椭圆函数型高低通互补滤波器的综合与实践

The Synthesis and Implementation of High-and-Low Pass Complementary Filter of the Elliptic Function Type

在微波通信系统中的彩色电视调制、解调机架上,有一图像、伴音分路(或合成)滤波器。本文介绍了用互补方式综合这一滤波器的全过程。提出了椭圆函数互补滤波器的实现条件。运用高斯变换法求椭圆函数的高精度近似值,解决了过去沿用椭圆积分表达不到精度要求的困难。在此基础上提出了求插入电流比函数分子多项式E(S)实根的新方法,比过去用牛顿法累次逼近求实根近似值简便精确。实践结果表明,高低通互补滤波器的各项技术指标均能满足要求。

There is a picture/sound separated (or combined) filter in the color television modulation and demodulation bay of microwave communication system. This paper presents the whole procedure of the synthesis for such a filter, using the complementary mode. The approach of realization of the elliptic function complementary filter has been given. Highly accurate approximations of the elliptic function are obtained in this paper through the use of Gauss transformation, which could not be obtained by the traditional method of using elliptic integral tables. A new method to find the real roots of the polynomial in the numerator of the inserted current ratio function is proposed on the basis mentioned above. It is a simple and more accurate method rather than the common Newton's method using successive approximation in finding the real roots.Practice shows the various items of technical specification of the introduced high-and-low pass complementary filter can be satisfied in the practical circuit.