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The Seven Hertz Ghost: Fourier Analysis and the Fast Fourier Transform
At a gas compression station, a new monitoring system raises a seven hertz pulsation alarm on a compressor whose physics says seven hertz should not exist. Engineer Mattias Ndlovu asks his colleague Yara one question: what sample rate did you configure? In episode one hundred and forty six we build the mathematics behind every spectrum chart. Fourier claims any shape is a chord of sines; a square wave rings with the Gibbs overshoot; linear systems leave sine waves unchanged, which is why frequency is the language of filters and control. Euler's rotating arrows carry amplitude and phase, and…
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