assignment 5 New - Signals and Systems (EENG 320)...

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Signals and Systems (EENG 320) Assignment (5) 1. Use either the Fourier transform analysis and synthesis equations or the Fourier transform properties to: a. Compute the Fourier transform of each of the following signals: i. 0 ), ( )] cos( [ > α ω t u t e o t ii. as shown in figure (1). ) ( t x t x(t) b. Determine the continuous-time signal corresponding to each of the following transforms: i. [] ) 2 ( ) 2 ( 3 sin 2 ) ( πω π = j X ii. ) 3 / 4 cos( ) ( + = j X 2. Determine which, if any, of the real signals depicted in Figures (2-4) have Fourier transforms that satisfy each of the following conditions: i. {} 0 ) ( = j X e ii. 0 ) ( = j X m Figure 1 1 2 2 3 4 -2 -1 -5 -3 -4 5 6 7 1 -6 0 …. …. t x(t) 2 1 -2 -1 Figure (2) 1
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t 2 /2 () t xt e = Figure (3) t 2 t x tt e = Figure (4) 3. If ) ( ω j X denotes the Fourier transform of the signal depicted in figure (5), ) ( t x t x(t) 2 -1 0 1 3 2 1 Figure (5) i. Find ) ( j X ii. Find ) 0 ( j X iii. Find +∞ ωω d j X ) ( iv. Evaluate +∞ d j X 2 ) ( v. Sketch the inverse Fourier transform of { } ) ( j X e
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assignment 5 New - Signals and Systems (EENG 320)...

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