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{title=<DFT> of $2 \sin(t) + \cos(4t)$ with 25 points}
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{disambiguate=Discrete Fourier transform}
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{description=This is a simple example of a <discrete Fourier transform>. It also illustrates how the <discrete Fourier transform of a real signal> is symmetric around the center point.}
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{description=This is a simple example of a <discrete Fourier transform> for a real input signal. It illustrates how the <DFT> takes N <complex numbers> as input, and produces N <complex numbers> as output. It also illustrates how the <discrete Fourier transform of a real signal> is symmetric around the center point.}
Copy file name to clipboardExpand all lines: ciro-santilli.bigb
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@@ -66,6 +66,11 @@ Ciro once saw some cartoon on <Wikipedia> help pages of a turtle with a book in
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Another analogous version of this fantasy more in touch with Ciro's <sinophily> is the ideal of the <Chinese scholar>, notably including their stereotypical attributes such as mastery of the <Four Arts>.
* <Diophantine equation> existence of solutions: <undecidable Diophantine equation problems>
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= Undecidability requires infinitely many inputs
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{parent=Undecidable problem}
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If there are infinitely many inputs, we can always construct a (potentially exponentially huge) <Turing machine> that hardcodes the outcome for every possible input, so the problem is never <undecidable>.
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The problem is of course deciding and proving the outcome for each possible input, notably as it is possible that calculation for some of the inputs may be <independent (mathematical logic)> from <ZFC>.
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= Mortal matrix problem
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{parent=Undecidable problem}
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@@ -301,9 +308,6 @@ The Busy Beaver problem is cool because it puts the <halting problem> in a more
@@ -329,6 +333,11 @@ The following things come to mind when you look into research in this area, espe
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* it is largely <recreational mathematics>, i.e. done by non-professionals, a bit like the <aperiodic tiling>. Humbly, they tend to call their results <lemma (mathematics)>[lemmas]
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* complex structure emerges from simple rules, leading to a complex <classification (mathematics)> with a few edge cases, much like the <classification of finite simple groups>
* https://www.reddit.com/r/math/comments/1dubva0/finding_the_6th_busy_beaver_number_%CF%836_aka_bb6_is/ "Finding the 6th busy beaver number (Σ(6), AKA BB(6)) is at least as hard as a hard Collatz-like math problem called Antihydra":
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