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20102ee113_1_homework6

20102ee113_1_homework6 - EE113 Digital Signal Processing...

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Some of the following problems are from the electronic versions of the chapters of An Undergraduate Course on Discrete-Time Signal Processing , by Prof. A.H. Sayed (posted on the class website): Problem 13.7, 13.8 In addition: Problem F. Evaluate the following series by using properties of the DTFT: 2 2 sin 3 n n n p p ¥ = æ ö ÷ ç ÷ ç ÷ ç ÷ ç ÷ ç ÷ ç ÷ ÷ ç è ø å and 2 1 cos 3 n n n p ¥ = å Hint : 2 2 1 1 6 n n p ¥ = = å Problem G. Using the plots of Fig. 13.9, plot the magnitude and phase responses of the modified DTFT: ( ) ( ) 2 ' 4 j w jw jw X e e X e p æ ö ÷ ç - + ÷ ç ÷ ç è ø = . Is the corresponding inverse transform ( ) ' x n a real sequence? Problem H. Show that an absolutely summable sequence always has finite energy. Hint : A sequence ( ) x n is absolutely summable (i.e. ( ) n x n ¥ =-¥ < ¥ å ) indicates that there exists a

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