Exploiting the relationship of the Gabor frame operator with the filter bank polyphase matrix, the authors provide a frame-theoretic analysis of filter banks. Conditions for perfect reconstruction are presented and the increased design freedom is illustrated by numerical simulations. In many applications the choice of the analysis window g and the lattice parameters a,b follows traditional rules of thumb. The author uses underspread operators to classify slowly time-varying processes. The optimization criteria for the adaptation are formulated in terms of the ambiguity function of g and the spreading function of the operator.
Numerical experiments demonstrate the practical performance of the proposed method.
Recently, the problem of signal detection based on linear time-frequency representations has received considerable attention. In Chapter 11 Ariela Zeira and Benjamin Friedlander formulate the problem of detecting a Gabor transient as problem of detecting a subspace signal in background noise. Using global ratio likelihood tests, they derive matched subspace detectors and discuss their sensitivity in terms of mismatch of the model parameters. Based on the sensitivity analysis they develop robust matched subspace detectors and analyze their performance. In Chapter 12 Yehoshua Y. Zeevi, Meir Zibulski and Moshe Porat present a detailed analysis of multi-window Gabor expansions.