2303/CH3/EX3.3/EX_3_3.sce


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//Ex.3.3
clc;
clear;
close;
x1=[1 -2 3 -4];         //assume
x2=[-1 2 -1 2];         //assume
a=1;
b=1;
y=abs(x1);             //y(n)=x(n)+c 

//Test for homogeneity
k=2;
hom=0;
for n=1: length (x1)
    if (k*y(n)==abs(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)=abs(x1(n));
    y2(n)=abs(x2(n));
    y3(n)=abs(x3(n));
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 ' );