a) Let ?(?) = cos(2??) and ?(?) = cos(20??). Write themathematical expression for the Fourier transform of ?(?) = 4[1 +0.5?(?)]?(?) as a function of both ? (rad/s) and ? (Hz) by hand.Moreover, plot the magnitude spectrum of ?(?) by hand as functionsof both ? (rad/s) and ? (Hz).
b) By using a 2x1 subplot, plot ?(?) signal in the first row.Take ? between -20 s and 20 s with an increment of 1 ms. Limit thex-axis between -2 s and 2 s. Moreover, calculate and plot themagnitude spectrum of ?(?) as a function of ? (Hz) in the secondrow of the subplot. Note that, Fourier Transform of ?(?) should becalculated and plotted by using fft and fftshift functions ofMATLAB. Limit the x-axis between -15 Hz and 15 Hz. Do not forgetaxis labels.
