Short-term Spectral Analysis and Synthesis improvements with oversampled inverse filter banks

The Short Term Fourier Transform (STFT) is a classical linear time-frequency (T-F) representation. Despites its relative simplicity, it has become a standard tool for the analysis of non-stationary signals. Since it provides a redundant representation, it raises some issues such as (i) “optimal” window choice for analysis, (ii) existence and determination of an inverse transformation, (iii) performance of analysis-modification-synthesis, or reconstruction of selected components of the time-frequency plane and (iv) redundancy controllability for low-cost applications, e.g. real-time computations. We address some of these issues, as well as the less often mentioned problem of transform symmetry in the inverse, through oversampled FBs and their optimized inverse(s) in a slightly more general setting than the discrete windowed Fourier transform.