Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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The image presents a signal processing problem involving a continuous-time (CT) linear time-invariant (LTI) system. The problem involves determining which plot correctly represents the output signal \( y(t) \). ### Description: 1. **Input Signal \( x(t) \):** - The input is depicted as an impulse train with impulses located at \(-2T, -T, 0, T, 2T, \ldots\). - Each impulse has an amplitude of \( A \). 2. **System Characteristics:** - The system is described as a CT LTI system with a frequency response \( H(j\omega) \). - The frequency response is a rectangular function centered around zero frequency, spanning from \(-\frac{3\pi}{T}\) to \(\frac{3\pi}{T}\). 3. **Diagram:** - **Block Diagram:** Shows \( x(t) \) as input to the LTI system with the output as \( y(t) \). ### Task: - Determine which plot (a) to (f) represents the output \( y(t) \). ### Plots: - **a)** An impulse train with impulses at \(-T, 0, T, \ldots\) and amplitude \(\frac{A}{T}\). - **b)** A continuous waveform oscillating sinusoidally between \(-\frac{A}{T}\) and \(\frac{A}{T}\), zero at intervals of \(T\). - **c)** An impulse train similar to (a) but starting from \(0\). - **d)** A sinusoidal waveform with higher frequency and amplitude spikes at integer multiples of \(T\). - **e)** Another sinusoidal waveform, oscillating between \(-\frac{A}{T}\) and \(\frac{A}{T}\), showing three cycles over one interval. - **f)** A constant line at amplitude \(\frac{A}{T}\). ### Graphical Explanation: - The frequency response \( H(j\omega) \) indicates that the system acts as a low-pass filter, allowing frequencies contained within the range of \(-\frac{3\pi}{T}\) to \(\frac{3\pi}{T}\). - The choice of the correct output plot \( y(t) \) will depend on the filtering effect on the spectral components of \( x
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Transcribed Image Text:The image presents a signal processing problem involving a continuous-time (CT) linear time-invariant (LTI) system. The problem involves determining which plot correctly represents the output signal \( y(t) \). ### Description: 1. **Input Signal \( x(t) \):** - The input is depicted as an impulse train with impulses located at \(-2T, -T, 0, T, 2T, \ldots\). - Each impulse has an amplitude of \( A \). 2. **System Characteristics:** - The system is described as a CT LTI system with a frequency response \( H(j\omega) \). - The frequency response is a rectangular function centered around zero frequency, spanning from \(-\frac{3\pi}{T}\) to \(\frac{3\pi}{T}\). 3. **Diagram:** - **Block Diagram:** Shows \( x(t) \) as input to the LTI system with the output as \( y(t) \). ### Task: - Determine which plot (a) to (f) represents the output \( y(t) \). ### Plots: - **a)** An impulse train with impulses at \(-T, 0, T, \ldots\) and amplitude \(\frac{A}{T}\). - **b)** A continuous waveform oscillating sinusoidally between \(-\frac{A}{T}\) and \(\frac{A}{T}\), zero at intervals of \(T\). - **c)** An impulse train similar to (a) but starting from \(0\). - **d)** A sinusoidal waveform with higher frequency and amplitude spikes at integer multiples of \(T\). - **e)** Another sinusoidal waveform, oscillating between \(-\frac{A}{T}\) and \(\frac{A}{T}\), showing three cycles over one interval. - **f)** A constant line at amplitude \(\frac{A}{T}\). ### Graphical Explanation: - The frequency response \( H(j\omega) \) indicates that the system acts as a low-pass filter, allowing frequencies contained within the range of \(-\frac{3\pi}{T}\) to \(\frac{3\pi}{T}\). - The choice of the correct output plot \( y(t) \) will depend on the filtering effect on the spectral components of \( x
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