2025A3_7S

# 2025A3_7S - f(0,f 1 4,f 1 2,f 3 4 into a sequence c,c 1,c 2,c 3 = ˆ f ˆ f 1 ˆ f 2 ˆ f 3 of four complex numbers a Use Fourier matrix 4 F Ω to

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MATH 2025 Spring 2007 Assignment 3 Due Friday, April 13, 2007 before the class Please show all work! 1. Let f = 3 ψ ϕ . What is the 2 × 2 matrix corresponding to f ? [Here ϕ := χ [0 , 1) and ψ := χ [0 , 1 / 2) - χ [1 / 2 , 1) ] (4 pts) 2. Assume that the Basic Two-Dimensional Haar Wavelet Transform of a sample ± s 00 s 01 s 10 s 11 produces the result ± 2 4 8 6 . (a) Explain how a = 2 relates to the sample. (5 pts) (b) Explain how h = 4 relates to the sample. (5 pts) (c) Find s 00 ,s 01 ,s 10 ,s 11 . (5 pts) 3. Calculate the two-dimensional Fast Haar Wavelet Transform for the data ˜ f = 3 1 9 7 7 9 5 7 8 6 7 3 2 4 8 6 . (6 pts) 4. Let f ( x ) = x 2 . The Discrete Fourier Transform transforms the se- quence of four numbers
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Unformatted text preview: f (0) ,f ( 1 4 ) ,f ( 1 2 ) ,f ( 3 4 ) into a sequence ( c ,c 1 ,c 2 ,c 3 ) = ( ˆ f , ˆ f 1 , ˆ f 2 , ˆ f 3 ) of four complex numbers. a) Use Fourier matrix 4 F Ω to ﬁnd ˆ f 3 . (5 pts) b) Use the RHS of the equation 4 F Ω = 1 0 1 0 1 i 1 0-1 0 1-i 1 1 0 0 1 i 2 0 0 0 0 1 1 0 0 1 i 2 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 . to ﬁnd the column vector [ ˆ f , ˆ f 1 , ˆ f 2 , ˆ f 3 ] T . (5 pts)...
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## This note was uploaded on 11/23/2011 for the course MATH 2025 taught by Professor Staff during the Spring '08 term at LSU.

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