Uncertainty principles related to quaternionic windowed Fourier transform

Abstract

In this paper, we first introduce uncertainty principles for the quaternion Fourier transform (QFT). We then provide a different proof of the well-known properties of the quaternionic windowed Fourier transform (QWFT) using properties of the QFT which is a little bit simpler than usual. Based on uncertainty principles for the QFT and the relationship between the QFT and QWFT, we establish uncertainty principles related to the QWFT.