Lecture Notes on Wavelet Transforms by Lokenath Debnath & Firdous A. Shah

Author:Lokenath Debnath & Firdous A. Shah
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

First, we choose a = a 0 m , where and the dilation step a 0 ≠ 1 is fixed. Then, for m = 0, it becomes natural as well to discretize b by taking only the integer multiples of one fixed b 0, where b 0 is approximately chosen so that the ψ(t − nb 0) cover the whole line. For different values of m, the width is a 0 m times the width of ψ(t), so that the choice will ensure that the discretized wavelets at level m “cover” the whole line in the same way as the ψ(t − nb 0) do. Thus, we choose a = a 0 m , b = nb 0 a 0 m , where the two positive constants a 0 and b 0 are fixed. With these choices of a and b, the continuous family of wavelets ψ a, b as defined in (3.2.8) becomes

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