Sparse Eigenvectors of the Discrete Fourier Transform

TL;DR

This paper constructs a basis of sparse eigenvectors for the N-dimensional discrete Fourier transform, nearly optimal in sparsity, and orthogonal when N is a perfect square, advancing efficient spectral analysis.

Contribution

It introduces a new basis of sparse eigenvectors for the DFT with near-optimal sparsity and orthogonality in special cases, improving computational efficiency.

Findings

Basis is nearly optimally sparse, within a factor of four.

When N is a perfect square, the basis is orthogonal.

Provides a new tool for efficient spectral analysis of signals.

Abstract

We construct a basis of sparse eigenvectors for the N-dimensional discrete Fourier transform. The sparsity differs from the optimal by at most a factor of four. When N is a perfect square, the basis is orthogonal.