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...

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Extracted 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="">