Abstract
The Wigner-Ville distribution (WVD) based on the linear canonical transform (LCT) (WDL) not only has the advantages of the LCT but also has the good properties of WVD. In this paper, some new and important properties of the WDL are derived, and the relationships between WDL and some other time-frequency distributions are discussed, such as the ambiguity function based on LCT (LCTAF), the short-time Fourier transform (STFT), and the wavelet transform (WT). The WDLs of some signals are also deduced. A novel definition of the WVD based on the LCT and generalized instantaneous autocorrelation function (GWDL) is proposed and its applications in the estimation of parameters for QFM signals are also discussed. The GWDL of the QFM signal generates an impulse and the third-order phase coefficient of QFM signal can be estimated in accordance with the position information of such impulse. The proposed algorithm is fast because it only requires 1-dimensional maximization. Also the new algorithm only has fourth-order nonlinearity thus it has accurate estimation and low signal-to-noise ratio (SNR) threshold. The simulation results are provided to support the theoretical results.
Highlights
The main elements of the modern signal processing are nonstationary, non-Gaussian, and nonlinear signals
There are many algorithms for estimating the parameters of quadratic frequency modulated (QFM) signal, such as the maximum likelihood (ML) method [11], the adaptive short-time Fourier transform method [12], the polynomial Wigner-Ville distributions (PWVDs) [13], the product high-order matchedphase transform (PHMT) [14], and the ambiguity function based on the linear canonical transform (LCT) method (LCTAF) [15]
We provide the definition of the cross-Wigner-Ville distribution function (WVD) based on the LCT here
Summary
The main elements of the modern signal processing are nonstationary, non-Gaussian, and nonlinear signals. The LCT as the generalization of the Fourier transform (FT) and the FRFT was first introduced by Moshinsky and Quesne [5] and Collins and Stuart [6] It has been applied for filter designing, time-frequency signal separating, signal synthesis, and signal encryption [7,8,9]. There are many algorithms for estimating the parameters of QFM signal, such as the maximum likelihood (ML) method [11], the adaptive short-time Fourier transform method [12], the polynomial Wigner-Ville distributions (PWVDs) [13], the product high-order matchedphase transform (PHMT) [14], and the ambiguity function based on the LCT method (LCTAF) [15]. In order to estimate QFM signal parameters, we define a new kind of Wigner-Ville distribution— the generalized Wigner-Ville distribution based on the linear canonical transform (GWDL).
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