Statistics of a multi-factor function from its Fourier transform

Matthew A. Herman and Stephen Doro

Papers from arXiv.org

Abstract: For a phenomenon~$\boldsymbol{f}$ that is a function of~$n$ factors, defined on a finite abelian group $G$, we derive its population statistics solely from its Fourier transform~$\hat{\boldsymbol{f}}$. Our main result is an \emph{$m$-Coefficient/Index Annihilation Theorem}: the $m$th moment of~$\boldsymbol{f}$ becomes a series of terms, each with precisely $m$ Fourier coefficients -- and surprisingly, the coefficient \emph{indices} in each term sum to zero under group addition. This condition acts like a filter, limiting which terms appear in the Fourier domain, and can reveal deeper relationships between the variables driving~$\boldsymbol{f}$. These techniques can also be used as an analytical/design tool, or as a feasibility constraint in search algorithms. For functions defined on $\mathbb{Z}_2^n$, we show how the skew, kurtosis, etc.~of a binomial distribution can be derived from the Fourier domain. Several other examples are presented.

Date: 2026-05
References: Add references at CitEc
Citations:

Downloads: (external link)
http://arxiv.org/pdf/2605.02248 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2605.02248

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().