# signals and systems

Discussion in 'Homework Help' started by juhir, Jul 6, 2008.

1. ### juhir Thread Starter New Member

Jul 6, 2008
3
0
for each of the following signals determine whether this signals are periodic or not?If periodic find fundamental period.

a. x(t)= cos2(2piet)
b.x(t)= (-1)^n

2. ### thingmaker3 Retired Moderator

May 16, 2005
5,073
8
What have you come up with thus far in your own efforts?

One way to solve these problems is to make a graph of the function. You will be able to tell whether they are periodic, and will be able to calculate any period easily.

Another way to solve these problems is to compare the function to known periodic functions and look for similarities.

3. ### Dave Retired Moderator

Nov 17, 2003
6,960
171
Simple intuition should illstrate that one signal is periodic, whereas the other is not. Btw, I think you have a misplaced "2" in question a).

Dave

4. ### juhir Thread Starter New Member

Jul 6, 2008
3
0
can u solve it and give. Its for the first time i am studying the topic

5. ### juhir Thread Starter New Member

Jul 6, 2008
3
0
Can u solve it and give

May 16, 2005
5,073
8
7. ### roddefig Active Member

Apr 29, 2008
149
0
You can prove that a signal is periodic if it repeats itself. The way to describe this concept mathematically is:

$
x(t) = x(t+T)
$

Basically, x(t) is equal to itself $T$ seconds later. You can generalize this as follows

$
x(t) = x(t+nT) \ \forall\ n
$

x(t) is equal to itself every $nT$ seconds, where $n$ is any integer.

If I remember my linear systems class correctly satisfying the first equation is enough to prove periodicity, but I would check with your notes to see what your professor wants.