090206HomeWork4

090206HomeWork4 - ECE 700 Digital Signal Processing Home...

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ECE 700 Digital Signal Processing Home Work 4 Due 2/16/09 1. (CWT ) Let CWT (,) Xa τ be the Continuous Wavelet Transform of the signal x ( t ). Show that a. If y ( t ) = x ( t - t 0 ), then CWT CWT 0 (, ) . Ya X at ττ =− b. If 1 () ( ) , t gt f s s = then CWT CWT ( , ) . a Ga X s s = 2. (Wavelets) Suppose that if φ ( t ) is an orthogonal scaling function with CTFT Show that . ΦΩ 2 (2 ) 1 l l π =−∞ . Φ Ω+ = 3. (Spline wavelets) The first order spline scaling function is defined as ,0 1 (2 ) , 1 2. 0, otherwise At t tA t t < < a) Find the value of A so that () 1 . t = Sketch ( t ) for this A . b) Find the coefficients h[n] so that ( t ) satisfies the scaling equation 2 [ ] (2 ) . n th n t φφ n = c) Assume that [ ] ( 1) [ 1 ]. n g nh N −− n Find N and the wavelet ψ ( t ) such that 2 ) , n tg n t ψφ =−∞ n = and ( t ) is non-zero only in the interval [0, 2]. 1
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Part II (MATLAB Exercises) 1. (Two channel orthogonal FIR filterbank) In this problem, you will design a 2 channel, real-coefficient, FIR orthogonal filterbank using the zero-phase, half-band filter approach.
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This note was uploaded on 04/18/2009 for the course ECE 700 taught by Professor Un during the Winter '09 term at Ohio State.

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090206HomeWork4 - ECE 700 Digital Signal Processing Home...

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