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Required information Consider the following statements. A signal x1(0 has a CTFT X1(. If x2(0 = x1(t + 4), IX1(5l and IX2(0l are different. True or False True False

Required information Consider the following statements. A signal x1(0 has a CTFT X1(. If x2(0 = x1(t + 4), IX1(5l and IX2(0l are different. True or False True False

Introductory Circuit Analysis (13th Edition)
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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### Required Information **Consider the following statements.** A signal \( x_1(t) \) has a Continuous-Time Fourier Transform (CTFT) \( X_1(f) \). If \( x_2(t) = x_1(t + 4) \), \( |X_1(f)| \) and \( |X_2(f)| \) are different. **True or False** - [True] [False] --- #### Explanation of Content This section presents a theoretical statement about signal processing, specifically related to the properties of the Continuous-Time Fourier Transform (CTFT). **Statement Analysis:** - **Signals**: - \( x_1(t) \): Original signal with its CTFT represented by \( X_1(f) \). - \( x_2(t) = x_1(t + 4) \): Time-shifted version of the original signal. - **Key Concept**: - Time-shifting a signal in the time domain corresponds to a phase shift in the frequency domain but does not alter the magnitude of its Fourier Transform. - **Conclusion**: - The magnitude spectra, \( |X_1(f)| \) and \( |X_2(f)| \), of the original and time-shifted signals are **not different** despite the phase change. #### Interactive Component: Users are asked to determine the truth value of the statement by selecting either "True" or "False." - **Correct Answer**: False, based on the principle that time shifts result in phase changes, not magnitude changes, in the Fourier Transform.
Transcribed Image Text:### Required Information **Consider the following statements.** A signal \( x_1(t) \) has a Continuous-Time Fourier Transform (CTFT) \( X_1(f) \). If \( x_2(t) = x_1(t + 4) \), \( |X_1(f)| \) and \( |X_2(f)| \) are different. **True or False** - [True] [False] --- #### Explanation of Content This section presents a theoretical statement about signal processing, specifically related to the properties of the Continuous-Time Fourier Transform (CTFT). **Statement Analysis:** - **Signals**: - \( x_1(t) \): Original signal with its CTFT represented by \( X_1(f) \). - \( x_2(t) = x_1(t + 4) \): Time-shifted version of the original signal. - **Key Concept**: - Time-shifting a signal in the time domain corresponds to a phase shift in the frequency domain but does not alter the magnitude of its Fourier Transform. - **Conclusion**: - The magnitude spectra, \( |X_1(f)| \) and \( |X_2(f)| \), of the original and time-shifted signals are **not different** despite the phase change. #### Interactive Component: Users are asked to determine the truth value of the statement by selecting either "True" or "False." - **Correct Answer**: False, based on the principle that time shifts result in phase changes, not magnitude changes, in the Fourier Transform.
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