The Performance of Two Mothers Wavelets in Function Approximation
Mohd Fazril Izhar Mohd Idris, Zaki Ahmad Dahlan, Hj. Kamaruzaman Jusoff · Journal of Mathematics Research · 2009
Research into Wavelet Neural Networks was conducted on numerous occasions in the past. Based on previous research,it was noted that the Wavelet Neural Network could reliably be used for function approximation. The research conductedincluded comparisons between the mother functions of the Wavelet Neural Network namely the Mexican Hat, GaussianWavelet and Morlet Functions. The performances of these functions were estimated using the Normalised Square RootMean Squared Error (NSRMSE) performance index. However, in this paper, the Root Mean Squared Error (RMSE)was used as the performance index. In previous research, two of the best mother wavelets for function approximationswere determined to be the Gaussian Wavelet and Morlet functions. An in-depth investigation into the two functions wasconducted in order to determine which of these two functions performed better under certain conditions. Simulationsinvolving one-dimension and two-dimension were done using both functions. In this paper, we can make a specificallyinterpretation that Gaussian Wavelet can be used for approximating function for the function domain [?1, 1]. WhileMorlet function can be used for big domain. All simulations were done using Matlab V6.5.