DWT and Filter Bank Algorithms
Jaideva C. Goswami, Andrew K. Chan · 2010
The continuous wavelet transform (CWT) places redundant information on the time-frequency plane. To overcome these deficiencies, the CWT is discretized and algorithms equivalent to the two-channel filter bank have been developed for signal representation and processing. The perfect reconstruction (PR) constraint is placed on these algorithm developments. This chapter develops these algorithms in detail, and shows the parallel between the algorithms of the discrete wavelet transform (DWT) and the two-channel filter bank. Since the semiorthogonal spline functions and the compactly supported spline wavelets require their duals in the dual spaces, signal representation and the PR condition for this case are developed along with the algorithms for change of bases. The chapter also discusses the basic concepts of sampling rate changes through decimation and interpolation, and then develops the algebra of the algorithms. The decomposition (analysis) algorithm discussed in the chapter is used most often in wavelet signal processing. Controlled Vocabulary Terms discrete wavelet transforms; filter banks