# 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.