Determining whether a sequence is periodic

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    Periodic Sequence
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Discussion Overview

The discussion revolves around determining whether the sequence defined by the expression cos((2pi/3)n + pi/6) + 2sin((pi/4)n) is periodic, specifically in the context of discrete time signals. Participants explore the periodicity of the individual components and their sum.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant asks for help in determining the periodicity of the sequence, noting confusion due to the presence of both cosine and sine components.
  • Another participant states that the sum of two periodic signals is periodic, suggesting that the sequence is periodic as well.
  • A suggestion is made to test with N = 24 to see if the periodicity holds.
  • A later reply clarifies that the sequence is a discrete time signal, questioning if this changes the periodicity analysis.
  • Further calculations are presented to show that substituting N = 24 results in the original sequence, implying periodicity, although the correctness of this conclusion is not established.
  • One participant confirms the periodicity, while another expresses gratitude for the assistance and inquires about the choice of N = 24.

Areas of Agreement / Disagreement

Participants express varying levels of confidence regarding the periodicity of the sequence. While some affirm that it is periodic, others raise questions about the implications of it being a discrete time signal, indicating that the discussion remains somewhat unresolved.

Contextual Notes

The discussion does not resolve the implications of the discrete nature of the signal on periodicity, and the choice of N = 24 is not justified within the conversation.

magnifik
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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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[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.
 
Take [itex]N = 24[/itex] and see what happens.
 
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?
 
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
 
yes.
 
Dickfore said:
yes.

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

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