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+//Ex.3.5
+
+clc ;
+clear;
+close;
+
+//Test for shift-variance
+k =2;
+N =10;
+for n =1: N
+x(n)=n;
+y(n)=x(n)^2;
+end
+inputshift =[x(N-k)]^2;
+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 4 9 16]; //y(n)=x(n)^2 for all x
+
+ //Test for homogeneity
+k=2;
+hom=0;
+for n=1: length (x1)
+ if (k*y(n)==[k*x1(n)]^2)
+ 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(n)^2;
+ y2(n)=x(n)^2;
+ y3(n)=x(n)^2;
+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 ' );