### Frequency-Domain Function AnalysisConsider the real, frequency-domain function illustrated in the given figure:---#### Diagram Explanation- **Graph Description:** - The horizontal axis represents frequency \( f \). - The vertical axis represents the magnitude of the function \( |X(f)| \). - The function is non-zero and constant over three frequency bands, forming a symmetrical shape resembling two continuous rectangles centered at the origin and extending both positively and negatively along the frequency axis. - The frequency bands are centered at \( f_1 = 95 \) kHz and \( f_2 = 105 \) kHz, with corresponding negative frequencies \( -f_1 \) and \( -f_2 \).---#### Inverse Continuous-Time Fourier TransformGiven:- \( A = 3 \)- \( f_1 = 95 \) kHz- \( f_2 = 105 \) kHzThe inverse Continuous-Time Fourier Transform (CTFT) of the given function is:\[x(t) = X \text{sinc}(Yt) \cos(Z \times 10^5 \pi t)\]#### Numerical Values of Constants- \( X = 50000 \) - \( Y = 10000 \)- \( Z = 2 \)---This description provides a detailed understanding of the frequency-domain function and how to derive its time-domain representation using inverse CTFT.

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Consider the real, frequency-domain function illustrated in the given figure. -f If A = 3, 4 = 95 kHz, and 2 = 105 kHz, the Inverse CTFT of the given function is z (t) Xsinc (Yt) cos (Z x 10°nt) The numerical values of the constants are X=| 50000 10000. and Z=

Consider the real, frequency-domain function illustrated in the given figure. -f If A = 3, 4 = 95 kHz, and 2 = 105 kHz, the Inverse CTFT of the given function is z (t) Xsinc (Yt) cos (Z x 10°nt) The numerical values of the constants are X=| 50000 10000. and Z=

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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Question

### Frequency-Domain Function Analysis

Consider the real, frequency-domain function illustrated in the given figure:

---

#### Diagram Explanation

- **Graph Description:**
- The horizontal axis represents frequency \( f \).
- The vertical axis represents the magnitude of the function \( |X(f)| \).
- The function is non-zero and constant over three frequency bands, forming a symmetrical shape resembling two continuous rectangles centered at the origin and extending both positively and negatively along the frequency axis.
- The frequency bands are centered at \( f_1 = 95 \) kHz and \( f_2 = 105 \) kHz, with corresponding negative frequencies \( -f_1 \) and \( -f_2 \).

---

#### Inverse Continuous-Time Fourier Transform

Given:
- \( A = 3 \)
- \( f_1 = 95 \) kHz
- \( f_2 = 105 \) kHz

The inverse Continuous-Time Fourier Transform (CTFT) of the given function is:

\[
x(t) = X \text{sinc}(Yt) \cos(Z \times 10^5 \pi t)
\]

#### Numerical Values of Constants
- \( X = 50000 \)
- \( Y = 10000 \)
- \( Z = 2 \)

---

This description provides a detailed understanding of the frequency-domain function and how to derive its time-domain representation using inverse CTFT.

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