The impetus for this post is figure 1.4 on page 6 of Burrus et al. (Since it’s been a while, that’s Burrus, C. Sidney; Gopinath, Ramesh A.; Guo, Haitao. Introduction to Wavelets and Wavelet Transforms, A Primer. Prentice Hall, 1998.ISBN 0 13 489600 9.)
They offered the figure as an illustration of four different scaling functions; in addition, these scaling functions were parameterized by two angles.
Now I know how to produce the drawings of those scaling functions — and I also know how to produce drawings of the corresponding mother wavelets, which they did not show on page 6. It also turns out that they have interchanged the legends for figures (a) and (b) — and when we can produce the drawings ourselves, that mistake becomes almost irrelevant.
This post also serves to reiterate the calculation sequence for plotting a scaling function and its corresponding mother wavelet. Read the rest of this entry »