1.     (a)     (10 marks) A causal system produces the output sequences

1,                         n = 0

0,                        otℎeTwise

when the following input sequence is applied:

−0.6,                n = 2

0,                       otℎeTwise

Using z-transform, determine its transfer function and comment on the stability of the system.

(b)    (15 marks) A Butterworth analog bandpass filter is to be designed with

the following specifications: passband edges at 10 Hz and 20 kHz,             stopband edges at 5 Hz and 25 kHz, peak passband ripple of 0.3 dB and  minimum stopband attenuation of 40 dB. Determine the bandedges and the order of the prototype analog lowpass filter. What is the order of the bandpass filter?

2.     (a)    (13 marks) Using impulse invariance method with a sampling rate of

100 Hz, convert the analog filter with system function Ha (s) =

into an IIR filter.

(b)    (12 marks) An analog filter with resonant frequency Ωr = 4 rad/s has

system function

Ha (s) =

A digital IIR filter with a resonant frequency of ωr = π/2 is to be               designed by applying bilinear transformation to the above analog filter. Determine the sampling interval using frequency pre-warping and         derive the transfer function of the desired IIR filter.