Power Spectra of Stationary Signals

Abstract

The Fourier transform X(f) of the sample paths of a stationary random signal X(t) does not exist in the usual sense, and analysis of the spectral contents of such signals requires a different, more subtle approach which has to rely on the concept of the mean power of the random signal. Only then we can investigate how the energy is distributed over different frequencies. The question is, of course, of fundamental importance in practical applications, as real-life signal processing devices such as measuring instruments, amplifiers, antennas, etc., transmit different frequencies with different attenuation.