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 Thomson 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 presented theory to
a numerically efficient, parallel concept for on-line signal enhancement.