Are two signals that make up a periodic signal necessarily periodic?

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SUMMARY

The discussion centers on the periodicity of two signals, b(t) and c(t), that compose a periodic signal a(t). It is established that even if a(t) is periodic, b(t) and c(t) are not necessarily periodic. The example provided, where b(t) = sin(t) + t and c(t) = sin(t) - t, illustrates that the addition of a non-periodic component (t) to a periodic function (sin(t)) results in a non-periodic function.

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  • Basic knowledge of signal composition
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ChickenChakuro
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Homework Statement



If a(t) is periodic and is composition of two signals such that a(t) = b(t) + c(t), then are b(t) and c(t) necessarily periodic?

2. The attempt at a solution

I think that b(t) and c(t) must be! Is this correct?
 
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No. b(t)=sin(t)+t. c(t)=sin(t)-t. Wasn't that easy?
 
Dick said:
No. b(t)=sin(t)+t. c(t)=sin(t)-t. Wasn't that easy?

Indeed it was. Thanks for your help!
 

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