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I see this as a confusing explanation of the algorithm for calculating coefficients, not as a line that explains what the Fourier transform is. As for a single
by onos 4y ago
I see this as a confusing explanation of the algorithm for calculating coefficients, not as a line that explains what the Fourier transform is.
As for a single line on intuition, can you beat: “method of decomposing a function into a sun of sines and cosines?”
- hgsgm 4y agoThen you have to get into why you are talking about sines and cosines, adding unnecessary complexity to the explanation. The OP is better. It's the frequency that matters for intuiook, the shape of the periodic function is a technical detail.
- cousin_it 4y agoSines and cosines are the best choice here because they're the "elementary periodic function" for a given frequency: the sum of two (possibly scaled and shifted) sinusoids at some frequency is also a (scaled and shifted) sinusoid at the same frequency. For other shapes of periodic function it's not true: for example, if you sum two triangle waves of the same frequency but offset from each other, you'll get a shape that's more complex than a triangle wave. Same for two square waves etc. So the most natural way to decompose a signal is into a sum of sinusoids rather than triangles or squares etc.
- PaulDavisThe1st 4y agoMinor note: "sinusoids" (as you say yourself in your final sentence) is enough. No need to mention sines & cosines as distinct types.