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Unformatted text preview: ECEN 314: Signals and Systems Solutions to HW 9 1. (3.34) The frequency response of the system is H ( jω ) = ∞ Z∞ ( e 4 t u ( t ) + e 4 t u ( t ) ) e jωt dt = Z∞ e t (4 jω ) dt + ∞ Z e t (4+ jω ) dt = 1 4 jω + 1 4 + jω (a) Here T = 1 and ω o = 2 π and a k = 1 for all k . The FS coefficients of the output are: b k = a k H ( jkω o ) = 1 4 j 2 kπ + 1 4 + j 2 kπ (b) Here T = 2 and ω o = π and a k = ‰ , k even 1 , k odd The FS coefficients of the output are: b k = a k H ( jkω o ) = ‰ , k even 1 4 jkπ + 1 4+ jkπ , k odd (c) Here T = 1, ω o = 2 π and a k = 1 / 2 , k = 0 , k even,k 6 = 0 sin πk 2 πk , k odd The FS coefficients of the output are: b k = a k H ( jkω o ) = 1 / 4 , k = 0 , k even,k 6 = 0 sin πk 2 πk • 1 4 jk 2 π + 1 4+ jk 2 π ‚ k odd 1 2. (3.35) The fourier series coefficients of y ( t ) are b k = H ( jkω o ) a k , where ω o is the fundamental fre quency of x ( t ) and a k are the FS coefficients of...
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This note was uploaded on 01/01/2012 for the course ECEN 314 taught by Professor Halverson during the Spring '08 term at Texas A&M.
 Spring '08
 HALVERSON
 Frequency

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