Snowbird, UT, USA
March 28, 1995 to March 30, 1995
A. Sri-Krishna , Center for Adv. Comput. Studies, Univ. of Southwestern Louisiana, Lafayette, LA, USA
Cheehung Chu , Center for Adv. Comput. Studies, Univ. of Southwestern Louisiana, Lafayette, LA, USA
M. Bayoumi , Center for Adv. Comput. Studies, Univ. of Southwestern Louisiana, Lafayette, LA, USA
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.
digital signal processing chips; wavelet transforms; filtering theory; convolution; fast Fourier transforms; computational complexity; transforms; estimation theory; FFT architecture; FFT algorithm; fast Fourier transform; discrete wavelet transforms; one dimensional sequence; DWT coefficients; DWT decomposition; control circuits complexity; non-recursive method; recursive dyadic decomposition; decimators; filter length; input sequence; convolution
A. Sri-Krishna, Cheehung Chu, M. Bayoumi, "FFT based fast architecture & algorithm for discrete wavelet transforms", DCC, 1995, Proceedings DCC '95 Data Compression Conference, Proceedings DCC '95 Data Compression Conference 1995, pp. 441, doi:10.1109/DCC.1995.515550