Abstract
Linear canonical transform as a general integration transform has been considered into Wigner-Ville distribution (WVD) to show more powerful ability for non-stationary signal processing. In this paper, a new WVD associated with linear canonical transform (WVDL) and integration form of WVDL (IWVDL) are presented. First, the definition of WVDL is derived based on new autocorrelation function and some properties are investigated in details. It removes the coupling between time and time delay and lays the foundation for signal analysis and processing. Then, based on the characteristics of WVDL over time-frequency plane, a new parameter estimation method, IWVDL, is proposed for linear modulation frequency (LFM) signal. Two phase parameters of LFM signal are estimated simultaneously and the cross term can be suppressed well by integration operator. Finally, compared with classical WVD, the simulation experiments are carried out to verify its better estimation and suppression of cross term ability. Error analysis and computational cost are discussed to show superior performance compared with other WVD in linear canonical transform domain. The further application in radar imaging field will be studied in the future work.
Highlights
The classical Wigner-Ville distribution (WVD), as an important and fundamental tool of time-frequency analysis, has been developed over the years in many engineering systems [1,2,3,4,5,6]
In order to enhance peak, we propose a integral way to Wigner-Ville distribution associated with linear canonical transform (WVDL) along with time axis
4.1 Results 4.1.1 Experiment 1: Mono-component Linear frequency modulation (LFM) signal In the observation time Ta = 16s, mono-component LFM signal in (35) with C = 1, f = 1, and k = −1 is shown in Fig. 1a, in which real part and imaginary part are blue solid line and red dotted line respectively
Summary
The classical Wigner-Ville distribution (WVD), as an important and fundamental tool of time-frequency analysis, has been developed over the years in many engineering systems [1,2,3,4,5,6]. It can be viewed as traditional Fourier transform (FT) kernel on autocorrelation function. Linear canonical transform (LCT) is a generalized integral transform of FT and fractional FT (FRFT) and defined as [7,8,9] +∞.
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