Jean-Bosco Mugiraneza; Amritasu Sinha

Analogue Wavelet Transform Based the Solution of the Parabolic Equation

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Author(s)

Jean-Bosco Mugiraneza ^1,* Amritasu Sinha ²

1. Department of Computer Science, Faculty of Science and Technology, Kigali Independent University, ULK, P. O. Box 2280 Kigali, Rwanda

2. Department of Mathematics, ETB, McMaster University, Canada

* Corresponding author.

DOI: https://doi.org/10.5815/ijitcs.2012.12.01

Received: 3 Feb. 2012 / Revised: 27 May 2012 / Accepted: 23 Aug. 2012 / Published: 8 Nov. 2012

Index Terms

Wavelet Transform, Morlet Wavelet, PDE, FFT, Power Spectral Density, Matlab, Parabolic Equation

Abstract

In this paper we have proved that the solution of parabolic equation and its Fast Fourier Transform generate continuous wavelet transforms. Indeed, we have solved the parabolic equation using PDETool, exported its solution and coefficients to Matlab workspace. We have then imported the solution from workspace to signal processing tool. We have sampled the imported solution with the sampling frequency of 8192Hz and applied the band pass filter with that frequency. The convolution of the sampled PDE solution with the impulse response of the band pass filter has generated wavelet transform. This algorithm computes the wavelet transform either directly of via Faster Fourier Transform. The computation of the FFT of the PDE solution has produced complex wavelet.

Cite This Paper

Jean-Bosco Mugiraneza, Amritasu Sinha, "Analogue Wavelet Transform Based the Solution of the Parabolic Equation", International Journal of Information Technology and Computer Science(IJITCS), vol.4, no.12, pp.1-20, 2012. DOI:10.5815/ijitcs.2012.12.01

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International Journal of Information Technology and Computer Science (IJITCS)