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Unformatted text preview: ESE 337 EXAM 1 FALL 2004 1. (a) Are the sinusoidal sequences sin3.1 πn and sin5 n , with T = 1, periodic? If yes, find the fundamental period for each sequence. What are their frequencies? (b) Consider the CT sinusoid x(t) = sin3 t . What are the frequencies of its sampled sequences with T = 0.5, 1, 2, 3? Which sequences have the same frequency as sin3 t ? (a) sin3.1 πn is periodic Fundamental period: P = 2πω = . 2π3 1 = 2.0 (NFR = ( π , π ] ) Frequency ω = 3.1 π 2 π 2 π = 0.9 π rad/s sin5 n is NOT periodic (NFR = ( π , π ] ) Frequency ω 0 = 5  2 π = 1.28 rad/s (b) T = 0.5 frequency = 3 (NFR = (2 π , 2 π ] ) T = 1 frequency = 3 (NFR = ( π , π ] ) T = 2 frequency = 3 π = 0.142 (NFR = (  π2 , π2 ] ) T = 3 frequency = 3  23 π = 0.906 (NFR = ( π3 , π3 ] ) when T = 0.5, T = 1, the sampled sequences have the same frequency as sin3 t 3. Compute the frequency spectrum of the sequence x ( nT ) = 1 for T = 0.5 and n = 2 : 2 and x ( nT ) = 0 for other n , at...
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 Fall '10
 ChiTsongChen
 Fourier Series, Frequency, NFR

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