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Required information Consider the following signals. x (t) 10sin (200rt) Graph the magnitude and the phase of the CTFT of the given signal.

Required information Consider the following signals. x (t) 10sin (200rt) Graph the magnitude and the phase of the CTFT of the given signal.

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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## Required Information Consider the following signals. \[ x(t) = 10 \sin(200 \pi t) \] Graph the magnitude and the phase of the CTFT of the given signal. ### Explanation: This section invites you to analyze a sinusoidal signal defined by the function \( x(t) = 10 \sin(200 \pi t) \). The task involves plotting the magnitude and phase of the Continuous-Time Fourier Transform (CTFT) for this signal. - **Magnitude Graph**: The magnitude of the CTFT for a sinusoidal function like this one typically results in two delta functions centered around the positive and negative frequencies of the waveform (100 Hz in this case, since the angular frequency is \( 200\pi \) rad/s). - **Phase Graph**: The phase of the CTFT will typically indicate the shift in the signal. For a simple sine wave, the phase is often a step function centered at the frequencies mentioned. ### Goals: - Understand and perform a Fourier transform of a basic sinusoidal signal. - Interpret the magnitude and phase plots to gain insights into the signal's frequency components.
Transcribed Image Text:## Required Information Consider the following signals. \[ x(t) = 10 \sin(200 \pi t) \] Graph the magnitude and the phase of the CTFT of the given signal. ### Explanation: This section invites you to analyze a sinusoidal signal defined by the function \( x(t) = 10 \sin(200 \pi t) \). The task involves plotting the magnitude and phase of the Continuous-Time Fourier Transform (CTFT) for this signal. - **Magnitude Graph**: The magnitude of the CTFT for a sinusoidal function like this one typically results in two delta functions centered around the positive and negative frequencies of the waveform (100 Hz in this case, since the angular frequency is \( 200\pi \) rad/s). - **Phase Graph**: The phase of the CTFT will typically indicate the shift in the signal. For a simple sine wave, the phase is often a step function centered at the frequencies mentioned. ### Goals: - Understand and perform a Fourier transform of a basic sinusoidal signal. - Interpret the magnitude and phase plots to gain insights into the signal's frequency components.
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