Help me please 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 canrecover 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 aboutusing a Butterworth filter with half-power frequency @, = 200z rad/s to achieve this. To ensure desirablefiltering 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).

Fourier Transform- It is the process in which either a time-domain signal is converted to the…

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.