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When we first covered the FS (Fourier Series) and FT (Fourier Transform) and the relation between the two in our Signals and Systems course in EE, I was amazed. It was the greatest thing I've ever learned, and I think it'll be hard to top.

Once you understand the FT, you basically understand how a signal is structured. By converting (or transforming) a time signal to the frequency domain, one can clearly see what frequency components (or harmonics) contribute to said signal. If one were to try the same in the time domain, it would be much more difficult to visualize.

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