Expected Values of Functions of Quantized Random Variables

The computation of expected values of functions of quantized random variables is treated by sampling theory methods, as an extension of Widrow's work on the statistical theory of quantization. It is shown that such expected values can often be evaluated readily when conditions analogous to Nyquist sampling constraints are satisfied. An example-computation of the autocorrelation of a phase-quantized angle-modulated signal-is provided to illustrate the use of the theory. Other potential areas of application are suggested.