Spectrum After the Time Shift I
Explore the effect of shifting a signal in the time domain on its spectrum from a magnitude and phase viewpoint.
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One of the most important skills to learn in DSP that proves immensely helpful in any kind of application is the impact of a time shift on the signal spectrum. This is what we explore in this chapter.
Phase at a single frequency
The time reference at zero sets the wave phases just like the zero of a measuring tape. Let’s consider a cosine wave that is shifted to the right by . Here, is the wave period.
Clearly, this becomes a sine wave. This is because a full period in time, i.e., , is analogous to traversing a full period in phase, i.e., . Therefore, corresponds to .
This is drawn in the figure below where the phase shift turns the cosine into a sine:
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