Hwk2_2006Fall

Hwk2_2006Fall - - x ( ) ( t- ) d (g) Determine the value of...

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ECE 3337 Homework 2 Fall 2006 Due: September 20 (Jansen), September 21 (Kalatsky), 2006 1. For the complex function de±ned by X ( z )= ( z 2 + e 2 )( z - j ) z ( z 2 +(1 . 8 cos π/ 4) z +0 . 81) , answer the following questions: (a) Determine the poles and zeros. (b) Compute the line integral for path P 1 :(0 ,j ) (1 ,j ). (c) Compute the contour integral with C 1 : | z | =1. (d) Compute the contour integral with C 1 : | z | =0 . 5. (e) Compute the contour integral with C 1 : | z +2 | =1. 2. A signal x ( t ) is de±ned by x ( t )= 1 - t 2 if - 1 <t 2 - 5+ t if 2 <t 5 0 elsewhere. (a) Sketch, to scale x ( t ). (b) Sketch, to scale x ( t - 3). (c) Sketch, to scale x (2(2 - t )). (d) Sketch, to scale x (1 - 3 t ). (e) Sketch, to scale x (2 + t/ 2). (f) Determine the value of
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Unformatted text preview: - x ( ) ( t- ) d (g) Determine the value of - x ( ) ( -2) d (h) Determine the value of - x ( t ) u ( t ) ( t + 1 . 5) dt 3. For each of the following signals, determine whether it is complex or real, periodic or nonperiodic (and compute the period, if possible), and sketch (to scale) the amplitude spectrum. (a) x 1 ( t ) = e j 10 t-j sin(10 t ) + cos(3 t ) 1 (b) x 2 ( t ) = je-j 10 t + cos(5 t ) (c) x 3 ( t ) = e j 10 t-sin(10 t + / 3) (d) Sketch, to scale, the phase spectrum for x 2 ( t ). 2...
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Hwk2_2006Fall - - x ( ) ( t- ) d (g) Determine the value of...

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