How to determine whether periodic or not

glorimda

Joined Oct 12, 2011
17
I've got stuck in here while solving exercise problem.

How can I determine whether this is periodic or not.

1.

I can't find way to do of this due to summation.

2.
y1(t)=x(2t) and y2(t)=x(t/2)

I need to determine whether followings are true and find the fundamental period.

<1> if x(t) is periodic, then y1(t) is periodic.
<2> if y1(t) is periodic, then x(t) is periodic.

Could anybody help me plz?

panic mode

Joined Oct 10, 2011
1,774
first of all what is 'periodic'?

as i recall it is a signal with value that eventually repeats itself (and not just once but over and over).

due to exponential term and n changing, magnitude will never be the same.
that is quite strong argument against 'periodic'.

alternatively - plot it.

Georacer

Joined Nov 25, 2009
5,154
Is the "star" the convolution operator or just an ordinary multiplication?

glorimda

Joined Oct 12, 2011
17
panic mode// As you mentioned, that seems obvious, but is that all I can answer? I mean I think I need to show it in some mathematical way.
Georacer// That is just an multiplication.

Georacer

Joined Nov 25, 2009
5,154
In general, a signal is periodic if x(t)=x(t+T), where T is the period.

However, right now my math fails to prove if it is indeed periodic. My gut says it's not.

glorimda

Joined Oct 12, 2011
17
It turned out to be aperiodic. you're right. But I want to prove it in mathematical way. Not just by intuition.