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Unformatted text preview: ELCT 321 Digital Signal Processing Homework Assignment # 4 (Sampling and Aliasing) by Dr. Yong-June Shin Assigned: October 11, 2011 Due: October 18, 2011 1. (30 Points) Consider following signal in time domain x ( t ) = cos(100 t )- 5sin(600 t ) + 3cos(200 t ) (a) Determine the fundamental frequency of the signal x ( t ) (b) Determine the Nyquist sampling rate such that no aliasing occurs in the sampled signal. (c) Assuming the sampling rate is 600 Hz, obtain the discrete time signal x[n] after the sampling. (d) The sampled signal x [ n ] obtained above is processed by the ideal D-to-C converters with the same sampling rate (600 Hz). Obtain the representation of the continuous signal y ( t ). 2. (20 Points) An amplitude-modulated (AM) cosine wave is repre- sented by the formula x ( t ) = [10 + cos(2 (2000) t ]cos(2 (10 4 ) t ) (a) Sketch the two-sided spectrum of this signal. Be sure to label important features of the plot....
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