a) Define the z-transform and explain how it can be used to evaluate the output frequency response of a digital filter with a sampled input signal when the impulse response h[n] of the filter is known. b) The following figure shows a sampled signal and the desired sampled signal. A digital signal processing system is-required to change the sampled signal to produce the desired output signal.

i) Design the required digital signal processing system and provide the z-transfer function. Determine and comment on the system's stability. ii) Determine the frequency response and magnitude response of the designed system. Calculate the magnitude response at a digital frequency of π/4. iii) Using the transfer function obtained in QB2(b)(i),determine the difference equation of the system. c) An ideal filter has exactly flat pass-bands with constant gain,exactly flat stop-bands with zero gain, and zero-width transition bands. Sketch an example of such an ideal filter-and explain why the ideal filter cannot be realised practically.