It’s literally the Heisenberg uncertainty principle, applied to signal processing.

For those who don't get this comment, the Heisenberg uncertainty principle applies to any two quantities that are connected in QM via a Fourier transform. Such as position and momentum, or time and energy. It is really a mathematical theorem that there is a lower bound on the variance of a function times the variance of its Fourier transform.

That lower bound is the uncertainty principle, and that lower bound is hit by normal distributions.

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Gannon6790 14 hours ago | parent | next [-]

thank you for that reminder/clarification. I forget sometimes how much we think we have clear pictures of how things like that work when really we're just listening to someone trying to explain what the math is doing and we're adding in detail.

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hahahahhaah 15 hours ago | parent | prev [-]

Thats. I always assumed it was more a quirk of the universe than something driven by pure mathematics. Amazing.

	▲	hammock 14 hours ago \| parent [-]
		Yes that’s fair to say. The tradeoff is mathematically inevitable. Physics just dictates the constants. It’s also the kind of thinking that can throw a wet blanket on the “beauty” of e.g. Eulers identity (not being critical, I genuinely appreciate the replies I got)