A modified fourth-order time-frequency distribution with complex-lag argument and its counterpart L-form

The 4th-order cross-term reduced time-frequency distribution with complex-lag argument (CTD) is analyzed and its frequency scale problem is pointed out. The conventional solutions to the problem are oversampling the signal or applying interpolation to the signal after it has been sampled, as they have been done in Wigner-Ville distribution (WVD). However, oversampling or interpolation results in excessive calculation amount. Therefore, a modified version of 4th-order cross-term reduced CTD (MCTD4) is proposed in this paper. The modifications include compressing the core function of CTD and making a periodic extension of the result. Because MCTD4 doesn´t have the frequency scale problem, oversampling or interpolation is not necessary. The counterpart L-form of MCTD4 is also included. It increases the time-frequency resolution of MCTD4. Effectiveness of the method is illustrated by examples.