Question 3 Given that rect (t/T) Tsinc (), use the properties of Fourier transform to show that 1. rect (t-5) sinc (%) e-j 2. sinc(t)erect (10) Question 4 13 2 1. Derive the Fourier transform for the following (Gaussian) signal 1 f(t) = e 202 2πσ (1) 2. Use Parseval's theorem to find out its energy. 3. Verify the above by deriving the energy as follows E₁ = f(t)²dt (2) Hint: The Gaussian distribution integrates to one regardless of the standard deviation, i.e., for any value of σ. 2πσ TO L e 20 dt = 1 (3)