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[A] The frequency response of a 2nd order LTI filter is H(e^jw)=(b0+b1e^-jw+b2*e^-2jw)/(1-a1*e^-jw-a2*e^-2jw)

Assume b1=b2=0. In each case state whether the filter is highpass, lowpass or band pass and draw the pole/zero plot.

i) a1=-1.8, a2=-.81
ii) a1=-1.27, a2=-.81
iii) a1=0,a2=-.81
iv) a1=1.27,a2=-.81

Explain the observations.

[B] The frequency response of an FIR filter is H(ejw)=b0+b1*e^-jw+b2*e^-2jw. In each case below, state whether the filter is highpass, lowpass, bandpass or band stop and draw the pole zero plot.

i) b0=1, b1=-1.8, b2=.81
ii) b0=1, b1=-1.27; b2=.81
iii) b0=1, b1=0, b2=.81

Explain the observations.

Solution Summary

The solution is provided with explanation and necessary plots in an attachment.