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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 :

$\pi / 2x[n]$

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  • $\begingroup$ What have you tried? $\endgroup$ Jul 26, 2020 at 10:25

1 Answer 1

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Hint:

differentiate from Fourier Transform equation:

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

and then find what you want.

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