Program 461 Telemetry Aliasing Error Analysis

Aliasing error occurs when interpolation is applied to data samples whose period between samples is too great to recover the higher frequency components in the data spectrum. Since the data spectrum generally contains high frequency components which are not of interest, the signal is low-pass filtered to attenuate the undesirable portion of the spectrum. It is this portion, although attenuated, that folds about the Nyquist frequency thereby causing aliasing error. Aliasing error may be reduced by faster sampling andor better filtering. Since it is mandatory that a high degree of accuracy be attained with a minimum sampling rate, an optimization analysis is clearly necessary. To accomplish this, the telemetry system is described mathematically by the transfer functions of its significant blocks. Mathematical functions are derived for the Program 461 payload telemetry system, and utilized to compute rms aliasing error versus data sampling rate. Three different interpolation filter types are compared a physically realizable Butterworth, an ideal rectangular shape with infinite slope, and an optimum filter whose characteristics are a function of the data spectrum. Both the high resolution and low resolution channels are analyzed. The computation was performed on an IBM 7094 computer, with a program written so that system parameters could be easily varied.