Question: Let f(x) = x. (a) Determine its Haar wavelet coefficients c j,k . (b) Graph the partial sums s r (x) of the Haar wavelet

Let f(x) = x.

(a) Determine its Haar wavelet coefficients c_j,k.

(b) Graph the partial sums s_r(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?

f(x) 2 cop(2) + 22-1 cjkW;;k(2). j=0 k=0 (9.136)

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