General rational approximation of Gaussian wavelet series and continuous-time gm-C filter implementation
A general method of rational approximation for Gaussian wavelet series and Gaussian wavelet filter circuit design with simple gm-C integrators is presented in this work. Firstly, the multi-order derivatives of Gaussian function are analysed 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 5th order continuous-time analogue first order derivative of Gaussian wavelet filter circuit is designed based on multiple loop feedback structure with simple gm-C integrator as the basic blocks. Finally, simulation results demonstrate 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 0.53V supply voltage and a bias current 2.5nA. The power dissipation of the wavelet filter circuit at the basic scale is 41.1nW. Moreover, the high accuracy QRS detection based on the designed wavelet filter has been validated in application analysis.