Time-frequency Localization Characteristics of A Novel Class of Complex Wavelet

In this paper, a novel class of complex wavelet is introduced. Time, frequency and time-frequency localization characteristics are investigated using time operator. Theoretical and numerical analysis shows that the new class of wavelet possesses excellent time-frequency localization. Many complex wavelets are constructed, which are approximate to the optimal time-frequency window function by changing two controlling parameters of the new wavelet.