# Questions tagged [periodic-functions]

Questions on periodic functions, functions $f(x)$ that satisfy the identity $f(x+c)=f(x)$, for some nonzero $c$.

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### Let $q\in\mathbb{Z}$. What is the smallest period of $\sin(2t)−\sin(qt)$?

Question: Let $q\in\mathbb{Z}$. What is the smallest period of $\sin(2t)−\sin(qt)$? My attempt: the period of $\sin(t)$ is $2\pi$, so the period of $\sin(2t)$ is $\pi$ and the period of $\sin(qt)$ is ...
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### Is there any research about a function with changing "period" like sin(1/x)?

I'm encountering a function with a "changing period". It has some sense of period but not exactly. For example: f(x) = cos(1/x). Generally, it has the form of f(x + g(x)) = f(x). I cannot ...
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### Time series analysis on ACF and PACF plots

So I have a non stationary time series that is hourly, daily and monthly recorded for a year and I have the ACF and PACF plots for the serie. ACF and PACF I applied the the Ljung-Box test and for ...
1 vote
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### Cyclic convolution of a periodic function with itself is a constant?

Let $f(x)$ be a periodic function of period $T$. Now let us define $c(x)$ the cyclic convolution (on the same period T) of $f$ with itself: $$c(x)=\int_t^{t+T}f(\tau)f(x-\tau)d\tau$$ I have the ...
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### Q : Let $f : \mathbb Z\to \mathbb Z$ such that, for all $x,y\in\mathbb Z:$ $f(f(x) − y) = f(y) − f(f(x)).$ Show $f$ is bounded.

I came to the conclusion that f is periodic with period |f(x0)| for x0 non-zero. But I don't see how the periodicity in domain translates to a bound in the codomain. It probably has something to do ...
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