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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

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)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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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.
Transcribed Image Text:### 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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