Digital PM Spectra by Transform Techniques

We derive an expression for the power spectrum of a class of nonstationary processes with periodicity in the two-dimensional autocorrelation function such that R(t1, t2) = R(t1+ T, t2+ T). Such a class includes many of the common digital signals. The method of derivation is based on the double Fourier transform which relates the spectrum of any signal to its autocorrelation function. This points to a very simple method of finding digital spectra. The results are applied to derive the general expression for the power spectrum of a wave phase modulated with a pulse stream Σ∞−∞ang(t − nT). The only restrictions on the pulse stream are that the an's are independent and have identical probability distributions, and g(t) is integrable and of finite length.