Make an m-file ftsamptest.m to do the following: First generate a sine wave signal x with frequency 400 Hz sampled at 8 kHz for n 1000 samples. Then, take a 1000 point FFT of x to produce hx and apply fftshift to hx to swap the first and second halves so that the zero frequency is in the middle Generate a vector fHz of frequencies in Hz corresponding to each point in hx. Plot the absolute value of the fftshift- ed hx vector against fHz. Is this what you expected? Now do the same thing for the integral frequencies of 405 Hz and 410 Hz and so on. What about 440 Hz? What is happening? What is special about 400 Hz and 440 Hz? (it might help to plot the sine signal). Try changing the number of points in the FFT. How does this affect the plot? Finally, compute and plot the DFT of this signal using 1024, 2024, 4096 samples at 8 kHz: x(t) = sin(2n400t) + 0.5 sin(2n420) + 0.25 sin(2n440t) Make an m-file ftsamptest.m to do the following: First generate a sine wave signal x with frequency 400 Hz sampled at 8 kHz for n 1000 samples. Then, take a 1000 point FFT of x to produce hx and apply fftshift to hx to swap the first and second halves so that the zero frequency is in the middle Generate a vector fHz of frequencies in Hz corresponding to each point in hx. Plot the absolute value of the fftshift- ed hx vector against fHz. Is this what you expected? Now do the same thing for the integral frequencies of 405 Hz and 410 Hz and so on. What about 440 Hz? What is happening? What is special about 400 Hz and 440 Hz? (it might help to plot the sine signal). Try changing the number of points in the FFT. How does this affect the plot? Finally, compute and plot the DFT of this signal using 1024, 2024, 4096 samples at 8 kHz: x(t) = sin(2n400t) + 0.5 sin(2n420) + 0.25 sin(2n440t)