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- Calculation of Fourier Transform Derivative d/dw (F{x(t)})=d/dw(X(w))

**Calculation of Fourier Transform Derivative d/dw (F{x(t)})=d/dw(X(w))**

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

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:

is it possible to express the derivative, d/dw (F{x(t)}), in frequency domain using terms of X(w) ???

Many Thanks,

Desperate Engineer.