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QUESTION 4 ITOTAL MARKS: 33 Q 4(a) [19 Marks] (i) Use the direct formula (as defined at the end of this paper) to calculate X1[n], the Discrete Fourier Transform (DFT) of the [13 marks] (ii) Using the result of part() above, calculate X2[n], the DFT of the sequence X1[k]= {1, 0, 1, 2} sequence X2[k] = {0,-1, 0, 1} Explain any assumptions that you make in doing so. 6 marks] Q 4(b) [14 Marks] (i) Draw a signal flow diagram for calculating the Discrete Fourier Transform (DFT) using the decimation-in-time (d-i-t) Fast Fourier Transform (FFT) algorithm, assuming that the input sequence is of [4 marks] length 4 (ii) Calculate the number of real additions and multiplications needed to calculate the DFT of any sequence of length 4, using the d-i-t algorthm. 23 real odd15 marks) (iii) Calculate the DFT of the sequence x2[k] (as given above in part [5 marks] (a)(ii)), using the d-i-t algorithm [End of Question 41

Please give me detailed solutions step by step, I am just trying to learn, thank you so much in advance! 2018

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