A straight line (y=x) can be written as a sum over sinusoids, known as a Fourier Series.pic.twitter.com/Obii1qd62T
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that's right, it converges to y=x in (-π,π) for the Fourier series (as opposed to the transform). Given that it does converge to a line on (-π,π), i wouldn't say i fibbed.. This is twitter,not an academic conference.The purpose of my tweets is to get across the basic idea in..
But ... isn't the "basic idea" that one can use a Fourier series to approximate any periodic signal? So why start with a "straight line", an inherently aperiodic object? Also, sorry for the nitpick, but it doesn't converge to y=x in (-π,π). The integral error converges to zero.
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Really what you're doing is finding a representation for the periodic extension of y=x on (-pi,pi). Note that even as the terms go to infinity the Fourier series remains at zero on the boundary; this is because nonperiodic functions lack certain (Dirichlet) boundary conditions
Thanks. Twitter will use this to make your timeline better. UndoUndo
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lines are precisely what sawtooth waves are..
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Respectfully no. They're line segments. A sawtooth wave is piecewise linear, not linear.
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