在数字信号处理和离散时间的控制理论中，双线性变换 (即 Tustin变换)被用来在连续时间系统与离散时间系统做转换。

双线性变换是一种特别的共行映射(即莫比乌斯变换)，常被用来将线性非时变系统滤波器在连续时域的传递函数 转换成线性且平移不变滤波器在离散时域的传递函数 。将S平面中位置在轴的点映射到复数平面上的单位圆 。其他的应用还有扭曲任何的离散时间线性系统的频率响应(例如用来估计人类听觉系统的非线性频率分辨率)或是被用在离散域以取代一个系统经过一阶全通滤波器的单位延迟。

这种变换保有稳定性且将连续时间滤波器的频率响应 中每一点映射到离散时间滤波器的频率响应中所对应的点，虽然频率会有点不同，这部分会在之后的频率扭曲中解释。对于模拟滤波器的频率响应中所看到的特征，在数字滤波器的频率响应中都有相同增益和相位平移的对应特征，虽然频率可能会有点不同，在低频时很难观察到但在频率接近奈奎斯特频率时就相当明显。

The bilinear transform (also known as Tustin's method) is used in digital signal processing and discrete-time control theory to transform continuous-time system representations to discrete-time and vice versa.

The bilinear transform is a special case of a conformal mapping (namely, the Möbius transformation), often used to convert a transfer function of a linear, time-invariant (LTI) filter in the continuous-time domain (often called an analog filter) to a transfer function of a linear, shift-invariant filter in the discrete-time domain (often called a digital filter although there are analog filters constructed with switched capacitors that are discrete-time filters). It maps positions on the axis, , in the s-plane to the unit circle, , in the z-plane. Other bilinear transforms can be used to warp the frequency response of any discrete-time linear system (for example to approximate the non-linear frequency resolution of the human auditory system) and are implementable in the discrete domain by replacing a system's unit delays with first order all-pass filters.