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

机译：基于线性规范变换的QFM信号参数估计算法

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摘要

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.
机译：在这项研究中，提出了一种基于线性典范变换（LCT）的新颖算法，用于估计二次调频（QFM）信号的参数。首先，定义了一种新型的广义LCT（GLCT），QFM信号的GLCT将产生脉冲。可以根据这种脉冲的位置信息来估计QFM信号的三阶相位系数。在补偿了三阶相位系数之后，可以将QFM信号近似为线性频率调制（LFM）信号，并且可以通过用于估计LFM信号的算法来估算二阶，一阶相位系数和幅度。所提出的算法由于只需要一维最大化，并且LCT也具有快速的数值算法，因此没有繁重的计算负担。此外，该算法具有准确的估计和较低的信噪比（SNR）阈值。同时，该算法只需较少的采样点即可获得较高的输出信噪比。与现有算法的比较验证了该算法在某些情况下在计算复杂度，准确性和输出信噪比方面具有良好的性能。

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