What is a Fourier transform? In the Adafruit Learn Guide FFT: Fun with Fourier Transforms, Tony DiCola write “At a high level the Fourier transform is a mathematical function which transforms a signal from the time domain to the frequency domain. This is a very powerful transformation which gives us the ability to understand the frequencies inside a signal. For example you can take an audio signal and detect sounds or tones inside it using the Fourier transform.” For more discussion, here’s The Guardian:
The equation was developed by the mathematician Baron Jean-Baptiste-Joseph Fourier and appeared in its final form in his 1822 book, The Analytical Theory of Heat. As the title suggests, Fourier was interested mainly in how heat flowed around materials but his mathematical tool turned out to be more fundamental than perhaps he realised.
In essence, it says that any complex wave-like signal you care to measure, that fluctuates over time or space, can be broken down into a sum of the familiar, regular, sine waves – the type that roll across the tops of oceans or vibrate along strings. Think of your complex signal as a cake. It contains flour, sugar, eggs and butter but you don’t taste any of these things individually when you take a bite of the finished product. If the cake is the waveform, the recipe is the Fourier transform, a list of ingredients and how to combine them. If you want to adapt the final waveform (cake) somehow, it is much easier to do it by isolating the ingredients first.
For a DIY project that works with Fourier transforms, check out FFT: Fun with Fourier Transforms, which uses Electret Microphone Amplifier.
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