Periodic generalized harmonic wavelet: transformation and reconstruction
Fan Kong1, Jie Li1, 2
1. School of Civil Engineering, Tongji University, Shanghai 200092; 2. State Key Laboratory Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China
Abstract：The Periodic Generalized Harmonic Wavelet (PGHW) and the algorithm for its Fast Wavelet Transform (FWT) and inverse fast Wavelet Transform (iFWT) are presented in this paper. The PGHW can be represented as a sum of several translated harmonic terms in the time domain, and of several function in the frequency domain. Compared to the Generalized Harmonic Wavelet (GHW) and the Harmonic Wavelet (HW), PGHW is orthogonal and periodic, while the later lose the orthogonality on a finite time interval. Considering the simplicity of the PGHW in the frequency domain, the FWT and iFWT is developed via the Fast Fourier Transform (FFT) technique. Numerical examples demonstrate the computational efficiency of the algorithm and perfect reconstruction of the PGHW.
2013, Vol. 32 
