The Performance of Two Mothers Wavelets in Function Approximation

Mohd Fazril Izhar Mohd Idris, Zaki Ahmad Dahlan, Hj. Kamaruzaman Jusoff

Abstract


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 conducted
included comparisons between the mother functions of the Wavelet Neural Network namely the Mexican Hat, Gaussian
Wavelet and Morlet Functions. The performances of these functions were estimated using the Normalised Square Root
Mean 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 approximations
were determined to be the Gaussian Wavelet and Morlet functions. An in-depth investigation into the two functions was
conducted in order to determine which of these two functions performed better under certain conditions. Simulations
involving one-dimension and two-dimension were done using both functions. In this paper, we can make a specifically
interpretation that Gaussian Wavelet can be used for approximating function for the function domain [?1, 1]. While
Morlet function can be used for big domain. All simulations were done using Matlab V6.5.

Full Text: PDF DOI: 10.5539/jmr.v1n2p135

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Journal of Mathematics Research   ISSN 1916-9795 (Print)   ISSN 1916-9809 (Online)

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