A novel method for computing the Hilbert transform with Haar multiresolution approximation

In this paper, an algorithm for computing the Hilbert transform based on the Haar multiresolution approximation is proposed and the L 2 -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.