The Generalized Haar Wavelet

The simple generalizing topic of the Haar wavelet is investigated in this paper. Firstly, an new concept called as the scaling coefficient function is presented and then introducing the time shift factor into the scaling coefficient function, the Haar wavelet is extended to the generalized Haar wavelets which an novel class of orthonormal wavelet. Secondly, the rationality of the simple generalizing method of the orthonormal wavelet, which presented in this paper, is studied theoretically and some properties of the generalized Haar wavelet are discussed. Finally, the closed form expression of the generalized Haar wavelet is given in both the time domain and the frequency domain.