Spectral Representation of WSS Processes

Abstract

Purpose We want to obtain a generalisation of the expression of purely harmonic processes ${{X}_{t}} = \sum\nolimits_{{k = 1,p}} {{{\xi }_{k}}e{}^{{2i\pi {{f}_{k}}t}}}$ in the case of WSS processes that would be of the form ${{X}_{t}} = \int_{\mathbb{R}} {{{e}^{{2i\pi ft}}}d\hat{X}(f)}$, where the nature of $d\hat{X}(f)$ should be specified. This representation will enable the filtering of stationary processes to be studied in a simple way in the next chapter.