4. a) i) ii) Design a length-5 Finite Impulse Response (FIR) band-stop filter with a symmetric impulse response, with the following specifications: |H(0)| = 1, |H(/2)| = 0 and |H()| = 0.6. Hence, determine the impulse response h[n] and the transfer function H(z). iii) Prove that the filter designed in part i) above has linear phase response. i) Draw a direct form realisation of the designed filter in part i) above using minimum number of multipliers. b) When designing FIR filters, the impulse response is usually modified by a windowing function. ii) Using a suitable window (other than the rectangular), design a 10th order FIR low-pass filter with cut-off frequency at 5 kHz if the sampling frequency is 40 kHz. Hence, find all filter coefficients. [Hint: Stop band ripples should be less than -40 dB]. Draw a direct form realisation of the filter designed in part i) above using minimum number of multipliers. iii) Using the filter you have designed in part ii) above as a starting point, design a high-pass filter with the same design specifications. 8 2 3 6 3 3 Total 25