FFT based fast architecture & algorithm for discrete wavelet transforms

Summary form only given. A non-recursive (unlike classical dyadic decomposition) and fast Fourier transform based architecture for computing discrete wavelet transforms (DWT) of a one dimensional sequence is presented. The DWT coefficients at all resolutions can be generated simultaneously without waiting for generation of coefficients at a lower octave level. This architecture is faster than architectures proposed so far for DWT decomposition (which are implementations based on recursion) and can be fully pipelined. The complexity of the control circuits for this architecture is much lower as compared to implementation of recursive methods. Consider the computation of the DWT (four octaves) of a sequence. Recursive dyadic decomposition can be converted to a non-recursive method as shown. We can move all the decimators shown to the extreme right (towards output end) and have a single filter and a single decimator in each path. We note that a decimator (of factor k) when so moved across a filter of length L will increase the length of the filter by a factor of k. Thus we will get first octave DWT coefficients by convolving input sequence with a filter of length L and decimating the output by a factor of 2.