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Animated GIFs Help Explain a Discrete Fourier Transform (DFT) – also Inphase and Quadrature Signals

In a recent talk I tried to explain how Fourier Transforms can be used to estimate the frequency content of signals (ie. the spectral content). Normally we would use maths to illustrate these concepts – but that doesn’t suit everyone, so here’s an attempt with only animated images!

(Hey that’s me!)

You might notice that the blue input is the same frequency as Ref2.  How can we use the reference phasors to estimate the input spectrum?

Assume that for each new sample, we multiply the signal magnitude by the reference magnitude (which is 1) and that we take the difference between their phases. This gives a product phasor for each new sample which will be added to the previous product (as in vector addition).  The result is shown below, with the references shown in different colours for clarity.

Big thanks to Rowetel for pointing out this blog at Bill Cowley’s lowSNRblog. (Hopefully Bill blogs more often because all his blog posts are really fun reads!)


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