Quantized Oversampled Filter Banks with Erasures

Oversampled filter banks can be used to enhance resilience to erasures in communication systems in much the same way that finite-dimensional frames have previously been applied. This paper extends previous finite dimensional treatments to frames and signals in l2(Z) with frame expansions that can be implemented efficiently with filter banks. It is shown that tight frames attain best performance. In particular, if encoding with a uniform frame, the quantization error is minimized if and only if the frame is tight. In case of one erasure and if encoding with a strongly uniform frame, tight frames are still optimal. In case of more erasures, an expression for the mean square error is given and some general considerations are presented.