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• s(t) = Asine²(), • v(t) = Bsinc³(), • w(t) = C'sinc(÷) 2T 4T cos(Tat/T) 1–4a²t² /T²

• s(t) = Asine²(), • v(t) = Bsinc³(), • w(t) = C'sinc(÷) 2T 4T cos(Tat/T) 1–4a²t² /T²

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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Given the following signals: • s(t) = Asinc (T), • v(t) = Bsinc (), • w(t) = C'sinc(÷) cos(Tat/T) 1-4a?t² /T² • x(t) = s(t) cos (), • y(t) = s(t) * s(t) where * denotes convolution, • z(t) = s(t) * [8(t – 5T) + 8(t – 10T)] where * denotes convolution, and • r(t) = s(t) – v(t – 100T). where A, B, C, T, and a are positive real-valued constants, 0 < a < 1, and * denotes convolution. Suppose we sample each signal. For each signal, calculate the lowest sampling rate, fs.min, that will allow us to reconstruct the signal from its samples: (a) s(t), (b) v(t), (c) w(t) [Hint: Compare with equation (6.19) on page 238 in Haykin&Moher (our textbook).] (d) x(t), (e) y(t), (f) z(t), and (g) r(t).
Transcribed Image Text:Given the following signals: • s(t) = Asinc (T), • v(t) = Bsinc (), • w(t) = C'sinc(÷) cos(Tat/T) 1-4a?t² /T² • x(t) = s(t) cos (), • y(t) = s(t) * s(t) where * denotes convolution, • z(t) = s(t) * [8(t – 5T) + 8(t – 10T)] where * denotes convolution, and • r(t) = s(t) – v(t – 100T). where A, B, C, T, and a are positive real-valued constants, 0 < a < 1, and * denotes convolution. Suppose we sample each signal. For each signal, calculate the lowest sampling rate, fs.min, that will allow us to reconstruct the signal from its samples: (a) s(t), (b) v(t), (c) w(t) [Hint: Compare with equation (6.19) on page 238 in Haykin&Moher (our textbook).] (d) x(t), (e) y(t), (f) z(t), and (g) r(t).
The modified pulse shape p(t)-that is, the inverse Fourier transform of the raised- cosine pulse spectrum P(f)-is defined by cos(2παBot) p(t) = VE sinc(2B0†) (6.19) 1 – 16a²Bột², The time function of Eq. (6.19) consists of the product of two factors: the factor VE sinc(2Bot) that defines the Nyquist channel, and a second factor that decreases as 1/t|² for large |t|. The first factor ensures zero crossings of p(t) at the desired sampling instants of time t = iT, with i an integer (positive and negative). The second factor reduces the tails of the pulse considerably below the Nyquist channel, so that the transmission of
Transcribed Image Text:The modified pulse shape p(t)-that is, the inverse Fourier transform of the raised- cosine pulse spectrum P(f)-is defined by cos(2παBot) p(t) = VE sinc(2B0†) (6.19) 1 – 16a²Bột², The time function of Eq. (6.19) consists of the product of two factors: the factor VE sinc(2Bot) that defines the Nyquist channel, and a second factor that decreases as 1/t|² for large |t|. The first factor ensures zero crossings of p(t) at the desired sampling instants of time t = iT, with i an integer (positive and negative). The second factor reduces the tails of the pulse considerably below the Nyquist channel, so that the transmission of
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