Checking Linearity of Filter Operation

close all;

clear all;

%it is given filter coefficients

a=[0.3 -014];

b=[1 0.8 0.22];

[h5,w5]=freqz(a,b);

h5=freqz(a,b,w5);

plot(abs(h5));

Fs=3000;

t=0:1/Fs:1;

%Signals

x1=sin(2*pi*5*t).*power(t,0.5);

x2=(1-t).*cos(2*pi*9*t);

x3=x1+x2;%input for determining the linearity

x1filt=filter(a,b,x1);% x1(t) is filtering thanks to filter coefficients.

x2filt=filter(a,b,x2);%x2(t) is filtering thanks to filter coefficients.

x3filt=filter(a,b,x3);%x1(t)+x2(t) is filtering thanks to filter coefficient

y12=x1filt+x2filt;%y12 is output of filtered (x1(t)+x2(t))

%We filter the signals separately and then we add filtered signals up.Than we filter the sum of signals %than compare the result of these two way with plotting the result which shows us filtering is a linear %function.

subplot(2,1,1);

plot(t,x3filt);

subplot(2,1,2);

plot(t,y12);