Question

Part-1 1. Create a length-$2^{24}$ sequence and find its DFT by using the `fft` command in MATLAB. Determine the elapsed time of the calculation using `tic` and `toc` commands. 2. Repeat previous problem for a length-($2^{24}$ - 2000) sequence. Why is the elapsed time so different? Part-2 3. Write a MATLAB program to calculate the DFT of a 2N-length real-valued sequence $x[n]$ by only N-point FFT algorithms. Verify the correctness of the program for the following signals by comparing their DFT obtained from the above program and from using 2N-point FPT algorithm in MATLAB (plot the magnitude spectrum of both DFT results): $\qquad x[n] = 2\cos\left(\frac{\pi}{2}n\right) - 3\sin\left(\frac{\pi}{11}n\right), \quad 0 \le n \le 43$

          Part-1
1. Create a length-$2^{24}$ sequence and find its DFT by using the `fft` command in MATLAB.
Determine the elapsed time of the calculation using `tic` and `toc` commands.
2. Repeat previous problem for a length-($2^{24}$ - 2000) sequence. Why is the elapsed time so
different?
Part-2
3. Write a MATLAB program to calculate the DFT of a 2N-length real-valued sequence $x[n]$
by only N-point FFT algorithms. Verify the correctness of the program for the following
signals by comparing their DFT obtained from the above program and from using 2N-point
FPT algorithm in MATLAB (plot the magnitude spectrum of both DFT results):
$\qquad x[n] = 2\cos\left(\frac{\pi}{2}n\right) - 3\sin\left(\frac{\pi}{11}n\right), \quad 0 \le n \le 43$

Part-1
1. Create a length-2^24 sequence and find its DFT by using the `fft` command in MATLAB.
Determine the elapsed time of the calculation using `tic` and `toc` commands.
2. Repeat previous problem for a length-(2^24 - 2000) sequence. Why is the elapsed time so
different?
Part-2
3. Write a MATLAB program to calculate the DFT of a 2N-length real-valued sequence x[n]
by only N-point FFT algorithms. Verify the correctness of the program for the following
signals by comparing their DFT obtained from the above program and from using 2N-point
FPT algorithm in MATLAB (plot the magnitude spectrum of both DFT results):
x[n] = 2cos((π)/(2)n) - 3sin((π)/(11)n), 0 ≤ n ≤ 43

Added by Christine B.

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