Phase Rotations
Learn how to rotate a complex number by using phases.
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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 plane by a phase is very simple.
- For a number and phase , we write a phase rotation as:
Since is a complex number with magnitude 1 and phase , the magnitude of the result stays constant while is added to the angle of that complex number.
- For a signal and phase , we write a phase rotation as:
Again, the magnitude of the result stays constant. This means that the individual and values change, but their squared sum remains the same. The impact of appears for all time instants.
Real signals
To understand the same process in terms of real signals, let’s multiply a complex number ...