Patent GB-1285562-A (GB)
Title: An apparatus for function generation by linear interpolation
Inventor: BURRAGE ROBERT GRAHAM
IPC: G06G7/30
Filed: 1968-10-17
Abstract: 1285562 Interpolation junction generators JOSEPH LUCAS (INDUSTRIES) Ltd 21 Nov 1969 [17 Oct 1968] 49333/68 Heading G4G Apparatus for generating a mathematical function y=f(x) by linear interpolation makes use of the formula y = y 1 [(x 2 -x)/(x 2 -x 1 )] + y 2 [(x-x 1 )/(x 2  - x 1 )] where x lies between values x 1 ,x 2  for which the values of y 1 , y 2  are known. The apparatus comprises interpolation function generators 35, 37, Fig. 5, which generate the two ratios in the formula, function generators 30, 31 for generating y 1 , y 2  from inputs x 1 , x 2 , multiplying circuits 34, 36 for producing either term of the formula, and an adding circuit 40 for adding the terms. The interpolation function generators 35, 37 are shown in detail in Fig. 1. Voltages 3, 9, Fig. 1, of equal magnitude and opposite polarity representing the input variable x are applied respectively over resistances 2, 8 to the anode of diode 1 and the cathode of diode 7. When the input voltage 3 is sufficiently positive to overcome the negative bias on diode 1 set by potentiometer 5, a current flows through potentiometer 12 and a positive voltage appears on the cursor 12a. The rate of change of this voltage with respect to the input 3 depends upon the setting of potentiometer 12. Similarly, a negative voltage varying proportionately to input 9 appears on the cursor 13a of potentiometer 13. These voltages are summed in amplifier 14 which is prevented from giving a negative output by diode 19. The output of interpolation function generator 35 is shown as a graph in which x is measured along the horizontal axis X and the output voltage is measured along the vertical axis Y. The voltage in line 17 rises from a point on the X axis representing the level of the bias applied to the diode 1 and the voltage in line 18 falls from a point on the X axis representing the level of the bias applied to the diode 7. The output characteristic of the summing amplifier 14 is therefore as shown in the upper graph of Fig. 5 where the peak of the graph occurs at an x value corresponding to the bias applied to diode 7. This is set to equal x 1  and to yield an output value equal to unity. The potentiometer 13 is set to cause the characteristic to fall to zero output as x approaches the value x 2 . By geometry, the output of generator 35 for an input x between x 1  and x 2  is the ratio in the first term of the formula for y. The potentiometers in interpolation function generator 37 are set to give the characteristic shown in the lower graph of Fig. 5 and the output represents the ratio in the second term of the formula for y. In each generator 35, 37, the peak of the character - istic occurs at a value of x corresponding to the input of the respective associated function generator 30, 31, and the characteristic falls to zero at a value of x corresponding to the input of the other function generator. The range of values of x may be extended by providing further interpolation generators and function generators all connected to the output adder 40 (Fig. 6, not shown). For each such interpolation generator, the characteristic falls to zero at the values of x which respectively provide the inputs to the next preceding andthe next subsequent function, generator. The function generators 30 31 &c. may be modified to produce an output y which is a function of one or more variables in addition to x.