Given a signal


How to determine if the given signal is linear or non linear?

I am getting so confused reading the theory. If someone could help step by step to determine this. It would be great thankyou

  • $\begingroup$ If you double $x(n)$ (or multiply by any other factor), will $y(n)$ scale accordingly? $\endgroup$
    – user32113
    Nov 21 '17 at 10:00
  • 1
    $\begingroup$ @user32113: This is the check for homogeneity. In general one must also check for additivity to make sure that the system is linear. $\endgroup$
    – Matt L.
    Nov 21 '17 at 12:20

As Matt L. says you'll need to check for homogeneity and, possibly, additivity.


That test says that if: $$ y[n] = f(x[n]) $$ then $$ A \cdot y[n] = f(A \cdot x[n]) $$ for all scalar $A$.


This test says that if $$ y_1[n] = f(x_1[n]) $$ and $$ y_2[n] = f(x_2[n]) $$ then $$ y_{\rm tot}[n] = f(x_1[n] + x_2[n]) = y_1[n] + y_2[n] $$

You just need to apply these for your system.

I say "possibly" because if the system fails one of these tests, then it will not be linear --- so there is little point testing the second condition.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.