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//Ex.3.4
clc ;
clear;
close;
//Test for shift-variance
k =2;
N =10;
for n =1: N
x(n)=n;
y(n)=x(1);
end
inputshift =x(N-k);
outputshift =y(N-k);
if( inputshift == outputshift )
disp ( 'THE GIVEN SYSTEM IS SHIFT INVARIANT ' )
else
disp ( 'THE GIVEN SYSTEM IS SHIFT VARIANT ' );
end
//Test for linearity
x1=[1 2 3 4]; //assume
x2=[1 2 1 2]; //assume
a=1;
b=1;
y=[1 1 1 1]; //y(n)=x(1) for all x
//Test for homogeneity
k=2;
hom=0;
for n=1: length (x1)
if (k*y(n)==k*x1(n))
hom=hom+1;
end
end
//Test for additivity
for n =1: length (x1)
x3(n)=a*x1(n)+b*x2(n)
end
for n =1: length (x1)
y1(n)=x(1);
y2(n)=x(1);
y3(n)=x(1);
end
for n =1: length (y1)
z(n)=a*y1(n)+b*y2(n);
end
count =0;
for n =1: length (y1)
if(y3(n)==z(n))
count = count +1;
end
end
if( count == length (y3) & (hom==length(y)))
disp ( 'It satisfies the homogeneity and additivity principle' );
disp ( 'THE GIVEN SYSTEM IS LINEAR ' );
else
disp ( 'It does not satisfy the homogeneity and additivity principle' );
disp ( 'THE GIVEN SYSTEM IS NON LINEAR ' );
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