Widft12 - ECE 421 - Sum 2010 Detailed Solutions Set 12 :...

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Unformatted text preview: ECE 421 - Sum 2010 Detailed Solutions Set 12 : Inverse Discrete Fourier Transform 1 12-1. Let a time domain signal x [ m be the M = 4 sample set given by the time-domain vector x , where x = h x [ ; x [ 1 ; x [ 2 ; x [ 3 i T = h 1 ; 1 ; 1 ; 1 i T Use the matrix interpretation of the DFT to compute the frequency-domain vector X , where X = h X [ ; X [ 1 ; X [ 2 ; X [ 3 i T DETAILED SOLUTION: Note that if we drew the x [ m by connecting the dots, we would see a DC waveform, a low frequency. Therefore, the DFT should produce a math result which is consistent with this observation. Substituting the x [ m from the problem statement into equation (4) from the Notes then gives 6 6 6 6 4 X [ X [ 1 X [ 2 X [ 3 7 7 7 7 5 = 6 6 6 6 4 1 1 1 1 1 e j = 2 e j e j 3 = 2 1 e j e j 2 e j 3 1 e j 3 = 2 e j 3 e j 9 = 2 7 7 7 7 5 6 6 6 6 4 1 1 1 1 7 7 7 7 5 a Evaluating the complex exponential terms in the matrix, you will see that equation...
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This note was uploaded on 09/07/2010 for the course ECE 421 taught by Professor Hallen during the Summer '08 term at N.C. State.

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Widft12 - ECE 421 - Sum 2010 Detailed Solutions Set 12 :...

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