Waveform error control in PCM telemetry

An optimum system for transmitting a sample function from a stationary second order process over the BSC in real time is formulated under the mean-integral-square error criterion. The optimum number of channel bits and the optimum assignment of these bits to the samples is determined for the SGM process with
R(\tau) = \exp(-|\tau})
. The system error is evaluated and compared to the error performances of systems using time sampling with and without data compression. Shannon's information rate is also computed for these systems and compared to the theoretical limit and to Goblick's BSQC digitizer. We also present a waveform representation technique based on Hotelling's method of principal components. The waveform-to-vector converter consists of a time sampler followed by a digital filter, and the vector-to-waveform reconstructor consists of a digita filter followed by a linear interpolator. Performance is shown to be comparable to KL sampling.