Before revision: We show that the T-SVD factorization of a third order real tensor  by going through Discrete Fourier Transform (DFT), standard matrix SVD and inverse DFT , decomposes that third order tensor to the T-product of two orthogonal tensors and an s-diagonal tensor .
After revision: We show that the T-SVD factorization of a third order real tensor is mapped to a special f-diagonal tensor by going through Discrete Fourier Transform (DFT), standard matrix SVD and inverse DFT , decomposes that third order tensor to the T-product of two orthogonal tensors and an s-diagonal tensor .