For the EE/Math nerds

[ga14]

How do you determine if a function is periodic or not without graphing it?

For example, cos^2(2pit) is periodic, as is sin^3(2t). But e^(-2t)cos(2pit) is nonperiodic, as is the discrete signal x[n]=cos(2n).

Does this have to do with Fourier series somehow? Is there an easier way to determine it? Thanks for any help.

 

[RaynorWolfcastle]

A function is periodic in continuous time if f(t) = f(t + nT) where n is some integer and T is the fundamental period T, similar in discrete time but you have the additional constraint that your samples have to be taken periodically as well (which is why your cos(2n) function isn't periodic, even thoough cos(2t) is clearly periodic).


Yes, it very much does have to do with Fourier series because you can only find a Fourier series representation of a periodic signal, otherwise you have to use a Fourier transform (assuming your signal is square integrable and satisfies Dirichlet conditions).

Oh, and I resent being called an EE nerd 😛

 

[TuxDave]

^^^ What he said.