Non-uniformly downsampled filter banks

The problem of perfect reconstructing non-uniformly down-sampled filter banks is considered using frame theory and filter bank theory. This problem can be reformulated to a uniformly downsampled filter bank thus allowing the usual analysis. Of special interest are those filter banks where the output of the analysis bank has a direct interpretation e.g., the sliding-window Fourier transform or the wavelet transform. The concept of the sliding-window Fourier transform can be extended by replacing the Fourier transformation by an arbitrary unitary transformation. As an example the sliding-window Kautz transformation is considered.