(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. |8(t) 0 G(f) (a) |8(1) G(f) 2t 0 1 0 2T (b) 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.

The signal continuous x(t) is given by the following equation: (image 001) The signal will be passed through a frequency shaping filter which has an impulse response: (image 002) a) With the help of the Fourier Transform table, determine the spectrum of x(t) and provide a plot for that spectrum (if needed you can provide a magnitude plot and a phase plot for the spectrum). b) With the help of the Fourier Transform table, determine the frequency response of the frequency shaping filter above and provide a plot for the frequency response (if needed you can provide a magnitude plot and a phase plot for the frequency response). c) If the output of the frequency shaping filter above is a signal y(t), then determine both y(t) and the representation of y(t) in the frequency region or spectrum of y(t). Provide a plot for the spectrum of y(t) (if needed you can provide a magnitude plot and a phase plot for the spectrum). Note: if necessary, use the help of the Fourier Transform Table

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answer part b,please.