On filter banks with rational oversampling

Despite the great popularity of critically-decimated filter banks, oversampled filter banks are useful in applications where data expansion is not a problem. We studied oversampled filter banks and showed that for some popular classes of filter banks it is not possible to obtain perfect reconstruction with rational (non-integer) oversampling ratios. Nevertheless, it is always possible to oversample the analysis filter bank by an integer factor, ie, there will be a similar synthesis bank which would provide perfect reconstruction. The analysis is carried within a time-aliasing framework development to analyze non-critically decimated filter banks.