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?
(c) What is the maximal deviation ΙΙ f − sr ΙΙ∞ = max{| f(x) − sr(x) || 0 ≤ x ≤ 1} for each of your partial sums?
Transcribed Image Text:
f(x) 2 cop(2) + 22-1 ΣΣ cjkW;;k(2). j=0 k=0 (9.136)
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