(1) Figure 1 is the illustration of the Fourier Transform pair in regard to a Rectangular pulse in the time domain and a Sinc function in the frequency domain. We want to observe the physical symptoms of the impact of time duration of rectangular pulse on the effective bandwidth and peak point. g(t) 1 τ 0 τ t 2 g(t) 0 Ce (a) G(f) τ C. (b) 0 G(f) 20 10 21 20 1-125 Fig. 1: Fourier Transform pair: Rectangular pulse and Sinc function a) Mathematically derive the fourier transform of rectangular pulse described in Fig. 1-(a). It is in general notated as g(t) = rect(t/t) = П(t/t). Show your work in the report. Make sure to indicate which properties or identities are utilized in each step. b) Create the magnitude plot and phase plot of the spectra (Fourier Transform) for t = 5, 10, 25 [seconds]. In other words, overlap three magnitude curves for t = 5, 10, 25 in one plot; and overlap three phase curves for t = 5, 10, 25 in the other plot.