Homework1

Homework1 - Homework #1. 1. Prove the following Fourier...

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Homework #1. 1. Prove the following Fourier Transform relations: a) F {1} = δ ( ν x ) δ ( ν y ) b) 11 {sgn(x)sgn(y)} = xy jj π νπ ν    F c) {f(x,y)} = {f(x,y)} = f(-x,-y) ±1 ±1 FF F F d) F {f(x,y)h(x,y)} = F {f(x,y)}* F {h(x,y)} e) 22 2 2 { f(x,y)} = - 4 ( + ) F { f(x,y)} πν ν F where 2 x y ∂∂ ∇= + is Laplasian operator 2. Suppose that a sinusoidal input f(x,y) = cos[2 (
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This note was uploaded on 04/02/2011 for the course ECE 264 taught by Professor Song during the Spring '11 term at UCSB.

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