Assignment1Sol - EE 308 Communication Systems IIT Bombay...

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EE 308: Communication Systems IIT Bombay, Dept. of Electrical Engineering Semester: Autumn 2009 Instructor: B. K. Dey Solution to Assignment 1: Fourier Series, Fourier transform Date: 14 August 2009 Ans 1: f ( t ) = e - at - ∞ ≤ t ≤ ∞ E ( t ) = Z -∞ | e - at | 2 d t = - 1 2 × a × [ e -∞ - e ] f(t) is not an energy signal. P ( t ) = lim T →∞ 1 T Z T/ 2 - T/ 2 | e - at | 2 d t = lim T →∞ e aT - e - aT 2 aT = lim T →∞ sinh( aT ) aT f(t) is not a power signal. If a = P ( t ) = lim T →∞ 1 T Z T/ 2 - T/ 2 | e - jωt | 2 d t = lim T →∞ e jωT - e - jωT 2 jωT = lim T →∞ sin( ωT ) ωT = 1 . Ans 2: g 1 ( t ) = g ( - t ) G 1 ( ω ) = G ( - ω ) G 2 ( ω ) = G ( ω ) e - + G ( - ω ) e - G 3 ( ω ) = G ( - ω ) e + G ( ω ) e - g 4 ( t ) = g ( t - 1) + g 1 ( t ) 1
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2 G 4 ( ω ) = G ( ω ) e - + G ( - ω ) g 5 ( t ) = 3 2 g ( t 2 - 2) G 5 ( ω ) = 3 G (2 ω ) e - j 2 ω . Ans 3:
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