One Dimensional Discrete Dyadic Wavelet Transform

2.1 General Structure and Channel Characteristics

A fast algorithm [19,20] for computing a ID redundant discrete dyadic wavelet transform (RDWT) is shown in Fig. 1. The left side shows its decomposition structure, and the right, reconstruction. For an N-channel structure, there are N ā€” 1 high-pass or band-pass channels and a low-pass channel. Thus, the decomposition of a signal produces Nā€” 1 sets of wavelet coefficients and a coarse signal.

Since there is no down-sampling and up-sampling shown in Fig. 1, this redundant discrete dyadic wavelet transform does not correspond to an orthogonal wavelet basis.

For simplicity of analysis, an equivalent multichannel structure is shown in Fig. 2. This computational structure also makes obvious the potential for high-speed execution by parallel processing.

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