A stable Hankel transforms algorithm based on Haar wavelet decomposition for noisy data (Q1664928)

Summary: We proposed the combination of signal denoising technology and Hankel transforms algorithm which were both based on Haar wavelet decomposition. Therefore, one can achieve above two purposes simultaneously while the wavelet decomposition is carried out just for once. The principle and its derivation of the Haar wavelet method for Hankel transforms were put forward. Numerical examples and engineering application showed that the precision of Haar wavelet method is about magnitude of \(1.0 E - 4\) and \(1.0 E - 5\); it can maintain good accuracy when using fewer wavelet coefficients. Moreover, it has better anti-noise performance and better computational stability than the filter method, so it can be applied to the Hankel transforms with noisy data.