# Inverse discrete time Fourier transform with differentiation

Consider a signal x[n] and its DTFT $$X(e^{jω})$$ . Assume $$X(e^{jω})$$ is differentiable. Compute the inverse DTFT of

$$j\frac{dX(e^{jω})}{d\omega}$$

You should write your answer in terms of $$x[n]$$ and elementary functions and constants, for example $$π/2x[n]$$ would be written :

$$\pi / 2x[n]$$

• What have you tried? – auspicious99 Jul 26 '20 at 10:25

$$X(e^{j\omega})= \sum\limits_{n=- \infty }^{\infty}x[n]e^{-jn\omega} \Rightarrow \frac{d}{d\omega}X(e^{j\omega})= \frac{d}{d\omega}\sum\limits_{n=- \infty }^{\infty}x[n]e^{-jn\omega}$$