A general method of rational approximation for Gaussian wavelet series and Gaussian wavelet filter circuit design with simple g_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 simple g_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.

中文翻译：

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高斯小波序列的一般有理逼近和连续时间GM-C滤波器的实现

本文提出了一种利用简单的g _m -C积分器对高斯小波级数和高斯小波滤波电路设计进行有理逼近的通用方法。首先，分析了高斯函数的多阶导数并将其证明为小波基函数。然后构造了一个高斯小波级数的高精度通用逼近模型，并利用量子微分进化（QDE）算法获得了高斯小波滤波器一阶导数的传递函数。第三，作为一个例子，高斯的第五阶连续时间模拟一阶导数小波滤波器电路是基于与一个简单的多回路反馈结构设计克_米‐C集成器作为基本模块。最后，仿真结果表明，该方法是实现小波变换的一种很好的方法。高斯小波滤波器电路的设计一阶导数采用0.53V电源电压和2.5nA偏置电流工作。小波滤波器电路的基本功耗为41.1 nW。此外，基于设计小波滤波器的高精度QRS检测已在应用分析中得到验证。