Design of Complex Wavelet Base in Analog Domain

Abstract

This paper proposes a method of pole-shared approximation for complex wavelet bases using hybrid genetic algorithm. The approximation process mainly includes the rational fraction approximation of the Gaussian envelope and the Laplace transform of the product of the approximation function and the sine or cosine function. According to the principle of pole-shared approximation, the mathematical approximation model is constructed first. And then, the complex Gabor wavelet is taken as an example to illustrate the approximation process of Gaussian envelope using hybrid genetic algorithm. The experimental results show that the approximation accuracy of the complex wavelet base is relatively high, and the approximation functions of the real part and the imaginary part have the same poles.