Evolutionary spectral analysis and the generalized Gabor expansion
Aydın Akan, L.F. Chaparro · 2002
We present a connection between the discrete Gabor expansion and the evolutionary spectral theory. Including a scale parameter in the Gabor expansion, we obtain a new representation for deterministic signals that is analogous to the Wold-Cramer decomposition for non-stationary processes. The energy distribution resulting from the expansion is easily calculated from the Gabor coefficients. By choosing Gaussian windows and appropriate scales, the expansion can represent narrow-band and wide-band signals, as well as their combination. As an application, we consider the masking of signals in the time-frequency space and provide an approximate implementation using the new Gabor expansion. Examples illustrating the time-frequency analysis and the masking are given.