Pole-Shared Realization of Complex Wavelet Base Using AFSA

In this paper, the method for pole-shared approximation of complex wavelet bases has been proposed, which mainly involves the rational fraction approximation of Gaussian envelope and the Laplace transform of the product of approximation function and sine or cosine function. To enhance the approximation accuracy of Gaussian envelope, the mathematical approximation model has been constructed, and the Artificial Fish Swarm Algorithm is used for the optimization. Finally, the complex Morlet wavelet is used as an example in this paper to illustrate the construction and optimization procedure of the approximation model for Gaussian envelope. Experimental results show that the approximation functions of the real and the imaginary part of complex wavelet base have the same poles, and also the approximation accuracy for modulus and phase is relatively high.