The Fractional Wavelet Transform
Huang Si-qi · 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 filtering process with dilated band-pass filters of the Fourier domain.The fractional Fourier transform which is the generalized form of the well-known Fourier transform has more flexible properties for signal processing.Comparing with the primitive multi-resolution analysis of signals in the time-frequency domain,a multi-resolution analysis of signals in the time-fractional Fourier domain is developed and a generalization of the wavelet transform which is the fractional wavelet transform(FRWT) is proposd.Then a generalization of the time-generalized frequency(fractional Fourier domains) boxes of FRWT which defines a tiling of the time-generalized frequency(fractional Fourier domains) plane,the scaling band-pass filtering in the fractional Fourier domain is analyzed.As a result,FRWT which is a flexible method for the signal processing with little complexity compared with the well-known wavelet transform has been proposed.It's obvious that the conventional wavelet transform theory is derivable only when letting the order of the fractional wavelet transform α=π/2.Finally,simulations verify the proposed theorem of FRWT.