HW9sol - 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

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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.

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HW9sol - 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

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