A Computational Method of Real-valued Discrete Fourier Series Transform (real-DFST) and Application

Abstract

In this paper, we propose a real-valued discrete Fourier series transform (real-DFST) and a computational method for the circular cross correlation. For images, the real-DFST presents the sub elements of frequency components in the DFT. And the space of the real-DFST is a real number space, therefore the real-DFST can be represented with a memory space for image-size real numbers. The real-DFST is a memory saving model for real-valued data and is faster than the DFT in computation. These advantages are important to implement hardware and to compute with large sequences/images. In implementation of system, proposed computational method could be used to enhance their systems through the better MCU computation-time by internal register memory or cache memory. According to increase the size of images, memory saving model is required necessarily. Experiments are suggested for the circular cross correlation processing in the real-DFST and experiments show the computational result for images.