clear clc Fs = 8000; Ts = 1/ Fs; t = 0:Ts:0.03; N = length(t); f = 500; xt = sin(2*pi*f*t); figure(1) subplot(311) plot(t,xt) title('Original Signal') Noise = sqrt(0.1)*rand(1,N); xN = xt+Noise; subplot(312) plot(t,xN) title('Noisy Signal') fc = [400 600]; [b,a] = butter(4,fc/(Fs/2),'bandpass'); yt = filter(b,a,xN); subplot(313) plot(t,yt) title('Filtered Signal') impulse = [1 zeros(1, N-1)]; impulse_response = filter(b, a, impulse); figure(2) plot(t, impulse_response) title('Impulse Response') xlabel('Time (s)') ylabel('Amplitude') fvtool(b,a) What is the mathematical solution to this code's system specification problem?