General rational approximation of Gaussian wavelet series and continuous-time g_m-C filter implementation

摘要

A general method of rational approximation for Gaussian wavelet series and Gaussian wavelet filter circuit design with simpleg(m)-C integrators is presented in this work. Firstly, the multiorder derivatives of Gaussian function are analyzed and proved as wavelet base functions. Then a high-accuracy general approximation model of Gaussian wavelet series is constructed, and the transfer function of first-order derivative of Gaussian wavelet filter is obtained using quantum differential evolution (QDE) algorithm. Thirdly, as an example, a fifth-order continuous-time analog first-order derivative of Gaussian wavelet filter circuit is designed based on multiple loop feedback structure with a simpleg(m)-C integrator as the basic blocks. Finally, simulation results demonstrate that the proposed method is an excellent way for the wavelet transform implementation. The designed first-order derivative of Gaussian wavelet filter circuit operates from a 0.53-V supply voltage and a bias current 2.5 nA. The power dissipation of the wavelet filter circuit at the basic scale is 41.1 nW. Moreover, the high-accuracy QRS detection based on the designed wavelet filter has been validated in application analysis.