Solved ELCT 222 Signals and Systems Computer Assignment 9

Consider the following circuit: where the input current source is given by a) (20 pts) Derive the Fourier transform of the source 𝑖𝑖𝑠𝑠(𝑡𝑡) for 𝐴𝐴 = 5 mA and 𝑇𝑇 = 3 s b) (20 pts) Determine the transfer function 𝐻𝐻(𝜔𝜔) = 𝑉𝑉out(𝜔𝜔) 𝐼𝐼𝑠𝑠(𝜔𝜔) for 𝑅𝑅1 = 0.5 kΩ, 𝑅𝑅2 = 2 kΩ, 𝐶𝐶 = 1 3 mF c) (20 pts) Obtain 𝑣𝑣out(𝑡𝑡) by using Fourier analysis (an analytical expression with inverse Fourier transform is sufficient) d) (20 pts) Plot 𝑖𝑖𝑠𝑠(𝑡𝑡) and 𝑣𝑣out(𝑡𝑡) by using 𝐼𝐼𝑠𝑠(𝜔𝜔) and 𝑉𝑉out(𝜔𝜔) with a numeric integration from -inf to inf in MATLAB (Hint 1: integral(@(omega) 1/2/pi*f(omega).*exp(1i*omega*t),-inf,inf)) (Hint 2: 𝑖𝑖𝑠𝑠(𝑡𝑡) should be the triangular function above after numeric integration) e) (20 pts) Plot the one-sided energy spectral density of 𝑣𝑣out(𝑡𝑡) in MATLAB.