(1+α)阶线性相位滤波器的优化设计

Optimal design of(1+α)order linear phase filters

针对分数阶Bessel滤波器的线性相位特性较差,该文提出了一种分数阶线性相位滤波器的优化设计方法。通过对一般形式的分数阶低通滤波器传递函数进行分析,提出一种合理的分数阶低通滤波器传递函数结构,并对分数阶低通滤波器相频特性优化问题进行建模和求解,得出一种具有线性相位特性的分数阶低通滤波器。经过分析可知,文中设计分数阶滤波器皆稳定,并且与整数阶滤波器相比分数阶滤波器可以通过调整阶数对通带的群延时和相位延时进行精细的调整。文中基于分数阶电容设计了1.7阶线性相位低通滤波器的有源电路,由于目前没有商用分数阶电容的生产,因此该电路中的分数阶电容用RC网络进行模拟。电路测试结果表明,1.7阶低通滤波器有源电路的频率响应与滤波器理论上频率响应之间的误差在可接受范围内。

Aiming at the fractional-order Bessel filter has poor linear phase characteristics,this paper proposes an optimal design method of fractional-order linear phase filter.A reasonable transfer function structure of fractional-order linear phase filter is derived from the general form of transfer function for fractional-order low-pass filter.The phase frequency characteristics of fractional-order filter are optimized,and a fractional-order filter with linear phase characteristics is obtained.The stability analysis and frequency domain analysis of the filter are carried out,the results show that the fractional-order filter designed in this paper is stable,compared with integer-order filter,fractional-order filter can adjust phase delay and group delay more precisely on the premise of ensuring the linear phase characteristics.An active circuit with a 1.7-order linear phase low-pass filter is designed based on fractional-order capacitors.Since there is no commercial production of fractional-order capacitors,the fractional-order capacitors in this circuit are modeled using RC networks,the circuit test results show that the error between the frequency response of the 1.7-order low-pass filter active circuit and the theoretical frequency response of the filter is within the acceptable range.