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must be sam 7.26. The sampling theorem, as we have derived it, pled at a rate greater than its bandwidth (or equivalently, a rate greater than twice its highest frequency). This implies that if x(1) has a spectrum as indicated in Figure P7.26(a) then x(1) must be sampled at a rate greater than 2002. However, since the signal has most of its energy concentrated in a narrow band, it would seem reason- able to expect that a sampling rate lower than twice the highest frequency could be as a bandpass signal. There are a variety of techniques for sampling such signals, used. A signal whose energy is concentrated in a frequency band is often referred to generally referred to as bandpass-sampling techniques. x(t) ... X(jw) лід -W₂ -w₁ W₁ W₂ (a) wo ** p(t) = 8(t-nT) -W₂ Xp (t) H(jw) H(jw) p(t) iu (b) W ... wp w x, (t) Figure P7.26

must be sam 7.26. The sampling theorem, as we have derived it, pled at a rate greater than its bandwidth (or equivalently, a rate greater than twice its highest frequency). This implies that if x(1) has a spectrum as indicated in Figure P7.26(a) then x(1) must be sampled at a rate greater than 2002. However, since the signal has most of its energy concentrated in a narrow band, it would seem reason- able to expect that a sampling rate lower than twice the highest frequency could be as a bandpass signal. There are a variety of techniques for sampling such signals, used. A signal whose energy is concentrated in a frequency band is often referred to generally referred to as bandpass-sampling techniques. x(t) ... X(jw) лід -W₂ -w₁ W₁ W₂ (a) wo ** p(t) = 8(t-nT) -W₂ Xp (t) H(jw) H(jw) p(t) iu (b) W ... wp w x, (t) Figure P7.26

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
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7.26. The sampling theorem, as we have derived it, states that a signal x(1) must be sam- pled at a rate greater than its bandwidth (or equivalently, a rate greater than twice its highest frequency). This implies that if x(1) has a spectrum as indicated in Figure P7.26(a) then x(1) must be sampled at a rate greater than 2002. However, since the signal has most of its energy concentrated in a narrow band, it would seem reason- able to expect that a sampling rate lower than twice the highest frequency could be used. A signal whose energy is concentrated in a frequency band is often referred to as a bandpass signal. There are a variety of techniques for sampling such signals, generally referred to as bandpass-sampling techniques. x(t) X(jw) MA @₁ W₂ (a) -W₂ -W₁ p(t) = Σ 8(t-nT) Io. Xp (t) H(jw) 1 -Wo n Wa p(t) H(jw) A+ (b) 3° W wp w x, (t) Figure P7.26
Transcribed Image Text:7.26. The sampling theorem, as we have derived it, states that a signal x(1) must be sam- pled at a rate greater than its bandwidth (or equivalently, a rate greater than twice its highest frequency). This implies that if x(1) has a spectrum as indicated in Figure P7.26(a) then x(1) must be sampled at a rate greater than 2002. However, since the signal has most of its energy concentrated in a narrow band, it would seem reason- able to expect that a sampling rate lower than twice the highest frequency could be used. A signal whose energy is concentrated in a frequency band is often referred to as a bandpass signal. There are a variety of techniques for sampling such signals, generally referred to as bandpass-sampling techniques. x(t) X(jw) MA @₁ W₂ (a) -W₂ -W₁ p(t) = Σ 8(t-nT) Io. Xp (t) H(jw) 1 -Wo n Wa p(t) H(jw) A+ (b) 3° W wp w x, (t) Figure P7.26
To examine the possibility of sampling a bandpass signal as a rate less than the total bandwidth, consider the system shown in Figure P7.26(b). Assuming that w₁w₂w₁, find the maximum value of T' and the values of the constants A, wa and , such that x,(t) = x(1).
Transcribed Image Text:To examine the possibility of sampling a bandpass signal as a rate less than the total bandwidth, consider the system shown in Figure P7.26(b). Assuming that w₁w₂w₁, find the maximum value of T' and the values of the constants A, wa and , such that x,(t) = x(1).
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