信号与系统中用旋转矢量描述负频率和相位角
A Description of Negative Frequency and Phase Angle by Rotating Vector

在一些信号与系统教材中，负频率被说成是没有物理意义的，相位角的定义也不够严格。本文用旋转矢量方法描述负频率和相位角，从几何意义来看如果正频率是矢量的逆时针旋转的角频率，则负频率是顺时针旋转的角频率，从工程角度来看，可以对应发电机的反向旋转。因此负频率不仅有明确的物理意义，也有重要的工程应用价值。一般的相位角采用反正切的三角函数来定义，但这样的定义方式导致相位角取值范围为？π/2到π/2，而实际的相位角应该是？π到π，这个问题可以采用旋转矢量来严格定义。
In some teaching materials of signals and systems, negative frequency is said to have no physical meaning, and the definition of phase angle is not strict enough. In this paper, the negative fre-quency and phase angle are described by the method of rotation vector. From the geometric sense, if the positive frequency is the counter clockwise rotation angular velocity of the vector, then the negative frequency is the angular velocity of clockwise rotation. From the engineering point of view, it can correspond to the reverse rotation of the generator. Therefore, negative frequency not only has clear physical significance, but also has important engineering application values. In general, the phase angle is defined by the arctangent trigonometric function, but the range of the phase angle is ？π/2 to π/2, the actual phase angle should be ？π to π. This problem can be strictly defined by rotation vector.