Clifford-Valued Wave-Packet Transform with Applications to Benchmark Signals

In pursuit of efficient time-frequency representation of Clifford-valued signals, we propose a novel integral transform coined as the Clifford-valued wave-packet transform. In the first instance, all the fundamental properties of the Clifford-valued wave-packet transform including the inner product relation, inversion formula and range theorem are studied. This is followed by the formulation of several uncertainty inequalities, such as the Heisenberg-Pauli-Weyl inequality, Pitt's inequality and logarithmic inequality for the proposed transform. We culminate our study by demonstrating the performance and efficiency of the Clifford-valued wave-packet transform for detection and orientation of pointwise singularities in the context of three-dimensional signal analysis.