Problem 3: Consider signal At) = sinc²(50zrt). (a) Find the Fourier transform of At). (b) Based on its Fourier transform, calculate its bandwidth and its Nyquist sampling rate. (c) Signal (t) is sampled with sampling rate 300r rad/s (or 150 Hz). Design an ideal low pass filter that can recover the original (unsampled) signal perfectly.
Problem 3: Consider signal At) = sinc²(50zrt). (a) Find the Fourier transform of At). (b) Based on its Fourier transform, calculate its bandwidth and its Nyquist sampling rate. (c) Signal (t) is sampled with sampling rate 300r rad/s (or 150 Hz). Design an ideal low pass filter that can recover the original (unsampled) signal perfectly.
Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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![Problem 3:
Consider signal (t) = sinc²(50zxt).
(a) Find the Fourier transform of At).
(b) Based on its Fourier transform, calculate its bandwidth and its Nyquist sampling rate.
(c) Signal At) is sampled with sampling rate 300x rad/s (or 150 Hz). Design an ideal low pass filter that can
recover the original (unsampled) signal perfectly.
(d) To recover the original signal from the sampled signal in (c), we can use a low-pass filter. Now, think about
using a Butterworth filter with half-power frequency @, = 200z rad/s to achieve this. To ensure desirable
filtering behavior, we want the filter to satisfy:
|H(jm)| 2 0.95 at o = 150z rad/s.
• [H(jo) < 0.05 at o = 400x rad/s.
Calculate the smallest order n of the Butterworth filter that can satisfy the above criteria.
(e) Find all the poles of the resulting Butterworth filter in (d).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe0f7fc28-236d-4700-805b-600820c80257%2F37042b37-36d1-47fc-8ef8-75ac8ec07106%2Fli352g_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 3:
Consider signal (t) = sinc²(50zxt).
(a) Find the Fourier transform of At).
(b) Based on its Fourier transform, calculate its bandwidth and its Nyquist sampling rate.
(c) Signal At) is sampled with sampling rate 300x rad/s (or 150 Hz). Design an ideal low pass filter that can
recover the original (unsampled) signal perfectly.
(d) To recover the original signal from the sampled signal in (c), we can use a low-pass filter. Now, think about
using a Butterworth filter with half-power frequency @, = 200z rad/s to achieve this. To ensure desirable
filtering behavior, we want the filter to satisfy:
|H(jm)| 2 0.95 at o = 150z rad/s.
• [H(jo) < 0.05 at o = 400x rad/s.
Calculate the smallest order n of the Butterworth filter that can satisfy the above criteria.
(e) Find all the poles of the resulting Butterworth filter in (d).
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