1a) Design a digital band stop filter of order 2 having Butterworth characteristics with a stop band from 2 kHz to 5kHz. Assuming a sampling frequency of 30 kHz, calculate the transfer function H(z), and give the difference equation of the digital filter. The accuracy of the numerical values of filter coefficients should be given up to 2 decimal places.(1: b) Canonic realisation of a digital filter is shown below.Determine the transfer function of the filter. Determine and comment on the system's stability. c) Determine whether the following statement is true or false.Explain your answer. Statement: If the bilinear z-transform method is used to transform an analogue all-pass filter to a digital filter, the resulting digital filter will also be an all-pass system.

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