Plot of the error between the integral and the sum as a function of the limits of integration/sum.pic.twitter.com/jP9zq7vr6u
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i'm not sure if this should be obvious, but it surprised me to find that both are equal to πpic.twitter.com/973xR17ilx
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I’d totally purchase a book from you if it consisted of nothing but an interesting equation per page with a tiny description at the bottom
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Another sophomore's dream!
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yes, that's a good name for it!
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Oh, this one is fun! It's a direct consequence of the fact that the Fourier transform of sinc(x) only has support at one of the integers (0), and the Poisson summation theorem.pic.twitter.com/lTaGzL4zU4
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This "integral equals sum" thing would be true for any function whose Fourier transform is only nonzero on the integers for n=0.
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This mean that descrite signal or system is equal to analog, very obvious and used in signal processing
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That's weird, especially if I use the Poisson summation formula on the RHS.
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Whoa.
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