### Transcription for Educational Website**Required Information**Consider the following signals.\[ x(t) = 18 \text{rect}(4t) \]Determine the numerical value of \( X(f) \) if \( f = 2 \).The numerical value of \( X(f) \) if \( f = 2 \) is \_\_\_\_\_. ---**Explanation**- **\( x(t) = 18 \text{rect}(4t) \)**: This equation describes a rectangular function scaled by 18 with a width inversely proportional to 4. The \(\text{rect}(4t)\) function represents a rectangular pulse centered at zero with a duration scaling factor affected by 4.- **Determine \( X(f) \) at \( f = 2 \)**: This task involves finding the Fourier Transform of the given time-domain signal \( x(t) \) and evaluating it at the frequency \( f = 2 \).The next step involves computing the Fourier Transform of the rectangular function, which is generally known to have a sinc function format, and determining its value at the specified frequency, completing the box with the calculated numerical result.

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x (t) = 18rect (4t) Determine the numerical value of X(f if f= 2. The numerical value of X(f if f= 2 is

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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Concept explainers

Fourier Transform

In mathematics, the Fourier transformation is a mathematical transformation that rotates responsibilities by using region or time into tasks depending on the local or temporal frequency, such as the rendering of a musical track in step with existing volumes and frequencies. The term Fourier amendment refers to each illustration of the frequency range and the mathematical functionality related to the representation of the frequency domain and the function of space or time.

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### Transcription for Educational Website

**Required Information**

Consider the following signals.

\[ x(t) = 18 \text{rect}(4t) \]

Determine the numerical value of \( X(f) \) if \( f = 2 \).

The numerical value of \( X(f) \) if \( f = 2 \) is \_\_\_\_\_.

---

**Explanation**

- **\( x(t) = 18 \text{rect}(4t) \)**: This equation describes a rectangular function scaled by 18 with a width inversely proportional to 4. The \(\text{rect}(4t)\) function represents a rectangular pulse centered at zero with a duration scaling factor affected by 4.
- **Determine \( X(f) \) at \( f = 2 \)**: This task involves finding the Fourier Transform of the given time-domain signal \( x(t) \) and evaluating it at the frequency \( f = 2 \).

The next step involves computing the Fourier Transform of the rectangular function, which is generally known to have a sinc function format, and determining its value at the specified frequency, completing the box with the calculated numerical result.

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