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Unformatted text preview: t ? (Recall 1 KHz = 1000 Hz = 1000 s1 ) Solution The maximum sampling period for perfect reconstruction is T 1/(2*50,000) = 105 s = 10 s (3) [4pts] A 10 KHz bandlimited signal is sampled at Nyquist rate. The only nonzero samples are: = = = ms t ms t t x 2 . 1 2 . 1 2 ) ( Compute x(0) (that is, x(t) for t=0 ms ). Recall 1 ms = 103 s . Solution The sampling period is T=1/(20,000) = 0.05 ms . Note that both 1.2 ms and 0.2 ms are integer multiples of the sampling period 0.05 ms . The reconstruction formula yields: ) 4 ( sinc ) 24 ( sinc 2 05 . 2 . sinc ) 2 . ( 0.05 (1.2)sinc ) 2 . 1 ( ) ( = + = = + = = t x t x x Hence x(0)=0. Alternatively, note that t=0 is one of the sampling times and the problem states that the sample value is zero. Hence x(0)=0....
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This note was uploaded on 05/05/2010 for the course MATH 464 taught by Professor Staff during the Spring '08 term at Maryland.
 Spring '08
 staff
 Math

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