The Hutlets - a biorthogonal wavelet family and their high speed implementation with RNS, multiplier-free, perfect reconstruction QMF

Abstract

The relationship between wavelets, Laplace pyramids and QMF are now well established. 1--3 In recent years biorthorgonal wavelets have become of increased interest because, compared with orthogonal wavelets, they are symmetric and linear phase. In this paper the Hut y function 4 is used as a scaling function (father wavelet) to construct a biorthogonal wavelet family, we call Hutlets. A realization with perfect reconstruction, multiplier- free quadrature mirror filters using RNS technic is proposed. The approximation-filter is a CIC lowpass, the detail-filter is a CHPC highpass, and the reconstruction filters are IIRs. Exact pole-zero annihilation is guaranteed by implementing polynomial filters, over an integer ring, in the residue arithmetic system (RNS). Since CIC and CHPC designs rely on the exact annihilation of selected poles-zeros, a new facilitating technology is required which is fast, compact, and numerically exact. How this can be achieved is the thrust of this paper. ..