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Consider the sampling system shown below: f(t) sampler impulse train 7(t) Here, the sampler converts the continuous-time signal f(t) into a continuous-time impulse train 7(1) carrying the sample values of f(t) every T = seconds. Suppose the input f(t) has the following spectrum (with the units of being radians/second): F(w)

Consider the sampling system shown below: f(t) sampler impulse train 7(t) Here, the sampler converts the continuous-time signal f(t) into a continuous-time impulse train 7(1) carrying the sample values of f(t) every T = seconds. Suppose the input f(t) has the following spectrum (with the units of being radians/second): F(w)

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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Consider the sampling system shown below: Diagram: A block labeled "sampler" with arrows indicating input \( f(t) \) and output impulse train \(\tilde{f}(t)\). Here, the sampler converts the continuous-time signal \( f(t) \) into a continuous-time impulse train \(\tilde{f}(t)\) carrying the sample values of \( f(t) \) every \( T = \frac{1}{20} \) seconds. Suppose the input \( f(t) \) has the following spectrum (with the units of \(\omega\) being radians/second): Graph for \( F(\omega) \): - A series of rectangular pulses centered around \( \omega = 0 \), extending from \(-10\pi\) to \(10\pi\), and repeating every \(20\pi\). The height of each pulse is 1. **This is a multiple-choice question: Which of the four plots below correctly shows the spectrum \(\bar{F}(\omega)\) of the impulse train \(\tilde{f}(t)\)?** (a) Spectrum \(\bar{F}(\omega)\): - A single rectangular pulse centered at \( \omega = 0 \), extending from \(-10\pi\) to \(10\pi\). (b) Spectrum \(\bar{F}(\omega)\): - Repeating rectangular pulses with a height of 20, extending from \(-80\pi\) to \(80\pi\), with gaps between the pulses. (c) Spectrum \(\bar{F}(\omega)\): - Repeating rectangular pulses with a height of 20, extending from \(-80\pi\) to \(80\pi\), with no gaps between the pulses. (d) Spectrum \(\bar{F}(\omega)\): - A single rectangular pulse centered at \( \omega = 0 \), extending from \(-10\pi\) to \(10\pi\). **Explanation:** The graphs illustrate potential frequency spectra for the impulse train \(\tilde{f}(t)\) obtained from the original signal \( f(t) \) by sampling at a rate of \( T = \frac{1}{20} \) seconds. Each plot shows a spectrum \(\bar{F}(\omega)\) with varying patterns of repeated pulses and different scaling. The correct choice should reflect the theoretical outcome of the
Transcribed Image Text:Consider the sampling system shown below: Diagram: A block labeled "sampler" with arrows indicating input \( f(t) \) and output impulse train \(\tilde{f}(t)\). Here, the sampler converts the continuous-time signal \( f(t) \) into a continuous-time impulse train \(\tilde{f}(t)\) carrying the sample values of \( f(t) \) every \( T = \frac{1}{20} \) seconds. Suppose the input \( f(t) \) has the following spectrum (with the units of \(\omega\) being radians/second): Graph for \( F(\omega) \): - A series of rectangular pulses centered around \( \omega = 0 \), extending from \(-10\pi\) to \(10\pi\), and repeating every \(20\pi\). The height of each pulse is 1. **This is a multiple-choice question: Which of the four plots below correctly shows the spectrum \(\bar{F}(\omega)\) of the impulse train \(\tilde{f}(t)\)?** (a) Spectrum \(\bar{F}(\omega)\): - A single rectangular pulse centered at \( \omega = 0 \), extending from \(-10\pi\) to \(10\pi\). (b) Spectrum \(\bar{F}(\omega)\): - Repeating rectangular pulses with a height of 20, extending from \(-80\pi\) to \(80\pi\), with gaps between the pulses. (c) Spectrum \(\bar{F}(\omega)\): - Repeating rectangular pulses with a height of 20, extending from \(-80\pi\) to \(80\pi\), with no gaps between the pulses. (d) Spectrum \(\bar{F}(\omega)\): - A single rectangular pulse centered at \( \omega = 0 \), extending from \(-10\pi\) to \(10\pi\). **Explanation:** The graphs illustrate potential frequency spectra for the impulse train \(\tilde{f}(t)\) obtained from the original signal \( f(t) \) by sampling at a rate of \( T = \frac{1}{20} \) seconds. Each plot shows a spectrum \(\bar{F}(\omega)\) with varying patterns of repeated pulses and different scaling. The correct choice should reflect the theoretical outcome of the
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