I'm given this difference equation, and I'm being asked to plot its response to an input $x[n] = 4\sin^3\left(0.25\pi n+\frac \pi 3\right)u(n)$:
$$ y(n) = 0.9051y(n-1)-0.598y(n-2)+0.29y(n-3)-0.1958y(n-4)+0.207x(n)+0.413x(n-2)+0.207x(n-4) $$
filter function, I implemented the following code:
num = [1 -0.9051 0.598 -0.29 0.1958]; den = [0.207 0 0.413 0 0.207]; x = 0:75; b1 = sin(0.25*pi*x+pi/3); for i = 1:length(b1) sincub(i) = b1(i)*b1(i)*b1(i); end inp = 4*sincub; z = filtic(num, den, [0 0 0 0]); y = filter(num, den, inp, z); stem(x, y, 'linewidth', 2);grid on xlabel('Time-index, n'); ylabel('Amplitude'); title('Response to x(n)');
The plot of the input function is attached and so is the response.
The problem I'm facing is that I'm being asked to find the steady-state value of the output when the output appears rather periodic in nature (
if x = 1:100 or
1:200 this will be clearer). Where is the transient response in such an output and what can be the steady state? Or is there something wrong in my code?
Any help would be much appreciated.