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# Use equation (1) to implement Discrete Fourier Transform for the following signal. X_{k}=\sum_{n=0}^{N-1} x_{n} e^{-j 2 \pi k n} \quad N=0,1,2, \ldots, N-1 x[n]=\left\{\begin{array}{ll} 0, & \text { for }

n \in[-128,-65] \\ 1, & \text { for } n \in[-64,63] \\ 0, & \text { for } n \in[64,127] \end{array}\right. Use the "stem" and “plot" commands to graph the original sequence, the magnitude of the spectrum, and the phase of the spectrum. 2. Use the "stem" command to graph the original sequence x[n].2. 3. Calculate the magnitude response of DFT and use the "stem" command to graph the magnitude spectrum of DFT, X[k].3. 4. Calculate the phase response of DFT and use the "stem" command to graph the phase response of DFT, X[k].4. 5.Use the built-in Matlab fft command on the sequence given in problem 1. Compare your results amplitude response to your DFT results. Plot it as a subplot. (Hint: The response should be similar in shape) QUESTIONS: 1. Compute 4 point (N=4) DFT of the sequence x(n)={0,1,2,3} and sketch Magnitude and Phase response by hand. These plots will be like stem plots.

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