Research On The Decomposition Algorithm Of Circular Analytic Signal

Any circular analytic signal can be decomposed as a product of a minimum phase signal and an all phase signal, the minimum phase signal is completely characterized by its envelope or phase within a constant difference, while the all phase has positive instantaneous frequencies. The research on the decomposition algorithm of circular analytic signal has important practical significance.First, we introduce the history of the study of instantaneous frequency of signal. Second, we analyze how to decompose the polynomial analytic signal and the rational analytic signal as a product of a minimum phase signal and an all phase signal. And as a further generalization of the above conclusion, we analyze the structure characteristics of circular analytic signal. Third, We introduce the properties of the minimum phase signal and all phase signal. In the decomposition algorithm of circular analytic signal, R.Kumarsan and A.Rao proposed a LPSD algorithm to extract the minimum phase signal and all phase signal. In this paper, we improve and generalize the LPSD algorithm. In the improved LPSD algorithm, We turn the error energy formula of multiplication situation into a division. In the division situation, The inverse signal coefficient H is smaller than the original, but it can achieve a better effect. In the generalized LPSD algorithm, we introduce the rational orthogonal basis to replace the trigonometric series. Compared with trigonometric series, the advantage of the rational orthogonal basis is that the coefficients of basis function can be adaptively chosen. In this paper, based on the energy decrease fastest method and the least mean square error method, we can choose the coefficients of basis function step by step. Compared with the LPSD algorithm, the generalized algorithm has greatly improved the time consuming and the number of iteration steps. Moreover, the fitting effect is better than that of LPSD algorithm.