In this paper we focus on the use of windows in the frequency domain processing of data for the purpose of spectral parameter estimation. Classical frequency domain asymptotics replace linear convolution by circulant convolution leading to approximation errors. We show how the introduction of windows can lead to slightly more complex frequency domain techniques, replacing diagonal matrices by banded matrices, but with controlled approximation error. We focus on the estimation of zero mean Gaussian data with a parametric spectrum model and show the equivalence of three approximation/estimation criteria: Itakura-Saito distance (ISD), Gaussian Maximum Likelihood (GML) and Optimally Weighted Covariance Matching (OWCM). We specialize the discussion to the case of single
microphone based separation of quasiperiodic sources with AR spectral envelope.
