I know that a system is linear if it satisfies

$$\mathscr{F}\{ a\,x(t)+b\,y(t) \} = a\,X(\omega)+b\,Y(\omega)$$

for Fourier transform, $X(\omega)\triangleq\mathscr{F}\{x(t)\}$

But what if $x(t)$ and $y(t)$ don't have the same period?

Can we use same linearity condition in Fourier transform?

  • $\begingroup$ Hi MertEge. You have an answer? Are you waiting for another one to show up? You can leave a reply by upvoting if found useful, or accepting if it gave you te asnwer. Or ask for further clarification if posisble. $\endgroup$ – Fat32 Dec 3 '18 at 15:47

Continuous time Fourier transform does not require the signals to be periodic, and therefore the linearity assumption holds. CTFT is a linear operator.

Furthermore, if you mean CT Fourier series, which require that both signals to be periodic by (a common period) $T_0$, that's also linear.

But if input signals have no common periods, then you cannot apply the linearity test for CTFS.


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.