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**Unformatted text preview: **EE533 Problem Set 2 1. Determine the DTFT of the rectangular window sequence w ( n ) = 1 , n M, , otherwise . Express your answer in the form W ( e j ) = e- jM/ 2 A ( ) where A ( ) is a real, even function of its argument. 2. Determine the inverse DTFT of X ( e j ) specified as X ( e j ) = j (4 + 2 cos + 3 cos 2 ) sin( / 2) e j/ 2 . What is the period of sin( / 2)? Is X ( e j ) periodic with period 2 ? 3. A periodic function F ( ) is defined in terms of a positive real number A for- : F ( ) = A + A/,- < ,- A + A/, . Determine the inverse DTFT of F ( ). Using this result, derive the DTFT of the sequence: x ( n ) = 1 /n, n 6 = 0 and x (0) = 0. Apply Parsevals theorem to this transform pair to obtain the value of n =1 1 /n 2 . 4. Evaluate X n =- sin( n/ 4) sin( n/ 6) 2 n 2 . The value of the summand at n = 0 is 1 / 24....

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