Question

Given below is the difference equation of an IIR Butterworth lowpass filter. The filter was designed...

Given below is the difference equation of an IIR Butterworth lowpass filter. The filter
was designed using bilinear transformation method where Ω? = 1.
?[?] =
2
3
(?[?] + ?[? − 1] +
1
2
?[? − 2])
(a) Plot the poles and zeros of the filter on the z-plane.

(b) Explain the causality and stability of the filter. Also, determine the ROC of the
filter.

(c) Find the cutoff frequency, ?? , of the filter.

(d) Compute |?(?)| for ? equals to 0, ??, and ?. Then sketch the |?(?)|.
(7 marks

Engineering   Electrical-Engineering   
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