# Hw7 - y n,m = x n,m h n,m Problem 4 Part a Find and sketch the Fourier Transform of x u,v x u,v = cos ± 2 π 7 u 2 π 15 v ² Part b Find and

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ECE 301 Homework 7 Due July 22, 2011 Problem 1 Find the 2D CTFT of the signals below and use Matlab to make three-dimensional images of spectra. Part a: x ( u,v ) = cos( πu + 2 πv ) Part b: h ( u,v ) = ( U ( u + 2) - U ( u - 2)) e -| v | Part c: y ( u,v ) = x ( u,v ) * h ( u,v ) Problem 2 Find the inverse 2D CTFT of the spectra below, and use Matlab to make three-dimensional images of the signals. Part a: X ( μ,ν ) = e -| μ | cos( πν )( U ( ν + 1 2 ) - U ( ν - 1 2 )) Part b: H ( μ,ν ) = e - j ( μ +5 ν ) Part c: Y ( μ,ν ) = X ( μ,ν ) H ( μ,ν ) Problem 3 Find the 2D DTFT of the signals below and use Matlab to plot the spectra. Part a: x [ n,m ] = ± 1 | n | ≤ N, | m | ≤ M 0 otherwise Part b: h [ n,m ] = 1 + e - j ( n + m )

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Part c:
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Unformatted text preview: y [ n,m ] = x [ n,m ] * h [ n,m ] Problem 4 Part a: Find and sketch the Fourier Transform of x ( u,v ). x ( u,v ) = cos ± 2 π 7 u + 2 π 15 v ² Part b: Find and sketch the Fourier Transform of p ( u,v ). p ( u,v ) = ∞ X k =-∞ ∞ X l =-∞ δ ( u-4 k,v-4 l ) Part c: Find the Fourier Transform of y ( u,v ). y ( u,v ) = x ( u,v ) p ( u,v ) Problem 5 Repeat the previous problem, this time using q ( u,v ) instead of p ( u,v ). q ( u,v ) = ∞ X k =-∞ ∞ X l =-∞ δ ( u-4 k,v-1-2 k )...
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## This note was uploaded on 02/14/2012 for the course ECE 301 taught by Professor V."ragu"balakrishnan during the Fall '06 term at Purdue University-West Lafayette.

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Hw7 - y n,m = x n,m h n,m Problem 4 Part a Find and sketch the Fourier Transform of x u,v x u,v = cos ± 2 π 7 u 2 π 15 v ² Part b Find and

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