Question

a) Impulse invariant and the bilinear z-transform are two methods that can be used to implement infinite impulse response (IIR) digital filters based upon analogue prototypes. Explain the two methods. For an analogue bandstop filter, which method(s) will result in a digital band stop filter? Explain your answer. b) An analogue filter is to be implemented as an IIR digital filter using the bilinear z-transform method. The required,frequency normalised, filter transfer function is given by: H(s)=\frac{s^{2}}{s^{2}+\sqrt{2} s+1} The implemented digital filter is required to have the above frequency behaviour based upon a cut-off frequency at 2.5kHz for sampling frequency of 8 kHz. Design and obtain the required IIR digital filter Transfer function H(z). c) Consider an analogue filter having the transfer function as shown below: H(s)=\frac{s+a}{(s+a)^{2}-b^{2}} i) Determine the impulse response of the filter. ii) Design a digital version of the analogue filter by employing the impulse invariance method with a sampling interval of t, milliseconds, and obtain its z-transfer function. Please note that in this design, a = 2,1, and to is an integer which is the last two digits of your student ID (if the last two digits of your student ID is 00, please use t = 1).

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