In this situation the Haar transform no matter what L is will have exactly 2 J

In this situation the haar transform no matter what l

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In this situation, the Haar transform (no matter what L is) will have exactly 2 J terms, so the length of x and w should be the same. If we interpret the input x as being scaling coefficients at scale J , then the vector w should consist of the scaling coefficients at scale J - L stacked on top of the wavelet coefficients for scale J - L stacked on top of the wavelet coefficients for scale J - L + 1, etc. Try your transform out on the data in blocks.mat and bumps.mat . For these two inputs, take a Haar wavelet transform with L = 3 levels, and plot the scaling coefficients at scale J - 3, and the wavelet coefficients at scales J - 3 down to J - 1. (For both of these signals, J = 10.) Also, verify that your transform is energy preserving. Turn in printouts of your code along with the plots mentioned above. 4. (Optional) Consider the function 1 ψ 0 ( t ) = 2 cos 3 πt 2 sin( πt/ 2) πt , and let ψ 0 ,n ( t ) = ψ 0 ( t - n ) . (a) Show that h ψ 0 ,n , ψ 0 ,k i = Z -∞ ψ 0 ,n ( t ) ψ 0 ,k ( t ) d t = ( 1 n = k 0 n 6 = k . (b) What is span ( { ψ 0 ,n ( t ) , n Z } )? That is, for what space is { ψ 0 ,n } n Z an orthobasis?
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