(m) to produce an error value E''. Step 5- 6 programming the computer to compare the error value E'' of step 5- 5 with the initial stored error value of step 1 and storing the lesser value. Step 5- 7 programming the computer to repeat steps 5- 3, 5- 4, 5- 5 and 5- 6 for the coefficient B(N 3) through B(1) to obtain and store the minimum error value E'' and the index of the coefficient for which the minimum value of E'' was calculated. Step 5- 8 programming the computer to calculate the value MAX equal to N minus 2 minus index where index is the value finally stored in step 5- 7.
References Cited (Backward Citations)
USPTO Annuity & Maintenance Windows
| Annuity Stage | Window Opens | Payment Deadline | Surcharge Period Until | Estimated Fee | Status |
|---|---|---|---|---|---|
| 3.5 Years (Year 4) | 1974-12-06 | 1975-06-07 | 1975-12-07 | $2000.00 | Window Closed / Lapsed |
| 7.5 Years (Year 8) | 1978-12-06 | 1979-06-07 | 1979-12-07 | $3760.00 | Window Closed / Lapsed |
| 11.5 Years (Year 12) | 1982-12-06 | 1983-06-07 | 1983-12-07 | $7700.00 | Window Closed / Lapsed |