A new complex wavelet: RI-Spline wavelet and its application to signal processing

In this paper, we propose a new complex-type wavelet which we call the real imaginary (RI)-spline wavelet. We show that the RI-spline wavelet can be used for continuous and discrete wavelet transform as the mother wavelet. We confirm the effectiveness of this wavelet in continuous and discrete cases by using a model signal and applying it to an unsteady signal analysis. The main results obtained are summarized as follows: the RI-spline wavelet can be used with both the continuous wavelet transform (CWT) and discrete wavelet transform (DWT) as the mother wavelet and in the case of DWT the shift invariance has been improved. The RI-spline wavelet has been applied to an unsteady turbulence analysis and removing the pulse noise form music. The experimental results obtained demonstrate the advantages of our approach.