Determining whether a sequence is periodic

In summary, the given sequence is periodic because the sum or product of two periodic signals is also periodic. In discrete time, setting N = 24 will result in the same signal and thus prove that it is periodic.
  • #1
magnifik
360
0
can someone help me determine whether this sequence is periodic?

[cos((2pi/3)n + pi/6) + 2sin((pi/4)n)] where n is all integers

i know that for a function to be periodic,
x(n) = x(n+N)

however, i am confused because both the cos and sin component contain n

please help. thx.
 
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  • #2
[tex]cos\left(\frac{2\,\pi}{3}\,n\,+\,\frac{\pi}{6}\right)\,+\,sin\left(\frac{\pi}{4}\,n\right)[/tex]

In general, in continuous time, the sum or product of two periodic signals is periodic, so your signal is periodic too.
 
  • #3
Take [itex]N = 24[/itex] and see what happens.
 
  • #4
VinnyCee said:
[tex]cos\left(\frac{2\,\pi}{3}\,n\,+\,\frac{\pi}{6}\right)\,+\,sin\left(\frac{\pi}{4}\,n\right)[/tex]

In general, in continuous time, the sum or product of two periodic signals is periodic, so your signal is periodic too.


sorry, i forgot to specify that this is a discrete time signal. does that change anything?
 
  • #5
Dickfore said:
Take [itex]N = 24[/itex] and see what happens.

n + N = n + 24
x(n+N) = cos(2pi/3(n + 24) + pi/6) + sin(pi/4(n + 24))
= cos(2pi/3(n) + 16pi + pi/6) + sin(pi/4(n) + 6pi)
= cos(2pi/3(n) + pi/6) + sin(pi/4(n) + 6/pi)
so it's equal to x(n) because 2*k*pi doesn't change cos or sin
is this correct? thanks.

sorry for the ugly formatting
 
  • #6
yes.
 
  • #7
Dickfore said:
yes.

thanks for the help. how did you get N = 24?
 

1. What is a periodic sequence?

A periodic sequence is a sequence of numbers that repeats itself in a specific pattern after a certain number of terms. This pattern can continue indefinitely.

2. How can you determine if a sequence is periodic?

To determine if a sequence is periodic, you need to check if there is a repeating pattern in the sequence. This can be done by looking for a specific number or set of numbers that is repeated throughout the sequence.

3. What are the possible ways to represent a periodic sequence?

A periodic sequence can be represented in various ways, such as using a formula, a graph, or a table. It can also be represented using a recursive formula, where each term is calculated using the previous terms.

4. What is the importance of identifying a periodic sequence?

Identifying a periodic sequence is important because it helps us understand the behavior and patterns of a sequence. It also allows us to make predictions about future terms in the sequence and can be used in various applications such as predicting stock prices or weather patterns.

5. Can all sequences be classified as periodic or non-periodic?

No, not all sequences can be classified as periodic or non-periodic. Some sequences may exhibit both periodic and non-periodic behavior, while others may not have a repeating pattern at all. It is important to carefully analyze a sequence to determine its classification.

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