# Supercharacters and the discrete Fourier, cosine, and sine transforms

## TL;DR

This paper uses supercharacter theory to identify matrices diagonalized by discrete Fourier, cosine, and sine transforms, providing a combinatorial interpretation of their entries.

## Contribution

It introduces a novel approach linking supercharacter theory with classical transforms, offering new insights into their structure.

## Key findings

- Matrices diagonalized by DCT and DST are characterized.
- Provides combinatorial interpretation of matrix entries.
- Connects supercharacter theory with classical harmonic analysis.

## Abstract

Using supercharacter theory, we identify the matrices that are diagonalized by the discrete cosine and discrete sine transforms, respectively. Our method affords a combinatorial interpretation for the matrix entries.