# Questions tagged [fourier-analysis]

Fourier analysis, also known as spectral analysis, encompasses all sorts of Fourier expansions, including Fourier series, Fourier transform and the discrete Fourier transform (and relatives). The non-commutative analog is (representation-theory).

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### Coefficient of variation of a periodic signal

Is there a way to estimate the coefficient of variation $\frac{\sigma}{\mu}$ of a non-zero mean periodic signal $x(t)$ from its Fourier Transform? I'd like to estimate the flatness'' of the signal
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### Using Sobolev embedding for a high frequency tail

Suppose $f\in L^p(\mathbb{R}^n)$ for some $1\leq p<2$. Let $\chi$ be a smooth function which is 1 outside the ball of radius 2 and 0 inside the unit ball (we can take it to be radial if desired). I ...
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### Any convex sequence induces a sequence $\{a_n\}$ to be the Fourier coefficients of a function $f\in L^1[0,2\pi]$

Let $\{a_n\}$ be an even sequence of non-negative numbers satisfying in $a_n\to 0$ and $a_{n-1}+a_{n+1}-2a_n\geq0$ for every $n>0$. We define $f=\sum_{n=1}^\infty n(a_{n-1}+a_{n+1}-2a_n)F_{n-1}$ ...
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