A Generalized Weighted Overlap-Add (WOLA) Filter Bank for Improved Subband System Identification

This paper addresses the challenges in short-time Fourier transform (STFT) domain subband adaptive filtering, in particular, subband system identification. Previous studies in this area have primarily focused on setups with subband filtering at a downsampled rate, implemented using the weighted overlap-add (WOLA) filter bank, popular in audio and speech-processing for its reduced complexity. However, this traditional approach imposes constraints on the subband filters when transformed to their full-rate representation. This paper makes three key contributions. First, it introduces a generalized WOLA filter bank that repositions subband filters before the downsampling operation, eliminating the constraints on subband filters inherent in the conventional WOLA filter bank. Second, it investigates the mean square error (MSE) performance of the generalized WOLA filter bank for full-band system identification, establishing analytical ties between the order of subband filters, the full-band system impulse response length, the decimation factor, and the prototype filters. Third, to address the increased computational complexity of the generalized WOLA, the paper proposes a low-complexity implementation termed per-tone weighted overlap-add (PT-WOLA), which maintains computational complexity on par with conventional WOLA. Analytical and empirical evidence demonstrates that the proposed generalized WOLA filter bank significantly enhances the performance of subband system identification.