Wiener filtering in the windowed DFT domain

We focus on the use of windows in the frequency domain processing of data for the purpose of Wiener filtering. Classical frequency domain asymptotics replace linear convolution by circulant convolution, leading to approximation errors. The introduction of windows can lead to slightly more complex frequency domain techniques, replacing diagonal matrices by banded matrices, but with controlled approximation error. Other work observed this recently, proposing general banded matrices in the frequency domain for filtering. Here, we emphasize the design of a window to optimize the banded approximation, and more importantly, we show that the whole banded matrix is in fact still parametrized by a diagonal matrix, which facilitates estimation. We propose here both some non-parametric and parametric approaches for estimating the diagonal spectral parts and revisit in particular the effect of the window on frequency domain Recursive Least-Squares (RLS) adaptive filtering.