An improved Gabor wavelet and its complete transforms

An improved Gabor wavelet is proposed in this paper, of which the two parameters have clear physical meanings. Among two parameters, the frequency parameter is the center of symmetry of the wavelet's amplitude spectrum and equal to the central frequency of the wavelet's frequency window. The resolution factor parameter can adjust the support interval of the wavelet's frequency spectrum function and the time-frequency resolutions of the wavelet function. Also, improved Gabor wavelet maps signals from a time domain to a time-frequency domain rather than the time-scale domain. Moreover, an inverse of this improved Gabor wavelet's transform is proposed. Especially, this inverse transform can realize lossless signal reconstruction without the requirement for Gabor wavelet to satisfy the admissible condition. Finally, this paper discusses differences between Gabor wavelet complete transform and S transform, and verifies them by a real application.