Math 464
Homework: Due on 4/30
1) Reconstruct g∈V3given these coefficients in its Haar wavelet decomposition:
a2= [1,4,5,−3], b2= [−3,−2,1,−1].
The first entry in each list correponds to k= 0. Sketch g.
2) Reconstruct h∈V3given these coefficients in its Haar wavelet decomposition:
a1= [3,−2] b1= [−2,−3] b2= [−3,−3,−1,−1].
The first entry in each list correponds to k= 0. Sketch h.
3) Let j≥0 be an integer. Let f∈Vjwith coefficients in its Haar wavelet decomposition aj, aj−1, . . . , a1, a0
and bj−1, bj−2,...,b1, b0. Assume that fis supported in the interval [0,1).
(a) Find a matrix that will transform ajinto {bj−1, bj−2,...,b0, a0}.
(b) Find a matrix that will transform {bj−1, bj−2,...,b0, a0}into aj.
(c) Verify that the matrices found in part a. and b. are inverse of each other.
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