DFT - ) with N L samples/2 will enable exact recovery of X(...

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1 EE 338 Discrete-time Signals and Systems Relationship between DTFT, DFS, DFT Example 1 : Finite-length sequence: x(n) = {0, 1, 2, 3} for 0 n 3 DTFT: ܺሺ߱ሻൌ݁ ି௝ఠ ൅2݁ ି௝ଶఠ ൅3݁ ି௝ଷఠ Sampling X( ω ) at N=4, 2, and 8 points per 2 π , respectively. In the frequency domain: In the time domain: If we sample X( ω ) N points per 2 π in the freq. domain, equivalently, in the time domain, we generate copies of x(n), shift the origin to integer multiples of N, and superimpose all replicas. If x(n)’s non-zero duration is L, to avoid time-domain aliasing, we should sample at least L samples per 2 π . Sampling X(
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Unformatted text preview: ) with N L samples/2 will enable exact recovery of X( ). 2 Example 2: 5-tap moving average: = otherwise n n x 4 1 ] [ DTFT: ) 5 . sin( ) 5 . 2 sin( ) ( 2 j e X = 5-point DFT: = = otherwise k k X 5 ) ( 10-point DFT: = = = 9 ,..., 2 , 1 1 1 5 ) ( 5 / k e e k k X jk jk Conclusion: = = otherwise N k X k X N k 1 | ) ( ) ( / 2 Increasing N (pad x[n] with more zeros) does not change the frequency spectrum but results in a denser sampling of the frequency spectrum....
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This note was uploaded on 12/20/2010 for the course E E 338 taught by Professor Vicky during the Spring '10 term at University of Alberta.

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DFT - ) with N L samples/2 will enable exact recovery of X(...

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