Patent GB-1014818-A (GB)
Title: Improvements in function generators
IPC: G06G7/28
Filed: 1962-12-21
Abstract: 1,014,818. Electric analogue calculating. COMPAGNIE GENERALE DE TELEGRAPHIE SANS FIL & SOC. MAROCAINE DE RECHERCHES, D'ETUDES ET DE DEVELOPPEMENTS. Dec. 21, 1962 [Dec. 29, 1961], No. 48445/62. Heading G4G. Electric analogue computing system generating a function of a variable x within the range of variation x 1 <x<x n  equal to a given function of x, for n values x 1  . . . x n  of such interval; comprising means generating a first unity reference voltage, a second voltage analogous to variable x, multiplying means generating from such voltages other voltages respectively analogous to x, x<SP>2</SP> . . . x<SP>n</SP>; means for performing a weighted summation of voltages 1, x, x . . . x n  and for deriving n voltages analogous to n polynomials P 1  . . . P i  . . . P n  of degree n-1; the polynomial of rank i (i = 1 . . . n), P 1 , being defined by the condition that it is equal to 1 for x = x i  and to zero for x = x j , j being equal to 1 . . . n but different from i, and further means for performing the weighted summation of said polynomials with respective coefficients a 1  . . . a n ; a 1  being equal to f(x 1 ). A unit voltage energizes a n electric analogue multiplying network M 1  (Fig. 3), driven by a servomotor S responsive to an input analogue signal x, together with other similar networks M 2  to M 5 ; -the output of M 1  energizing M 2 ; the output of M, energizing M 3 ; and so on to develop voltages representing 1, x, x<SP>2</SP>, x<SP>3</SP>, x<SP>5</SP> which are supplied to a combination of summing and multiplying networks MF (which may be of the kind described in Specification 703,178) having outputs representing six predetermined polynomials P 1  to P 6  arranged respectively to have values of unity at x 1  = -1, x 2  = - 0À6, x 3  = - 0À2, x 4  = +0À2, x 5  = +0À6, x 6  = +1 in succession and zero at all other values. The polynomial voltages are supplied to a further multiplier network C 1  where they are multiplied by adjustable coefficients f(x p ) and the outputs are added to S to produce a voltage S = #f(x p )p p  representing approximately a desired function f(x). The analogue voltages of P 1  to P 6  are also applied to a multiplier network C 2  for multiplication by coefficients g(x p ) and the outputs are added to produce a voltage representing a further function g(x). The apparatus is e.g. applicable to evaluate a trigonometrial function y = cos #x/2. In a modification (Fig. 5), a unity voltage (= u 1 ) and the output u 2  = x of multiplying network M 1  are applied to network MF, while x energizes M 2  to produce a voltage x<SP>2</SP> which is multiplied by 2 at L 2 , and unity is subtracted from the output at N 2  to produce a voltage analogue of u 3  = 2x<SP>2</SP> - 1. Similarly, other multiplying and subtracting networks L 3  N 3  associated with M 3  L 4 , N 4  associated with M 4 , L 5  N 5  associated with N 5  produce outputs u 4  = 4x<SP>3</SP> - 3 x , u 5  = 8x<SP>4</SP> - 8x<SP>2</SP> + 1, u 6  = 16x<SP>5</SP> - 20x<SP>3</SP>+5x all applied to network MF producing the voltage analogues of polynomials P 1  to P 6  which are respectively multiplied by f(x 1 ) to f(x 6 ) as before and added to give the voltage analogue of f(x).