(a) Use (9 142) to construct the mother wavelet corresponding to the hat function (9 140) (b) Is the hat function orthogonal to the mother wavelet (c) Is the hat function orthogonal to its integer translates w(x) (1)k cp k P (2x k) k 0 cp (2x) Cp 1' 14(2x 1) Cp 2 (2x 2) P 2 c (2x p) (9 142)

Question: (a) Use (9.142) to construct the mother wavelet corresponding to the hat function (9.140). (b) Is the hat function orthogonal to the mother wavelet? (c)

(a) Use (9.142) to construct the “mother wavelet” corresponding to the hat function (9.140).

w(x) = (1)k cp_k P (2x k) k=0 = cp (2x) -

Cp-1' 14(2x 1) + Cp_2 (2x 2) + P-2 c (2x p).

(b) Is the hat function orthogonal to the mother wavelet?

w(x) = (1)k cp_k P (2x k) k=0 = cp (2x) - Cp-1' 14(2x 1) + Cp_2 (2x 2) + P-2 c (2x p). (9.142)

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a To construct the mother wavelet corresponding to the hat function we need to determine the values of the coefficients Cp for each term in the equation 9142 The hat function wx is defined as wx 1pk C... View full answer

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