Matched multiwindow methods for the estimation and filtering of nonstationary processes

The short-time Fourier transform (STFT) and its squared magnitude, the spectrogram, are classical tools for linear and quadratic time-frequency signal representation. The choice of the STFT window entails a well-known duration-bandwidth tradeoff. Multi-window methods, as originally introduced by Thompson for spectrum estimation, help to overcome this tradeoff at the cost of a more complicated concept. The present paper extends multiwindow methods from spectral estimation to filtering of nonstationary processes. By using the Kohn-Nirenberg correspondence, new results about STFT-based filter design are obtained. For quasistationary processes with small product of temporal and spectral correlation width (underspread processes), it is shown that one and the same set of orthogonal windows is appropriate for both the estimation and the nonstationary Wiener filtering. This fact makes the present theory suitable to a numerically efficient, parallel concept for on-line signal enhancement.