Optimally Karhunen-Loeve-like STFT expansion of nonstationary processes

To any nonstationary process, characterized by its correlation function, there corresponds an optimal window such that the short-time Fourier transform (STFT) coefficients are minimally correlated. The author makes this statement precise and derives a compact window optimization criterion in terms of the ambiguity function of the window and the expected ambiguity function of the process. As an application, he proposes a two-step procedure for time-varying spectral estimation: (I) window optimization based on an estimate of the expected ambiguity function, and (II) a spectrogram using the optimized window. An iterative algorithm is presented for the discrete-time window optimization, and experimental results are shown.<>