A wavelet algorithm for Fourier-Bessel transform arising in optics (Q277602)

Summary: The aim of the paper is to propose an efficient and stable algorithm that is quite accurate and fast for numerical evaluation of the Fourier-Bessel transform of order \(\nu\), \(\nu >-1\), using wavelets. The philosophy behind the proposed algorithm is to replace the part \(t f(t)\) of the integral by its wavelet decomposition obtained by using CAS wavelets thus representing \(F_{\nu}(p)\) as a Fourier-Bessel series with coefficients depending strongly on the input function \(t f(t)\). The wavelet method indicates that the approach is easy to implement and thus computationally very attractive.