Space Science Journal(SSJ)

Doctor of Technical Sciences, Russia

Publications

• Review Article   
  Fourier Transform of a Single-Frequency Octonion
  Author(s): Vadim Sovetov*
  
  A method for Fourier transforms in 8D space of a single-frequency octonion for 8 different pulses is presented. The octonion Fourier transform is calculated using the fundamental matrix of the octonion by integrating the product of the signal vector with this matrix. The inverse Fourier transform uses the transposed fundamental matrix multiplied by the spectrum vector. Spectra of different pulses were obtained. It is shown that the pulse spectra are formed using the theorem of shifting spectra along the frequency axis in accordance with their shift in time. In this case, the shift of the signal vector elements is performed using a direct and quadrature shift matrix. As is known, the octonion is used to form a MIMO system with 8 inputs and 8 outputs. Therefore, the spectra of each pulse are located on each axis of spatial coordinates of 8D space. In this case, we obtain the sum of the .. Read More»
  

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