Research On Fast Algorithm Of Wavelet Transform And Its Hardware Implementation

As one of the most important signal processing tool raising after fourier transform,wavelet transform has drawn more and more attention recently.It overcomes the disadvantages,which the fourier transform and short time fourier transform have, that the time-frequency window is fixed and has no adaptability and is not suitable for multiresolution analysis and transient process.It is an efficient way to deal with instable signal especially for signals in which high frequency element last short time and low frequency element last long time.It can be localized both in time domain and frequency domain and is well known as "mathematical microscope'Mt has great significance for the development of wavelet transform to do research on the fast algorithm and hardware implementation circuit either in theory or in practice.Starting with the definition of wavelet transform and theory of multi-resolution,a new fast algorithm based on arithmetic fourier transform(AFT) is put forward after analyzing various wavelet transform fast algorithms.As multiplications of computing DFT are just 0(N) and the time needed can be reduced 90% through AFT especially for the length of large prime factor or prime length itself. On the other hand, the desconstruction and construction algorithm of Mallat can be computed by DFT,and so break a new path by connecting AFT and Mallat algorithm.A continuous and a discrete hardware implementation circuits are also proposed combining with logarithmic circuit filter and parallel pipeline.It is characterisized by simple structure,fast speed,small distortion and large dynamic range for continuous hardware implementation circuit.For discrete hardware implementation circuit,it has single phase clock,small gate delay time.In addition,coding algorithm is also adopted to cut down the amount of adders(subtracters) and registers for the purpose of better computing wavelet transform.