论文部分内容阅读
提出了一种非90°移相希尔伯特变换器的等波纹逼近设计方法。非90°移相器本质上是一种指定相位特性的全通滤波器。对于平稳的数字全通滤波器,其分母多项式一定具有最小相位。通过构造一个纯虚奇对称相位函数的方法推导出了分母多项式的相位函数与其复倒谱序列之间的关系;利用加权最小二乘法求得分母相位的等波纹逼近函数,进而利用上述关系求出其倒谱序列;依据复倒谱的基本理论,通过求解一个非线性递归差分方程得到分母多项式系数。设计实例表明,这种方法能够使设计的非90°移相器的相位函数在指定频带上实现等波纹逼近的要求,从而提高了非90°移相器的频率选择性。
A kind of isokinetic approximation design method for non-90 ° phase-shifted Hilbert transformer is proposed. A non-90 ° phase shifter is essentially an all-pass filter that specifies the phase characteristics. For a smooth digital all-pass filter, the denominator polynomial must have the smallest phase. The relationship between the phase function of the denominator polynomial and the complex cepstrum sequence is deduced by constructing a purely virtual odd-symmetric phase function. The equi-ripple approximation function of the denominator phase is obtained by the weighted least square method, and then the relationship Its cepstrum sequence. According to the basic theory of complex cepstrum, the denominator polynomial coefficient is obtained by solving a nonlinear recursive difference equation. The design example shows that this method can make the phase function of the designed non-90 ° phase shifter realize the requirement of equal wave approximation on the specified frequency band, and improve the frequency selectivity of the non-90 ° phase shifter.