Cyclic wavelet transform and its application

The concept of cyclic wavelet transform and its fast algorithm are introduced. A process of transforming original wavelet into corresponding cyclic wavelet is discussed in detail. A general formula of cyclic wavelet decomposition of a signal is given by wrapping round and adding process. A uniform description of even Daubechies cyclic wavelet transform matrix for a signal with the arbitrary power of 2 lengths is presented. The extraction procedure of impulse response via cyclic wavelet transform for structural system identification is introduced, then simulation of the presented procedure for two DOF and cantilever system is studied. In the simulation, ensemble-averaging performance and influence of using the Daubechies wavelet with variable length on the identification accuracy is discussed and compared with that of the extraction procedure based on the FFT.