A continuous-time system is described by the differential equation
and the system is excited by
We can write a MATLAB program to graph y(t).
kmax = 1000 ; % Maximum harmonic number in representation of input and output signals
% Initialize the differential equation coefficients
b2 = 1 ; b1 = 0 ; b0 = 250000 ;
a2 = 1 ; a1 = 20 ; a0 = 250100 ;
T0 = 3*2*pi/sqrt(b0) ; % Fundamental period of the square wave
w = T0/2 ; % Pulse width of square wave
N = 1024 ; % Number of samples in one fundamental period
dt =2*T0/N ; % Time between samples
t = dt*[0:N]' ; % Time vector for graphing input and output signals
y = 0*t ; % Initialize output signal to zero
% Do the CTFS summation in a for loop
for k = -kmax:kmax,
y = y + (b2*(j*2*pi*k/T0)^2 + b1*j*2*pi*k/T0 + b0)...
*(w/T0)*sinc(w*k/T0)*exp(j*2*pi*k*t/T0)...
/(a2*(j*2*pi*k/T0)^2 + a1*j*2*pi*k/T0 + a0) ;
end
y = real(y) ; % Remove any residual imaginary parts due to roundoff
% Graph the output signal
figure('Position',[20,20,1800,1000],'PaperPosition',[0.5,0.5,18,10]) ;
ttl = ['Square-Wave Fundamental Period {\itT}_0 = ',num2str(1000*T0),' ms'] ;
ptr = xyplot(1000*t,y,[0,25,0,1],'{\itt} (ms)','y({\itt})','Times',24,'Times',18,...
ttl,'Times',36,'n','c','k',{'ahtsg','ahtsg'}) ;
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