In this paper, an algorithm for computing the Hilbert transform based on the Haar multiresolution approximation is proposed and the L2-error is estimated. Experimental results show that it outperforms the library function 'hilbert' in Matlab (The MathWorks, Inc. 1994-2007). Finally it is applied to compute the instantaneous phase of signals approximately and is compared with three existing methods. © 2008 Elsevier B.V. All rights reserved.
Zhou, C., Yang, L., Liu, Y., & Yang, Z. (2009). A novel method for computing the Hilbert transform with Haar multiresolution approximation. Journal of Computational and Applied Mathematics, 223(2), 585–597. https://doi.org/10.1016/j.cam.2008.02.006