Signal Sampling and Quantization - Digital Signal Processing: Fundamentals and Applications - page 49

2.6 PROBLEMS

2.1. Given an analog signal

xðtÞ¼ 5cos ð 2 p$ 1 ; 500 tÞ; 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 up to 20 kHz.

2.2. Given an analog signal

xðtÞ¼ 5cos ð 2 p$ 2 ; 500 tÞþ 2cos ð 2 p$ 3 ; 200 tÞ; 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.

2.3. Given an analog signal

xðtÞ¼ 3cos ð 2 p$ 1 ; 500 tÞþ 2cos ð 2 p$ 2 ; 200 tÞ; 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.

2.4. Given an analog signal

xðtÞ¼ 3cos ð 2 p$ 1 ; 500 tÞþ 2cos ð 2 p$ 4 ; 200 tÞ; 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.

2.5. Given an analog signal

xðtÞ¼ 5cos ð 2 p$ 2 ; 500 tÞþ 2cos ð 2 p$ 4 ; 500 tÞ; 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;