Algorithm based on the linear canonical transform for QFM signal parameters estimation

In this study, a novel algorithm based on the linear canonical transform (LCT) is proposed for parameters estimation of a quadratic frequency modulated (QFM) signal. First, a new kind of generalised LCT (GLCT) is defined and the GLCT of the QFM signal will generate an impulse. The third-order phase coefficient of the QFM signal can be estimated in accordance to the position information of such impulse. After compensating off the third-order phase coefficient, the QFM signal can be approximated to linear frequency modulated (LFM) signal and the second-order, first-order phase coefficient and the amplitude can be estimated by algorithms for estimating the LFM signal. The proposed algorithm does not suffer a heavy computational burden because it only requires one dimensionality maximisation and the LCT has fast numerical algorithm as well. Moreover, the proposed algorithm has accurate estimation and low signal to noise ratio (SNR) threshold. Meanwhile, high-output SNR of the proposed algorithm can be gotten with a small number of sampling points. Comparisons with existing algorithms verify that the proposed algorithm has a good performance in the aspects of computational complexity, accuracy and output SNR in some cases.