Problem 1:
(a) A designer has available a number of 4-point FFT chips. Show how three of these chips should be connected together so as to implement a 12-point DFT. Show your workings clearly.
(b) Write a Matlab code to demonstrate your solution in part (a). A suggested answer would include the following steps
(i) Generate 12 random values and use the fft command in Matlab to find its 12-point DFT.
(ii) Write Matlab code following your workings in part (a) to compute again its 12- point DFT.
(iii) Find a way to show that the results in the two steps above are indeed the same.
Problem 2: Consider the low-pass filter given by the following difference equation
yn = 1/6 (xn + xn-1 + 2xn-2 + xn-3 + xn-4) (1)
(a) What is the frequency response of the filter? Show your workings clearly.
(b) What are the amplitude and the phase response of the filter? Clearly show that the filter indeed has a linear phase response. Show your workings clearly.
(c) Write Matlab code to plot the amplitude and the phase response of the filter using the analytical expressions obtained in part (b). Place the zero-frequency at the centre of these responses. You are not allowed to use the freqz function in Matlab as part of your answer but you can use it for comparison purpose.
(d) Use the fft function in Matlab and zero-padding to compute the amplitude and the phase response of the filter.
(e) Visually show that the results in part (c) and part (d) are identical.