Hi, would you be able to solve Q2 please and explain how you did it?Thanks,

Section B Answer the following three questions. Each question carries 10 marks. 1. A function of variable w is given by 1 ( w ) = Im for - b Sw sb 0 otherwise Find the function r(t) that has f as its Fourier Transform, that is, find a(t) such that I ( w ) = f ( w ). Find the signal y(t) which arises from modulation of r, so that y ( w ) = e-jati (w). 2. The Fourier Identity is Use this identity to find the Fourier transform of the function x(t) = Asin(wot). Explain the meaning of your result in terms of the concept of frequencies. Apply the time-frequency duality that arises from the Fourier Identity to find the signal that has spectrum given by f ( w) = Bsin(aw). 3. The discrete signal r is a single pulse of length P: m for n P Let N be the length of the signal. The signal therefore contains P values of value m and the other N - P values are taken to be 0. (a) Write the Discrete Fourier Transform [k] of the signal zin] in closed form. (b) Explain the meaning of the term 'zero padding'. In particular, show what happens to the terms of the transform [k] if the value of N is doubled