Exercise 5. Derivative in frequency Assume that $X(e^{j\omega})$, the DTFT of the sequence $x[n]$, is differentiable with respect to $\omega$. Compute the inverse DTFT of $j\frac{d}{d\omega}X(e^{j\omega})$.

          Exercise 5. Derivative in frequency
Assume that $X(e^{j\omega})$, the DTFT of the sequence $x[n]$, is differentiable with respect to $\omega$.
Compute the inverse DTFT of $j\frac{d}{d\omega}X(e^{j\omega})$.

Exercise 5. Derivative in frequency
Assume that X(e^jω), the DTFT of the sequence x[n], is differentiable with respect to ω.
Compute the inverse DTFT of j(d)/(dω)X(e^jω).

Added by Carla W.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Zhumagali Shomanov

05/10/2022

Step 1

The inverse DTFT of X(ejw) is given by x[n] = (1/2π) ∫[0,2π] X(ejw) e^(jwn) dw. Show more…

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Exercise 5. Derivative in frequency Assume that x(e^(jomega )), the DTFT of the sequence x[n], is differentiable with respect to omega . Compute the inverse DTFT of j(d)/(domega )x(e^(jomega )). Exercise 5. Derivative in frequency Assume that X(ej), the DTFT of the sequence x[n], is differentiable with respect to w. Compute the inverse DTFT of j d X(ej").