Filterbänke mit Überabtastung

Oversampled filter banks offer more design freedom, better numerical stability, and less sensitivity to quantization noise as compared to critically sampled filter banks. These advantages come at the cost of increased computational complexity. Therefore, oversampled modulated filter banks allowing a particularly efficient implementation are of practical interest. Furthermore, in certain applications (such as image coding) it is important to have linear phase filters in all channels of the filter bank. In this paper we discuss oversampled filter banks with emphasis on cosine-modulated filter banks and linear phase filters. We establish a relation of oversampled filter banks with redundant signal expansions. We also perform an analysis of the numerical sensitivity of oversampled filter banks. The increased design freedom in oversampled filter banks is demonstrated both theoretically and by means of simulation examples. Finally, we present a unified theory of cosine-modulated filter banks.