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Unformatted text preview: University of Minnesota Dept. of Electrical and Computer Engineering EE3015 – Signals and Systems Discussion Session #11: Sampling 1. The following signal ) ( t x has been sampled at a rate of 10 samples/second ⋅ = t t t t t x π π π π ) 3 sin( ) 2 sin( ) ( a. Indicate if ) ( t x can be recovered from its samples ) ( s nT x , ,... 2 , 1 ± ± = n . Using properties, the FT of ) ( t x , namely ) ( ω j X , is given by ) ( * ) ( 2 1 ) ( 2 1 ω ω π ω j X j X j X = Where = t t FT j X π π ω ) 2 sin( ) ( 1 and = t t FT j X π π ω ) 3 sin( ) ( 2 . We know that < = → ← = Otherwise W j Y t Wt t y FT 1 ) ( ) sin( ) ( ω ω π Thus, ) ( ω j X is the convolution of two square signals centered at the origin. The convolution results in The maximum frequency of ) ( t x is π 5 = W rad/sec. The sampling frequency is 10 / 1 = = s s T f samples/sec or equivalently π π ω 20 10 2 = ⋅ = s rad/sec. Because W s 2 > ω the sampled signal will be recovered....
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- Fall '08
- Digital Signal Processing, Sin, jω, ωs ω