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Mathematics
Calculus
Calculation of Fourier Transform Derivative d/dw (F{x(t)})=d/dw(X(w))
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[QUOTE="Alexei_Nomazov, post: 6218685, member: 625103"] [B]TL;DR Summary:[/B] Calculation of Fourier Transform Derivative d/dw (F{x(t)})=d/dw(X(w)) [B]Calculation of Fourier Transform Derivative d/dw (F{x(t)})=d/dw(X(w))[/B] Hello to my Math Fellows, Problem: I am looking for a way to calculate w-derivative of Fourier transform,d/dw (F{x(t)}), in terms of regular Fourier transform,X(w)=F{x(t)}. Definition Based Solution (not good enough): from [IMG]https://wikimedia.org/api/rest_v1/media/math/render/svg/25905b02d53ae042b113c038d50ac131fcf020d0[/IMG] I can find that w-derivative of Fourier transform for x(t) is Fourier transform of t*x(t) multiplied by -j: d/dw (F{x(t)})=d/dw(X(w))=-j*F{t*x(t)}Question: But, taking into account the differentiation and duality properties of Fourier transform: [ATTACH=full]247991[/ATTACH] is it possible to express the derivative, d/dw (F{x(t)}), in frequency domain using terms of X(w) ? Many Thanks, Desperate Engineer. [/QUOTE]
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Forums
Mathematics
Calculus
Calculation of Fourier Transform Derivative d/dw (F{x(t)})=d/dw(X(w))
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