Iterative Method for the Design of DFT Filter Bank

Abstract

Multirate adaptive filters have numerous advantages such as low computational load, fast convergence, and parallelism in the adaptation. Drawbacks when using multirate processing are mainly related to aliasing and reconstruction effects. These effects can be minimized by introducing appropriate problem formulation and employing sophisticated optimization techniques. In this paper, we propose a formulation for the design of a filter bank which controls the distortion level for each frequency component directly and minimizes the inband aliasing and the residual aliasing between different subbands. The advantage of this problem formulation is that the distortion level can be weighted for each frequency depending on the particular practical application. A new iterative algorithm is proposed to optimize simultaneously over both the analysis and the synthesis filter banks. This algorithm is shown to have a unique solution for each iteration. For a fixed distortion level, the proposed algorithm yields a significant reduction in both the inband aliasing and the residual aliasing levels compared to existing methods applied to the numerical examples.

Periodic, Strict, and Quasi-Invariance in Linear Systems

“…The above proposed framework applies to the multirate signal processing in the 1-D domain, which encompasses several applications such as filter banks design [13], high rate circuit design [14], resampling or non-uniform sampling of signals [12]. Dealing with multidimensional systems, the typical techniques employed in the 1-D case can not simply be exported to the D case, since typically change of domains imply complex integer matrix operations [4].…”

Optimization of switchable windows for low-delay spectral analysis-synthesis

“…hearing aids, where the overall delay of the spectral analysis-synthesis system must be small, e.g., below 10 ms, and must not vary when the analysis window is switched. While in the last years a couple of approaches for the optimal numerical design of analysis and synthesis filters have been proposed (e.g [4], [5], [6]), there has been less attempts in finding sets of optimal switchable windows for spectral analysis and synthesis. In [7] necessary conditions for perfect reconstruction are derived for a system with biorthogonal lapped transform using switchable spectral analysis and synthesis windows.…”

2m-Band Interleaved DFT Modulated Filter Banks With Perfect Reconstruction

“…Typically, oversampled DFT-FBs can provide most of the desired characteristics except critically sampled. 11,12 Based on stable, causal, IIR analysis and synthesis prototype filters, critically sampled PR DFT-FBs can be designed. 13 Recently, modified DFT modulated filter banks (MDFT-FBs) 14 and modified exponentially modulated filter banks (EMFBs) 15 are proposed, which own many properties such as critically sampled, PR, and FIR.…”