The Discrete Stationary Wavelet Transform
D. Sundararajan · 2015
The computation of the discrete wavelet transform (DWT) involves the downsampling operation, which is time variant. The discrete Fourier transform (DFT) of a data and that of its time-shifted version are related by the time-shift property. This chapter talks about the discrete stationary wavelet transform (SWT) which is essentially a DWT without downsampling, with assumed periodicity of the data. The SWT can be computed with DWT filters as well. The chapter presents algorithms for computing the SWT and the ISWT (inverse stationary wavelet transform). It shows the computation of a 2-level 4-point SWT and ISWT using a two-stage two-channel analysis filter bank. In computing the 2-D SWT, two downsampling operations are left out compared to the row-column computation of the 2-D DWT. To find the inverse, four different combinations of the coefficients are formed, and the 2-D IDWT is computed and averaged.