The Uncertainty Principle of the Octonion Quadratic-Phase Fourier Transform

In the fields of signal processing and applied mathematics, the uncertainty principle plays a significant role. Motivated by the theoretical significance of the octonion quadratic-phase Fourier transform (OQPFT), we present a systematic investigation of uncertainty relations for this transform. Firstly, we derive the differential properties of the OQPFT. Secondly, we systematically derive four corresponding uncertainty principles for the OQPFT, covering both deterministic and random octonion signal scenarios. Finally, three sets of simulation experiments using 3D octonion chirped signals are performed, including two Gaussian-modulated cases with different complexity and a constant-coefficient rectangular-window non-Gaussian case for comparative verification. Full three-dimensional spectral observation shows that the OQPFT achieves superior frequency-domain aggregation compared with the octonion Fourier transform (OFT). Further comparative analysis demonstrates that this spectral aggregation advantage is not limited to Gaussian signals, but also holds for non-Gaussian windowed signals. This paper enriches the uncertainty theory in the hypercomplex domain and provides theoretical support for the frequency-domain analysis of high-dimensional quadratic-phase signals.