10Fall_hw10 - * ( t ) ←→ 2 πf * ( ω ) (b) Apply (a)...

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ECE210 - Fall 2010 - Homework 10 (Prof. Allen) (Due: Nov 03, 2010 at 5 p.m.) For all the following problems, it is assumed that f ( t ) ←→ F ( ω ) represents a Fourier transform (FT) pair unless otherwise indicated. 1. Problem 8.1 from text. 2. Problem 8.3 from text. 3. Problem 8.4 from text. 4. Use the “symmetry property” to find another FT relationship, starting from: f ( t ) = δ ( t - T o ) ←→ e - jωT o = F ( ω ) 5. Given a FT pair f ( t ) ←→ F ( ω ) , prove that (a) F
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Unformatted text preview: * ( t ) ←→ 2 πf * ( ω ) (b) Apply (a) to the FT pair δ ( t-T ) ←→ e-jωT (i.e., from problem 4) 6. Find the FT of f (3 t ) ←→ ??? 7. Find the FT of j πt 8. If f ( t ) = e-t u ( t ) and g ( t ) = sgn ( t ) = (-1 , t < 1 , t > , then compute the FT of ´ ∞-∞ f ( t-x ) g ( x ) dx 9. Define the term modulator, and describe in a sentence what it does or how it is used. 1...
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This note was uploaded on 03/05/2011 for the course ECE 210 taught by Professor Staff during the Fall '08 term at University of Illinois, Urbana Champaign.

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