# Uncertainty Principle for the multivariate two sided continuous quaternion Windowed Fourier transform

## TL;DR

This paper introduces a generalized multivariate two-sided continuous quaternion windowed Fourier transform and explores its key properties, expanding the mathematical framework for quaternion-based signal analysis.

## Contribution

It presents a novel generalization of the quaternion windowed Fourier transform and derives fundamental properties using the two-sided quaternion Fourier transform.

## Key findings

- Established properties of the new transform
- Extended the mathematical framework for quaternion analysis
- Potential applications in multivariate signal processing

## Abstract

In this paper we generalize the continuous quaternion windowed Fourier transform called the multivariate two sided continuous quaternion windowed Fourier transform. Using the two sided quaternion Fourier transform we derive several important properties.