Fractional Time-frequency Distribution Series And Its Applications

Time-frequency distribution is a basic tool of signal processing,which represents the energy distribution of signals in joint time-frequency domain.Wigner distribution is an effective method,but there is cross-term interference.Therefore,the suppression of Wigner distribution cross-term interference has attracted much attention in the field of signal processing.Time-frequency distribution series decomposes Wigner distribution,and suppresses cross-term interference on the premise of retaining useful components.However,only the time shift and frequency shift characteristics of atoms are considered in the time-frequency distribution series,and the rotation characteristics of signals in the time-frequency plane are not considered.The basic function of time-frequency distribution series shows time-shift and frequencyshift characteristics in time-frequency domain,and has no signal rotation characteristics.However,fractional signal processing can adapt to the time-frequency rotation characteristics of signals.In view of this,based on the time-frequency distribution series,the idea of fractional signal processing is introduced to propose the fractional time-frequency distribution series.The main results can be summarized as follows:Firstly,the Wigner distribution is analyzed by Radon transform,and the behavior of cross-term interference is discussed.It is pointed out that Wigner distribution has energy distribution characteristics along any direction in time-frequency plane.At present,it is known that the edge characteristics of Wigner distribution are its special case results.Secondly,starting from the short-time fractional Fourier transform,the definition of fractional Gabor expansion is given.The complete reconstruction condition and biorthogonal condition are discussed.The fractional Zak transform is introduced and the corresponding analytical function solution method is obtained by combining the frame theory,and the simple inverse transformation is given.The Wigner distribution is decomposed by fractional Gabor,and the fractional time-frequency distribution series is obtained.The properties of time-frequency distribution series are discussed,and the selection principle of basic functions is analyzed.Finally,the fractional Gabor expansion and fractional time-frequency distribution series are discretized.Simulation verification is carried out,and the influence of each parameter on the series of fractional time-frequency distribution is analyzed.Compared with other distribution methods,the relationship between fractional time-frequency distribution series and other time-frequency distribution methods is discussed,and the results of theoretical analysis are verified.