Question

A. Discrete Fourier Transform and zero padding For the signals x1[n] and x2[n] answer the following questions: x2 [n] = cos(2m30/100) + 0.5 cos(2nn40/100) 1) Compute and plot the length-N DFT magnitude of signals x1[n] and x2[n] with respect to frequency fr, where f and N is the number of samples. For this purpose, take 10 samples from the signals and display the spectrum for-1/2 f < 1/2· i. Which signal has a symmetric spectrum and why? ii. Is it possible to distinguish both frequency components in the plots? Explain the reason. ili.Explain why you see other frequency components in the plot for DFT(,In]) d the signals x1[n] and x2[n] with 490 zeros, then compute and plot the length-500 DFT 3) Repeat part (1) by taking 100 samples from each signal. Plot the signals spectrums and identify 4) Zero-pad the signals x1[n] and x2[n] with 400 zeros, then compute and plot the length-500 DFT of both signals. Do you see any improvement? which signal has a symmetric spectrum and why? of both signals. Do you see any improvement? Note 1: To zero-pad a signal, we add zeros to the beginning and end of a time-limited signal. Note 2: To avoid introducing high frequencies to the signal, it is a good idea to add zeros where the signal value is closest to zero. A large discontinuity such as jumping from 7 to zero, adds high frequencies to the spectrum.

Can someone please help me with all these questions please? I desperately need it asap! Must be done with MATLAB. Thumbs up will be guaranteed! Thank you so much!!

Answer 1

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