I. Introduction
Real-life signals encountered in various fields of engineering are often collected in noisy environments, corrupting effects of which are difficult to suppress during the stage of signals acquisition and transmission. At the point of analysis of such signals, time-frequency distributions (TFDs) are versatile tools for extracting their indicative features [1]–[5]. The mixture of noise and signal components may be modeled as [6]–[10] \begin{align} y(t)=x(t)+\nu (t), \tag{1} \end{align} where is deterministic and independent, stationary, additive white Gaussian noise (AWGN). In terms of continuous variables of time, , and frequency, , the general Quadratic class of TFDs of the analytic signal associated with a real signal is defined as [2]: \begin{align} \rho (t,f)=\underset{t \rightarrow f}{\mathcal {F}}\left \lbrace G(t, \tau)\underset{t}{*}\left[z\left(t+\frac{\tau }{2}\right)z^{*}\left(t-\frac{\tau }{2}\right)\right]\right \rbrace \tag{2} \end{align} where , and represents the time-lag kernel. When the discrete form of the signal in Eq. (1) is considered \begin{align} y(n)=x(n)+\nu (n), \tag{3} \end{align} with being the number of samples, the general Quadratic TFD in terms of discrete variables is obtained by sampling at and , with and being integers, and time-lag limited so that for , where and are positive integers. The discrete Quadratic TFD takes the form [2] \begin{align} \rho (n,m)=\underset{l \rightarrow m}{DFT}\lbrace G(n,l)\underset{n}{*}(z(n+l)z^*(n-l))\rbrace ; l\in \langle L \rangle, \tag{4} \end{align} with being the analytic discrete time signal corresponding to , and being the kernel in the discrete time-lag domain. The structure of the TFD is dictated by the kernel filter since it controls time and frequency supports of the signal components together with the intensity of interference phenomena [11]–[20].