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 . Here, an s-diagonal tensor is a special f-diagonal tensor.
After 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 . We call such an f-diagonal tensor an s-diagonal tensor is a special f-diagonal tensor.