Question

Date of Submission: (10 pts) The Fourier Transform of a non-periodic rectangular pulse waveform fo having amplitude A and width t is given by V(f) AT (a) Consider a rectangular pulse waveform with amplitude A-20V and width τ 1 ms. Using (b) What is the value of spectrum at de? At what frequency does the first zero crossing occur? (c) Ifthe non-periodic waveform is multiplied by a sinusoid asM9cos2m×106, what will the Matlab, plot the frequency spectrums of the given pulse signal for frequencies ranging from -3kHZ to 3kHz. What is the bandwidth required to transmit this signal? frequency spectrum look like? Show mathematically using the frequency shift theorem.

just ba and c please

Answer 1

b) At dc (f = 0) V(0) = A tau = (20) (1m) V(0) = 0.02 (Spectrum value at dc) first zero crossing will occur at f_1 = 1/T = 1/1m = Vertical-bar K Vertical-bar Vertical-bar Z Band width = 1/tau - (-1/tau) = 2/tau = 2 KHz waveform C) Frequency shifting Theorem f(t) e^jwct Doubleheadarrow FT F (w - w_c) f(t) cos (2 pi (10^6)t + + e -j 2 pi (10^6) t)/ 2 Doubleheadarrow F.T [F (f - 10^6) + F (ft 10^6)/2] A tau/2 [sin [pi (f - 10^6)tau/ pi (f - 10^6) + sin pi (f + 10^6) tau/ pi (f + 106) tau]