双线性变换法原理的解释

Explanation about the Principle of Bilinear Transformation Method

现有信号与系统教材或数字信号处理教材对数字滤波器设计中的双线性变换公式未给出完全的物理概念解释 ,这在一定程度上影响了初学者对双线性变换法原理的理解和掌握。考虑到讲授对象为初学者及课堂讲授时间的限制 ,根据笔者的教学体会 ,本文从连续时间系统的基本环节、积分的数值计算、一阶系统和高阶系统的离散实现等几个步骤 ,对双线性变换法的原理作简单而系统的阐述 ,以供参考。

In existed textbooks of digital signal processing or signals and systems, this is not a complete explanation regarding the formulation of bilinear transformation, which is used in digital filter design. This affects, to a degree, learner's understanding and mastering of the principle of bilinear transformation. Considering that audience of the lectures are beginner and the class hours are limited, and based on author's experience of lecturing, this paper presents for reference a simple and systematic statement about the principle of bilinear transformation from several steps: basic elements of first order continuous time system, numeric calculating of integral, discrete realization of first and high-order systems.