一类分数阶模拟小波滤波器的电路实现

Circuit Realization of a Class of Fractional Analog Wavelet Filters

通过计算分数阶小波滤波器传递函数通式中的系数,设计一种可行的电路方案实现分数阶模拟小波滤波器.首先,在频域中对高斯族小波进行有理分式逼近,构建结构简单且分子仅一项的数学近似模型.其次,利用FosterⅠ型RC串并联网络逼近分数阶电容,从而保证分数阶阻抗器件的实现.最后,以元件阻抗值的比例形式确定传递函数的系数,从而实现6.4阶Marr小波滤波器电路.仿真结果表明,所设计的电路结构能对高斯族小波进行良好的逼近,并具有高精度、高灵活性的优点.

By calculating the coefficients in the general formula of the transfer function of the fractional wavelet filter,a feasible circuit scheme was designed to realize the fractional analog wavelet filter.Firstly,the rational fraction approximation of Gaussian-like wavelet in the frequency domain was carried out,and a mathematical approximation model with simple structure and only one term in the molecule was constructed.Secondly,the fractional-order capacitance was approximated by the Foster Ⅰ type RC series-parallel network,thus ensuring the realization of the fractional-order impedance device.Finally,the coefficient of the transfer function was determined in the form of the ratio of the impedance value of the element,thus realizing the 6.4 order Marr wavelet filter circuit.The simulation results show that the circuit structure designed in this paper can approximate the Gaussian-like wavelet well,and has the advantages of high precision and high flexibility.