Transfer function of a low-pass filter with cut-off freq. 6.5 (rad/s) is LPS (513 + 2s2 + 2s' + 1)3' ; s' = 5/6.5 Verify that HLp(s) has the poles of a 3rd order Butterworth LP filter. Next, show that bilinear transformation s = 2-1 = 20 -1 leads to the digital TIR filter Hup(z) with cut-off freq 0.0176 (2+1) HLP(Z) = -0.53) (22-1.232+0.53) (1) Note that cut-off freq's of CT and DT filters are related by freq. warping relationship sect = ) tan01); determine poles and zeros of the transfer function H(z); now, determine frequency response H, (W) = HP(Z = e) of the DT filter; Next we want to calculate and plot magnitude of HW), based on distances to poles ad zeros (as we did in class for a CT filter). However, for Fourier transform of DT filters, we move point z = ejw on unit circle from w = 0 to w = 211, determine its distance to poles and zeros of Hz), and calculate || H || from 14, d || HLp (z) || = Nd where d? and d are distances to the M zero and N poles of HLp (z). Verify LP- filtering behavior by plotting magnitude of frequency response using Matlab. Transfer function of a low-pass filter with cut-off freq. 6.5 (rad/s) is LPS (513 + 2s2 + 2s' + 1)3' ; s' = 5/6.5 Verify that HLp(s) has the poles of a 3rd order Butterworth LP filter. Next, show that bilinear transformation s = 2-1 = 20 -1 leads to the digital TIR filter Hup(z) with cut-off freq 0.0176 (2+1) HLP(Z) = -0.53) (22-1.232+0.53) (1) Note that cut-off freq's of CT and DT filters are related by freq. warping relationship sect = ) tan01); determine poles and zeros of the transfer function H(z); now, determine frequency response H, (W) = HP(Z = e) of the DT filter; Next we want to calculate and plot magnitude of HW), based on distances to poles ad zeros (as we did in class for a CT filter). However, for Fourier transform of DT filters, we move point z = ejw on unit circle from w = 0 to w = 211, determine its distance to poles and zeros of Hz), and calculate || H || from 14, d || HLp (z) || = Nd where d? and d are distances to the M zero and N poles of HLp (z). Verify LP- filtering behavior by plotting magnitude of frequency response using Matlab