The uncertainty principle for the octonion Fourier transform

Abstract

The octonion Fourier transform (OFT) is a hypercomplex Fourier transform that generalizes the quaternion Fourier transform. However, in octonion algebra, there are two major obstacles that are presented in the loss of associativity and commutativity. Researchers have been trying to extend the results of the Euclidean Fourier transform to quaternion‐valued signals using special techniques to overcome these two problems. In this context, we intend to generalize the Heisenberg uncertainty principles associated with covariance and Hardy's uncertainty principle for octonion multivector valued signals over using the polar form of an octonion, the quaternion decomposition, and the relationship between the OFT and the three‐dimensional (3D)‐Clifford‐Fourier transform.