I am studying linear systems from the book "Signals and Systems Laboratory with MATLAB". I have performed an example on MATLAB myself in this regard. Code is as follow:
clc clear all close all t=-3:.1:3; x1=sin(t); x2=cos(t); a1=2; a2=3; z=a1*x1+a2*x2; y1=2*z+2*cos(pi*t/3) plot(t,y1); ylim([-1 11]); figure; z1=2*x1+2*cos(pi*t/3); z2=2*x2+2*cos(pi*t/3) y2=a1*z1+a2*z2; plot(t,y2); ylim([-1 19]);
When I run this program I get two figures containing two same shapes that are curve-like but amplitude/size/height is not same.
I am confused if my this system defined by equation
y=2*z*cos(pi*t/3) used in program above is linear or not? If still yes, then why (as we have size difference in both curves)?