(a) If the input to the three-scale FWT filter bank of Fig. 7.30(a) is the Haar scaling fu...

(a) If the input to the three-scale FWT filter bank of Fig. 7.30(a) is the Haar scaling function φ(n) = 1 for n = 0, 1,…, 7 and 0 elsewhere, what is the resulting transform with respect to Haar wavelets?

FIGURE 7.30 A three-scale FWT filter bank: (a) block diagram; (b) decomposition space tree; and (c) spectrum Splitting characteristics.

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(b) What is the transform if the input is the corresponding Haar wavelet function ψ(n) = {1, 1, 1, 1, −1, −1, −1, −1} for n = 0, 1,…, 7?

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(c) What input sequence produces transform {0, 0, 0, 0, 0, 0, B, 0} with nonzero coefficient Wψ(2, 2) = B?