A Propose for a Quadrature – Phase as Full Orthogonal Matrix Transform Compared with FFT Matrix Multiplication and Applied in OFDM System (Safe Transform the Fourier Twins)

In this paper, we will introduce a set of fully-orthogonal matrices for a transform that is more orthogonal than the Fast Fourier Transform (FFT), and prove that they are orthogonal for all rows and columns, as well as for each element and its neighbor elements, the basic matrix for this transform is founded upon the Quadrature -phase mapper principle, and can be extended by using the Hadamard matrix, this will provide orthogonality for all rows, columns and even single elements it will seen that the sum of all element be zero and applied in OFDM [1]system.