# Spectral Domain Sampling of Graph Signals

## TL;DR

This paper introduces spectral domain sampling methods for graph signals that preserve frequency domain characteristics, improving upon traditional vertex domain sampling, with potential applications in fractional sampling and Laplacian pyramid representations.

## Contribution

The paper proposes novel spectral domain sampling techniques for graph signals that maintain frequency characteristics, unlike conventional vertex domain sampling methods.

## Key findings

- Spectral sampling preserves frequency domain properties.
- Theoretical analysis compares spectral and vertex sampling effects.
- Examples demonstrate improved signal processing on graphs.

## Abstract

Sampling methods for graph signals in the graph spectral domain are presented. Though conventional sampling of graph signals can be regarded as sampling in the graph vertex domain, it does not have the desired characteristics in regard to the graph spectral domain. With the proposed methods, the down- and upsampled graph signals inherit the frequency domain characteristics of the sampled signals defined in the time/spatial domain. The properties of the sampling effects were evaluated theoretically in comparison with those obtained with the conventional sampling method in the vertex domain. Various examples of signals on simple graphs enable precise understanding of the problem considered. Fractional sampling and Laplacian pyramid representation of graph signals are potential applications of these methods.