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**Unformatted text preview: **EE533 Problem Set-3 1. Consider the length-9 sequence x ( ) = { 2 , 3 , (- 1) , ,- 4 , 3 , 1 , 2 , 4 } . Evaluate the following functions of X ( e j ) without computing the transform itself: (a) X ( e j ) (b) X ( e j ) (c) R - X ( e j ) d (d) Z - | X ( e j ) | 2 d (e) Z - dX ( e j ) d 2 d Determine the following: (a) Inverse-DTFT of X ( e- j ) (b) Inverse-DTFT of X (- e j ) 2. An LTI system with impulse response { h ( n ) } and frequency response H ( e j ) has the following properties: (a) the system is causal; (b) H ( e- j ) = H * ( e j ); (c) the DTFT of the sequence { h ( n + 1) } is real; (d) H ( e j ) = 0; (e) R - H ( e j ) d = 4 . From the above information, determine h ( ) completely. 3. Determine the Inverse-DTFT of (a) X ( e j ) = cos N , for an arbitrary integer N &gt; 0. (b) Y ( e j ) = cos N ( / 2), for an arbitrary even integer N &gt; 0....

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