Let f(x) = x. (a) Determine its Haar wavelet coefficients c j,k . (b) Graph the partial

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Let f(x) = x.


(a) Determine its Haar wavelet coefficients cj,k


(b) Graph the partial sums sr(x) of the Haar wavelet series (9.136) where j goes from 0 to r = 2, 5, and 10. Compare your graphs with that of f and discuss what you observe. Is the series converging to the function? Can you prove this? 


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(c) What is the maximal deviation ΙΙ f − sΙΙ∞ = max{| f(x) − sr(x) || 0 ≤ x ≤ 1} for each of your partial sums?

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Applied Linear Algebra

ISBN: 9783319910406

2nd Edition

Authors: Peter J. Olver, Chehrzad Shakiban

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