Two-sided quaternion wave-packet transform and the quantitative uncertainty principles

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