Describe what the Fourier transform does - takes a signal from the time domain to the frequency s-domain. So I looked into the Fourier series a lot a A-level when I trying to make sense of how the app Shazam works1. From this I can tell you that to be able to apply the FT you don’t need to be a mathematical wizz, BUT of course making sense of what’s happening when we ‘transform’ a function from a time to frequency domain need more understanding. In this article, I want to elaborate further on what a s-domain is how this makes it easier to analyse an analogue wave.
Outline use cases - control theory (audio, images, radar, sonar, x-rays, crystallography etc.).
Have the complex version of the formula and then show how this leads to the 3 equations.
Describe the s-domain
Have the graphs to show a wave in the time domain.
Then 3D graphs for the s-domain showing the fractions of the waves at each harmonic.
My absolute favourite app! (Description of how it works) ↩
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