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Complementary Fractional Dimensional Order of Nyquist Sinc Sequences for Time Division Multiplexing

High speed data transmission is enabled by time and wavelength division multiplexing. Here is introduced fractional dimension order of Nyquist pulses sequences for orthogonal time division multiplexing. Firstly, with a representation of the Nyquist sinc sequence by a cosine Fourier series, in one side it is introduced the complementary Nyquist sinc sequences as a better option for data transmission. On the other side, a possibility of optical time delay by an electrical phase shifter for optical time division multiplexing is theoretically demonstrated. In continue, the fractional dimensional order of signal is defined to open a new window for data transmission. Moving of function in fractional dimension can be realized as a new freedom for a signal processing. In other words, dimension itself is a dimension. In this regard, dimensional transformation is introduced to give a mapping of the function in dimensional domain or variations of function in fractional dimension. This mapping gives more information about signal in different point of view like Fourier transformation. Then, the complementary fractional dimensional order of Nyquist sinc sequences is defined to reach higher data rate. It has not a unique solution, however; the best set of solutions for data transmission must be taken in to accounted. Furthermore, the trajectory of fractional dimension can be found by a numerical iterative algorithm which will be explained in the appendix.

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