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ENEE241hw08

# ENEE241hw08 - ENEE 241 02 HOMEWORK ASSIGNMENT 8 Due Tue...

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ENEE 241 02* HOMEWORK ASSIGNMENT 8 Due Tue 04/05 The MATLAB functions OSHIFT , OFLIP and FDIAG found in the Assignment 8 folder can be used for circular shifts, circular reversals and products with Fourier sinusoids (by means of F ). You may use these functions to verify your results for Problem 8A. Copy these M-files to a local directory and include that directory in the MATLAB path. Problem 8A Suppose the signal s = a b c d e f g h T of Problem 7C has DFT S = 4 1 + 2 j 5 3 j 7 3 j 5 1 2 j T Without computing any DFTs or inverse DFTs, determine (in numerical form) the DFTs of the signal vectors s (1) through s (7) constructed in that problem. Problem 8B Let x be a real-valued vector of length N = 64 whose DFT X satisfies X [ k ] = 0 for k = 0 : 13 and X [ k ] = 0 for k = 14 : 32 Explain your answers to (i) (v) below. (i) (4 pts.) For what values of k between 33 and 63 does X [ k ] equal zero? (ii) (4 pts.) Let x (1) [ n ] = x [ n ] cos(3 π n/ 8) , n = 0 : 63 For what values of k does X (1) [ k ] equal zero? (iii) (4 pts.) Let x (2) = P 4 x + P 4 x For what values of k does X (2) [ k ] equal zero? (iv) (4 pts.) Let y = x + Rx What is the imaginary part of the vector Y ? Is it true that Y = RY ?

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ENEE241hw08 - ENEE 241 02 HOMEWORK ASSIGNMENT 8 Due Tue...

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