I.I.D. stochastic analysis of PWM signals

A stochastic analysis for pulse width modulation (PWM) is given. Under a discrete random generator process with independent identically distributed (i.i.d.), continuous, range-limited samples, stochastic models for different PWM signals are proposed. Using randomization of the signal starting point, wide sense stationarity (WSS) of proposed PWM signals are shown. Autocorrelation functions and their corresponding power spectrum densities (PSD) are derived in terms of the modified complementary cumulative distribution function of i.i.d samples. For the case where the samples are i.i.d. uniformly distributed, the proposed autocorrelation functions are tested with simulations.