Frequencies estimation of two-dimensional harmonics based on quaternion model

For quaternion model of two-dimensional harmonics, the singular values decomposition (SVD) method of quaternion matrix presented to estimate frequency pairs of two- dimensional harmonics. This method may estimate the number of signals by singular values. The left and right singular vectors of quaternion matrix were used to estimate frequency pairs. This method needs lesser data and data matrix is very simple. Simulations show that this method can decrease computation burden effectively than other methods.