Two-sided Quaternion Wave-packet Transform and the Quantitative Uncertainty Principles

Abstract

Abstract. In this article, we introduce the notion of two-sided quaternion wave-packet transform which inherits the advantages of both the quaternion windowed Fourier and wavelet transforms with some additional promising features. The preliminary analysis encompasses the derivation of fundamental properties including, orthogonality relation, energy preserving relation, inversion formula and the range theorem by utilizing the machinery of two-sided quaternion Fourier transforms. Besides, we also derive the Heisenberg’s
and logarithmic uncertainty principles for the proposed transform. We culminate our investigation by presenting some illustrative examples.