Periodicity in Time reflected in Frequency domain

[Vishnu M]

Why is it that periodicity in the time domain is reflected in the frequency domain, as stated in the Filter video from Module 2 (timestamp 6:22).

I thought that the frequency domain was showing us the frequencies present during a single period of the waveform in the time domain. SO I don’t quite understand why the periodicity/repetitions in time domain would be reflected in the frequency domain

[Simon]

In the magnitude spectrum (i.e., the frequency domain), we see the frequencies present in whatever signal we are analysing: the analysis frame. In the video and that time point, the analysis frame is the visible portion of waveform on the left, which has a duration of 30 ms and contains multiple pitch periods.

You can use the DFT to analyse any amount of waveform (= the analysis frame) that you wish. If you analyse only one pitch period, you will not see any evidence of periodicity. If you analyse a waveform that contains multiple pitch periods (like in the video at the time point) then you will see evidence of periodicity in the magnitude spectrum: harmonics.

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