Fast algo-tectures for discrete wavelet transforms
Krishna Aditya, Chee‐Hung Henry Chu, Harold H Szu · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1996
Here we present an FFT based architecture and algorithm for computing discrete wavelet transform of one dimensional discrete signals. The presented architecture is non recursive unlike dyadic subband decomposition and discrete wavelet transform coefficients at all resolutions can be generated simultaneously without waiting for generation of coefficients at a higher resolution. For long wavelet filters, this architecture is faster than architectures proposed so far, for DWT computation based on time domain convolvers. This architecture can be fully pipelined and complexity of control circuits for this architecture is much lower as compared to time domain convolvers and their systolic array implementations (which involve complex routing of data) proposed before. In time-domain convolution based architectures, with a single set of convolver, computation of DWT for an N-point signal takes a minimum of N cycles, whereas the proposed architecture, with full hardware implementation (no multiplexing of hardware) and when fully pipelined takes only a fraction of N cycles. This architecture will be suitable for analysis of signals like EEG, seismic data, etc., which are quasi-infinite, one dimensional signal streams. The speed advantage comes by using FFT based frequency domain convolutions and also due to consequent introduction of more parallelism.