PCM Processing in Bandpass Signals

Abstract

Several types of errors are generated when a bandpass analog signal is sampled such that it can be encoded into a sequence of digital words. Two of these types of errors are particularly dependent on the frequency band occupied by the input signal. These are: (1) the aliasing errors due to generation of unwanted spectral components and, (2) pulse width errors due to the use of finite width, flat topped pulses when regenerating-the analog signal. Expressions are presented for the spectral densities and total power of these error sources. The particular dependence of each on the location in frequency of the input signal is investigated and discussed. Quantization noise and distortion due to the smoothing filter which is used to reconstruct the signal are not considered in this paper. It is determined that the aliasing noise power as a function of the ratio of the signal center frequency to the sampling frequency has a series of relative minimums and maximums. A relationship defining the ratios at which the minimums occur is presented. An approximate formulation for the sample pulse width error is presented which allows a simple estimate of its magnitude to be made without knowledge of the smoothing filter transform or the sampling frequency. Quantitative results are presented as a function of the percentage bandwidth of the signal and the ratio of the sample pulse duration to the period of the center frequency of the signal. The results of the analyses are interpreted as design constraints.