4. The Discrete Fourier Transform (DFT) of a signal s(n) is given below: 2k s(k) = S(n) A. Calculate the DFT and, from i

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4 The Discrete Fourier Transform Dft Of A Signal S N Is Given Below 2k S K S N A Calculate The Dft And From I 1 (35.13 KiB) Viewed 63 times

4. The Discrete Fourier Transform (DFT) of a signal s(n) is given below: 2k s(k) = S(n) A. Calculate the DFT and, from it, the magnitude and phase spectra of the following two signals: 8(n) = (1,0,0,0) *(n) = [0,1,0,-1] (15 marks) B. Explain the computational cost of calculating the DFT. Assuming that the time it takes a computer to perform a multiplication is approximately 0.1 ms, estimate the time necessary to calculate the DFT of 0.5 s of audio signal sampled at 44.1 kHz. (9 marks) C. Assume that we have a discrete x(n) time-domain sequence of samples obtained from sampling an analog signal x(t). If x(n) contains N = 500 samples and it was obtained at a sample rate of f. = 3000 Hz: i. Calculate the resolution of the DFT of x(n) (in Hz). 11. What is the highest frequency spectral component that can be present in the analog signal x(t) where no aliasing errors occur in (6 marks) x(n)?