1. Net 222: Communications and networks fundamentals (Practical Part)
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Lab 5 : linear and Time invariance system

2. Lecture Contants Linear system Time invariance system
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3. Linear System
If a system is linear, this means that when an input to a given system is scaled by a value, the output of the system is scaled by the same amount.
Ya[n]=Yb[n] is linear system.

4. Linear system coding
We could write a system that test if the giving input are linear or NOT
Eg: yn[n]=x[n]^4
By Assuming :
X[n]1=sin(3)
X[n]2=sin(5)
Scaling value a=4
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5. Example 1 x1 = sin(3); x2 = sin(5); a= 4; yn1=(x1)^4 ; yn2=(x2)^4 ;
y1= a*yn1;
y2=a*yn2;
ya=y1+y2;
fprintf('system YA = ' );
disp(ya);
xn1=x1*a;
xn2=x2*a;
y=xn1+xn2;
yb=y^4;
fprintf('system yb = ');
disp(yb);
if (ya == yb )
fprintf('system is linear ');
else
fprintf('system is not linear ');
end

6. Output ex 1
After running the code check out the command window to show the result
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7. Example 2 Another Eg: yn[n]= 2*x[n] X[n]1=sin(3) X[n]2=sin(5)
Scaling value a=4
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8. Code 2
X1=sin(3);

9. Output ex 2
After running the code check out the command window to show the result
YA = YB
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10. Time-Invariant System :
X[n]
Y1[n]=y[n-n0] S T
Y2[n]=T{x[n-n0]}
Y1[n]=Y2[n] for all n
T is time invariant
22-Sep-18
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11. Example 3
We could write a system that test if the giving input are linear or NOT
Eg: yn[n]=x[n]*sin(3)
By Assuming :
X[n]=3
Shifting value n0=4
output
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12. Code 3

13. Output ex 3
After running the code check out the command window to show the result
YA != YB
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14. The End
Any Questions ?
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