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Wdft11 - ECE 421 Sum 2010 Detailed Solutions Set 11...

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ECE 421 - Sum 2010 Detailed Solutions - Set 11: Discrete Fourier Transform 1 11-1. Let the sampling interval T s 10 8 seconds in this problem. Let an analog signal be x t sin 2 π 10 6 t 0 t T 0 else 1 where the length T of the signal is a variable. Let x m be the sampled signal corresponding to equation (1) with T s 10 8 . Using this value of T s , compute the value of M which corresponds to the following values of duration T : (a) T = 4 μ sec. (b) T = 1 μ sec. DETAILED SOLUTION: This problem asks us to find the number of points M in a time span. From the Notes we know the following: given a sampling interval T s and a number of points M then the product M T s spans t M seconds, where t M M T s a Therefore, setting T in the problem statement equal to t M in a then gives T M T s b With T s 10 8 sec from the problem statement, equation b may be solved for M , giving M T T s T 10 8 c For T = 4 μ sec = 4 10 6 sec in part (a), equation c gives M 4 10 6 10 8 400 points d For T = 1 μ sec = 10 6 sec in part (b), equation c gives M 10 6 10 8 100 points e
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