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I remember fondly a college lab experiment where we had to design a circuit that modulated a signal on a carrier (basic FM modulator).

The prep for the lab included a paper running all the math predicting the outcome, that included fourier transforms.

The moment we hooked the circuit's output to an spectral analyzer was the first time I saw years of theoretical math resulting on something "tangible": the carrier signal's peak and +/- modulated peaks around it.




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