4 ms·
Re: Sinusoidal vs Sawtooth patterns, in fourier analysis a sawtooth is just a bunch of sinusoids with the phase aligned. I wonder if these sharp transitions jus
by phreeza 11y ago
Re: Sinusoidal vs Sawtooth patterns, in fourier analysis a sawtooth is just a bunch of sinusoids with the phase aligned. I wonder if these sharp transitions just occur when many factors with different frequencies happen to align in phase. 1848 and 1968 come to mind as years when this seems to have happened.
- moyix 11y agoIn Fourier analysis, everything is just a bunch of sinusoids ;) And it seems to me that there are also sawtooth patterns that aren't clearly the alignment of lots of sinusoidal patterns, such as market bubbles.
- jmount 11y agoThere are definitely graphs that can only be approximated by Fourier methods (such as square waves). The issue is related to Gibbs phenomena: https://en.wikipedia.org/wiki/Gibbs_phenomenon https://en.wikipedia.org/wiki/Gibbs_phenomenon
- moyix 11y agoYou're correct; I was thinking of L^p (p > 1) convergence almost everywhere.
- phreeza 11y agoThe emphasis was supposed to be on the part with the phases being aligned (at the point of the steepest slope) :)