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3.47. Show the following properties for the Laplace transform: (a) If x(1) is even, then X(-s) = X(s); that is, X(s) is also even. (b) If x(t) is odd, then X(-s) = - X(s); that is, X(s) is also odd.

3.47. Show the following properties for the Laplace transform: (a) If x(1) is even, then X(-s) = X(s); that is, X(s) is also even. (b) If x(t) is odd, then X(-s) = - X(s); that is, X(s) is also odd.

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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3.47. Show the following properties for the Laplace transform: (a) If x(1) is even, then X(-s) = X(s); that is, X(s) is also even. (b) If x(t) is odd, then X(-s) = – X(s); that is, X(s) is also odd. (c) If x(t) is odd, then there is a zero in X(s) at s = 0.
Transcribed Image Text:3.47. Show the following properties for the Laplace transform: (a) If x(1) is even, then X(-s) = X(s); that is, X(s) is also even. (b) If x(t) is odd, then X(-s) = – X(s); that is, X(s) is also odd. (c) If x(t) is odd, then there is a zero in X(s) at s = 0.
Ans: 3.47. Нint: (a) Use Eqs. (1.2) and (3.17). (b) Use Eqs. (1.3) and (3.17). (c) Use the result from part (b) and Eq. (1.83a). A signal x(1) or x[n] is referred to as an even signal if x(-1) = x(1) (1.2) x[-n] = x[n] A signal x(1) or x[n] is referred to as an odd signal if x(-1) = -x(t) x[-n] = -x[n] %3| (1.3) m -To No (1.83) eso' x(t) → X(s – so) R' = R+ Re(so) (3.17)
Transcribed Image Text:Ans: 3.47. Нint: (a) Use Eqs. (1.2) and (3.17). (b) Use Eqs. (1.3) and (3.17). (c) Use the result from part (b) and Eq. (1.83a). A signal x(1) or x[n] is referred to as an even signal if x(-1) = x(1) (1.2) x[-n] = x[n] A signal x(1) or x[n] is referred to as an odd signal if x(-1) = -x(t) x[-n] = -x[n] %3| (1.3) m -To No (1.83) eso' x(t) → X(s – so) R' = R+ Re(so) (3.17)
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