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CEN352 Digital Signal Processing by Dr. Anwar M. Mirza Assignment No. 01 Date: September 22nd, 2012

Due Date: September 29th, 2012

Note: For this assignment, your Handwritten, hard-copy solution is due on or before September 29th, 2012. Question No. 1 Given an analog signal:

x ( t ) =5 cos ( 2 π ∙ 1500 t ) , for t ≥ 0 , sampled at a rate of 8,000 Hz, a. sketch the spectrum of the original signal b. sketch the spectrum of the sampled signal from 0 kHz to 20 kHz.

Question No. 2 Given an analog signal:

x ( t ) =5 cos ( 2 π ∙ 2500 t ) +2 cos ( 2 π ∙ 3200 t ) , for t ≥ 0 , sampled at a rate of 8,000 Hz, a. sketch the spectrum of the sampled signal up to 20 kHz; b. sketch the recovered analog signal spectrum if an ideal lowpass filter with a cutoff frequency of 4 kHz is used to filter the sampled signal in order to recover the original signal.

Question No. 3 Given an analog signal:

x ( t ) =5 cos ( 2 π ∙ 2500 t ) +2 cos ( 2 π ∙ 4500t ) , for t ≥ 0 , sampled at a rate of 8,000 Hz, a. sketch the spectrum of the sampled signal up to 20 kHz; b. sketch the recovered analog signal spectrum if an ideal lowpass filter with a cutoff frequency of 4 kHz is used to filter the sampled signal in order to recover the original signal; c. determine the frequency / frequencies of aliasing noise.

Question No. 4 Given an analog signal:

x ( t ) =10 cos ( 2 π ∙ 5500 t) +5 sin ( 2 π ∙ 7500 t) , for t ≥ 0 , sampled at a rate of 8,000 Hz, a. sketch the spectrum of the sampled signal up to 20 kHz; b. sketch the recovered analog signal spectrum if an ideal lowpass filter with a cutoff frequency of 4 kHz is used to filter the sampled signal in order to recover the original signal; c. determine the frequency / frequencies of aliasing noise.

Question No. 5 Consider the analog signal:

x ( t ) =3 cos ( 100 πt )

Department of Computer Engineering

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College of Computer & Information Sciences, King Saud University Ar Riyadh, Kingdom of Saudi Arabia

CEN352 Digital Signal Processing by Dr. Anwar M. Mirza Assignment No. 01 Date: September 22nd, 2012

Due Date: September 29th, 2012

a. Determine the minimum sampling rate required to avoid aliasing. b. Suppose that the signal is sampled at the rate of 200 Hz. What is the discrete-time signal obtained after sampling? c. Suppose that the signal is sampled at the rate of f s=75 Hz . What is the discrete-time signal obtained after sampling? d. What is the frequency 0...