# Periodic or Aperiodic signal

Discussion in 'Homework Help' started by Anthony Quah, Mar 26, 2008.

1. ### Anthony Quah Thread Starter Active Member

Dec 1, 2007
80
0
Guy,

I am doing Signal and System home work..i need some help to confirm if my step were the correct method of doing it... here goes

*Determine whether the signals is periodic? and state its period.

Question 1 :
x(n) = u(n) - u(n-10)

Solution :
x(n) = u(n - T) - u(n - T - 10)
x(n) = u(n - kT) - u(n - lT - 10 )

since l/k cannot be express therefore the signal is not periodic.

Question 2 :
x(n) = sin (n)

Solution :
x(n + T) = sin (n + T)
T = 2 pie
= 2 x 3.142
= 6.238
T is not integer, therefore x(n) = sin (n) is not periodic signal

2. ### surbhi New Member

Mar 26, 2008
5
0
periodic signal is that which satisfy the following equation, i.e.

x(n) = x( n+t)
t is any part of periodic signal or it may be 2 pie

Question 1 :
x(n) = u(n) - u(n-10)

Solution :
this problem can be solved by using diagram method
as u(n) = 1, n>0

u(n-10) = 1, n>10

when these terms are subtracted, we get x(n) = 1, 0<n<10
so we can't say that x(n) is periodic
u can show its diagram also.

Question 2 :
x(n) = sin (n)

Solution :
x(n + T) = sin (n + T)
T = 2 pie

sin(n) = sin ( n + 2 pie)

so x(n) is a periodic signal.

3. ### Anthony Quah Thread Starter Active Member

Dec 1, 2007
80
0
anyone can confirm if this was right?

4. ### veritas Active Member

Feb 7, 2008
167
0
yes, surbhi is correct

5. ### Anthony Quah Thread Starter Active Member

Dec 1, 2007
80
0
in Question 2 base on my own calculation it show that it is not a periodic signal when 2 pie is not an integer BUT Surbhi say is periodic signal?

6. ### veritas Active Member

Feb 7, 2008
167
0
If you are referring to a discrete signal, then an irrational period will create an aperiodic signal. The fact that it is not an integer is irrelevant.

For continuous signals, then any period will create a periodic signal.

*edit*
to clarify for you:

I think you mean to say "single L/K cannot be expressed as the ratio of two integers, the signal is therefore not periodic"

7. ### Anthony Quah Thread Starter Active Member

Dec 1, 2007
80
0
ok..thank guy..i will need time to digest it.. ^^