Tustin变换(又称双线性变换)是数字滤波器的设计、实时数字仿真、数控及辩识等领域流行的方法,有关s域和z域系数值的相互计算问题前人已进行过研究,但均未建立直接的数学关系式。本文运用矩阵相乘代替多项式的相乘,再利用二项式定理以及二次型的有关结论,导出了s域和z域上系数值之间的数学关系式,并在这一成果的基础上,建立了一个算法。 Tustin transform (also known as bilinear transformation) is a popular method in the field of digital filter design, real-time digital simulation, numerical control and identification. The mutual calculation of s-domain and z-domain coefficient has been studied in the past, However, no direct mathematical relationship has been established. In this paper, we use the matrix multiplication instead of the polynomial multiplication, and then use the binomial theorem and the related conclusions of the quadratic form to derive the mathematical relation between the values ​​of s domain and z domain. On the basis of this result , Built an algorithm.