GB1360104A - Function interpolator - Google Patents

Abstract

1360104 Interpolators A NATHAN 6 July 1972 [7 July 1971] 31851/71 Heading G4A A plurality M (# 4) of electrical signals representing samples of a function f(x) are multiplied with respective signals representing similar sampling functions of x and the resulting product signals are summed to produce a signal representing interpolation of the samples, each sampling function comprising a predetermined linear combination of a constant and a plurality k of sinusoidal functions having a linear frequency progression, and having a maximum value at the associated sampling point, k being the highest integer not greater than ¢M. The interpolating circuits described are hybrid, but entirely digital or entirely analogue circuits could be used. In the embodiment shown in Fig. 7 the variable x is split into an integral digital part xd and an analogue part #x taking values between 0 and 1. Function generators 30-33 derive the sampling functions of #x and the multiplication is effected by multiplying digital to analogue converters 34-37 supplied with a digital sample value of f(x) e.g. from a digital computer. To avoid discontinuities in #x during updating of the sample values fj, the signal #x may be replaced by linear saw-tooth signals which assume the values 0 and 1 at alternate sampling points. It is not necessary for the sampling points to be evenly spaced. In a further embodiment Fig. 15 (not shown) the variable is time, and the sampling functions are derived from a master oscillator by suitable processing and phase shifting of its output, the oscillator synchronizing the supply of sample values fj to the multipliers.