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.