Properties of the Fractional Wavelet Transform
XU Xing-wu · Measurement & Control Technology · 2009
The wavelet transform can be viewed as multi-resolution analysis of signals in the time-frequency(the Fourier domain) domain or as the linear time-variant filtering process with dilated band-pass filters.Comparing with the primitive multi-resolution analysis of signals in the time-frequency domain,the fractional wavelet transform(FRWT),a generalization of the wavelet transform,which is a flexible method for the signal processing with trivial complexity compared with the well-known wavelet transform,develops multi-resolution analysis of signals in the time-fractional Fourier domain.The properties of the fractional wavelet are analyzed.Conclusions verify that the fractional wavelet transform can be viewed as the linear time-variant filtering process with dilated band-pass filters of the fractional Fourier domain and there are orthogonal bases of fractional wavelets with limitable condition associated with the fractional wavelet transform.