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5. For a lowpass signal with a bandwidth of 6000HZ, what is the minimum sampling frequency for perfect reconstruction of the signal? What is the minimum required sampling frequency if a guard band of 2000 Hz is required? If the reconstruction filter has the frequency response - K Ifl < 7000 Ifl – 7000 H(f) = K – K 7000 < |f] < 10,000 3000 otherwise Answer: e For no aliasing to occur we must sample at the Nyquist rate fs = 2 · 6000 samples/sec = 12000 samples/sec With a guard band of 2000 fs – 2W = 2000 ==fs = 14000 The reconstruction filter should not pick-up frequencies of the images of the spectrum X(f ). The nearest image spectrum is centered at fs and occupies the frequency band [fs – W, fs + W]1. Thus the highest frequency of the reconstruction filter (= 10000) should satisfy 10000 16000 For the value fs = 16000, K should be such that K fs = 1 ==K = 1/(16000)-

5. For a lowpass signal with a bandwidth of 6000HZ, what is the minimum sampling frequency for perfect reconstruction of the signal? What is the minimum required sampling frequency if a guard band of 2000 Hz is required? If the reconstruction filter has the frequency response - K Ifl < 7000 Ifl – 7000 H(f) = K – K 7000 < |f] < 10,000 3000 otherwise Answer: e For no aliasing to occur we must sample at the Nyquist rate fs = 2 · 6000 samples/sec = 12000 samples/sec With a guard band of 2000 fs – 2W = 2000 ==fs = 14000 The reconstruction filter should not pick-up frequencies of the images of the spectrum X(f ). The nearest image spectrum is centered at fs and occupies the frequency band [fs – W, fs + W]1. Thus the highest frequency of the reconstruction filter (= 10000) should satisfy 10000 16000 For the value fs = 16000, K should be such that K fs = 1 ==K = 1/(16000)-

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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5. For a lowpass signal with a bandwidth of 6000HZ, what is the minimum sampling frequency for perfect reconstruction of the signal? What is the minimum required sampling frequency if a guard band of 2000 Hz is required? If the reconstruction filter has the frequency response ´K Ifl < 7000 H(f) = Ifl – 7000 К — К 7000 < |f| < 10,000 3000 otherwise Answer: - For no aliasing to occur we must sample at the Nyquist rate fs = 2 · 6000 samples/sec = 12000 samples/sec With a guard band of 2000 fs – 2W = 2000 ==fs = 14000 The reconstruction filter should not pick-up frequencies of the images of the spectrum X(f). The nearest image spectrum is centered at fs and occupies the frequency band [fs – W, fs + W 1. Thus the highest frequency of the reconstruction filter (= 10000) should satisfy 10000 <fs – W==fs >16000 For the value fs = 16000, K should be such that K · fs = 1 ==K = 1/(16000)
Transcribed Image Text:5. For a lowpass signal with a bandwidth of 6000HZ, what is the minimum sampling frequency for perfect reconstruction of the signal? What is the minimum required sampling frequency if a guard band of 2000 Hz is required? If the reconstruction filter has the frequency response ´K Ifl < 7000 H(f) = Ifl – 7000 К — К 7000 < |f| < 10,000 3000 otherwise Answer: - For no aliasing to occur we must sample at the Nyquist rate fs = 2 · 6000 samples/sec = 12000 samples/sec With a guard band of 2000 fs – 2W = 2000 ==fs = 14000 The reconstruction filter should not pick-up frequencies of the images of the spectrum X(f). The nearest image spectrum is centered at fs and occupies the frequency band [fs – W, fs + W 1. Thus the highest frequency of the reconstruction filter (= 10000) should satisfy 10000 <fs – W==fs >16000 For the value fs = 16000, K should be such that K · fs = 1 ==K = 1/(16000)
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