Consider the decaying exponential u(t) = 2e-³t [0,∞) (t). (a) Find and sketch y₁(t) = (u* u) (t). (b) For v(t) = u(-t), find and sketch y₂(t) = (u * v)(t). (c) How would your answers in (a) and (b) change if you replace u(t) by a delayed and scaled version, u(t) = 2u(t — 1).
Consider the decaying exponential u(t) = 2e-³t [0,∞) (t). (a) Find and sketch y₁(t) = (u* u) (t). (b) For v(t) = u(-t), find and sketch y₂(t) = (u * v)(t). (c) How would your answers in (a) and (b) change if you replace u(t) by a delayed and scaled version, u(t) = 2u(t — 1).
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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Transcribed Image Text:Consider the decaying exponential u(t)
3t
= 2e-³t
= 2e-³t [[0,∞) (t).
(a) Find and sketch y₁ (t) = (u ⋆ u)(t).
(b) For v(t) = u(-t), find and sketch y2(t) = (u* v) (t).
(c) How would your answers in (a) and (b) change if you replace u(t) by a delayed and scaled
version, u(t) = 2u(t — 1).
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