2. A pulse input x(t) is applied to the RC circuit shown below. The expected capacitor voltage output, y(t), is also shown. J(o)- Note : RC = 1 )Derive the impulse response, h(), by applying the circuit laws and solving the 1t order differential equation. The solution is of the form y(t) =Ae-t/(RC) + B where A and B can be solved from initial and final conditions. Note that the constants differ for 01. (b) Verify the ilaplace. Note Solution with MATLAB's Symbolic Math Toolbox functions, laplace and with tNote that the input can be expressed as x(t) heaviside(t) - heaviside(t-1) and the output can be plotted with the statements t 0:0.01:5; y = subs(y, t); plot(t, y), grid (C) The code below performs discrete convolution over 50 samples, and shows a stem plot of the output. Run the code and compare the peak value of yn to y from part (b). N 50; n-0:N-1; xn- [ones(1, N/2) zeros(1, N/2)]; hn exp(-2* n/N); yn = (2/ N) * conv(xn, hn); n 0:2 (N - 1); stem(n, yn), xlabel('n'), ylabel("'yn')