The aim of this paper is to further investigate the properties of octonion Fourier transform (OFT) of real-valued functions of three variables and its potential applications in signal and system processing. This is a continuation of the work started by Hahn and Snopek, in which they studied the octonion Fourier transform definition and its applications in the analysis of the hypercomplex analytic signals. First, the octonion algebra and the new quadruple-complex numbers algebra are introduced. Then, the OFT definition is recalled, together with some basic properties, proved in some earlier work. The main part of the article is devoted to new properties of the OFT, that allow us to use the OFT in the analysis of multidimensional signals and LTI systems, i.e. derivation and convolution of real-valued signals.