Phase Rotations

Learn how to rotate a complex number by using phases.

We'll cover the following

Phase rotations impact a signal in a variety of ways. Therefore, understanding how a signal is rotated inphase is important for a DSP learner.

Complex signals

In complex notation, rotating a complex number in the IQIQ plane by a phase θ\theta is very simple.

  • For a number VV and phase θ\theta, we write a phase rotation as:

W=VejθW= V\cdot e^{j\theta}

Since ejθe^{j\theta} is a complex number with magnitude 1 and phase θ\theta, the magnitude of the result WW stays constant while θ\theta is added to the angle of that complex number.

Get hands-on with 1200+ tech skills courses.