Short-time special affine Fourier transform for quaternion-valued functions

The special affine Fourier transform is a promising tool for analyzing transient signals with more degrees of freedom via a chirp-like basis. In this article, our goal is to introduce a novel quaternion-valued short-time special affine Fourier transform in the context of two-dimensional quaternion-valued signals. In addition to studying all fundamental properties of the proposed transform, we also formulate some notable uncertainty inequalities including the Heisenberg-Weyl inequality, logarithmic inequality and local-type inequalities by employing the machinery of quaternionic Fourier transforms. Nevertheless, an illustrative example is presented to endorse the obtained results.