Question

(1) $Re\{X(j\omega)\} = 0$ (2) $Im\{X(j\omega)\} = 0$ (3) There exists a real $\alpha$ such that $e^{j\alpha\omega}X(j\omega)$ is real (4) $\int_{-\infty}^{\infty} X(j\omega) d\omega = 0$ (5) $\int_{-\infty}^{\infty} \omega X(j\omega) d\omega = 0$ (6) $X(j\omega)$ is periodic

Name: 1 rexjomega 0 2 imxjomega 0 3 there exists a real alpha such that ejalphaomegaxjomega is real 4 int inftyinfty xjomega domega 0 5 int inftyinfty omega xjomega domega 0 6 xjomega is periodi 98464
Uploaded: 2024-05-23T12:14:23-08:00
Duration: 1 min 26 s
Channel: Adi S
Description: 1 rexjomega 0 2 imxjomega 0 3 there exists a real alpha such that ejalphaomegaxjomega is real 4 int inftyinfty xjomega domega 0 5 int inftyinfty omega xjomega domega 0 6 xjomega is periodi 98464

          (1) $Re\{X(j\omega)\} = 0$
(2) $Im\{X(j\omega)\} = 0$
(3) There exists a real $\alpha$ such that $e^{j\alpha\omega}X(j\omega)$ is real
(4) $\int_{-\infty}^{\infty} X(j\omega) d\omega = 0$
(5) $\int_{-\infty}^{\infty} \omega X(j\omega) d\omega = 0$
(6) $X(j\omega)$ is periodic

1 rexjomega 0 2 imxjomega 0 3 there exists a real alpha such that ejalphaomegaxjomega is real 4 int inftyinfty xjomega domega 0 5 int inftyinfty omega xjomega domega 0 6 xjomega is periodi 98464

Added by Nancy H.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Adi S

05/23/2024

Step 1

The Fourier Transform of an odd function is purely imaginary. Therefore, $Re\{X(j\omega)\} = 0$ is true. Show more…

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(1) $Re\{X(j\omega)\} = 0$ (2) $Im\{X(j\omega)\} = 0$ (3) There exists a real $\alpha$ such that $e^{j\alpha\omega}X(j\omega)$ is real (4) $\int_{-\infty}^{\infty} X(j\omega) d\omega = 0$ (5) $\int_{-\infty}^{\infty} \omega X(j\omega) d\omega = 0$ (6) $X(j\omega)$ is periodic