Show that the derivative of a 1-D signal, I=I(x), amplifies the higher frequency components of the signal. Then, prove that even a slight amount of noise n=n(x), can be responsible for a large difference between the derivative I and I+n (Hint: Assume that n can be written as εsin(ωx) for some very small ε and very large ω).
Show that the derivative of a 1-D signal, I=I(x), amplifies the higher frequency components of the signal. Then, prove that even a slight amount of noise n=n(x), can be responsible for a large difference between the derivative I and I+n (Hint: Assume that n can be written as εsin(ωx) for some very small ε and very large ω).
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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Show that the derivative of a 1-D signal, I=I(x), amplifies the higher frequency components of the signal. Then, prove that even a slight amount of noise n=n(x), can be responsible for a large difference between the derivative I and I+n (Hint: Assume that n can be written as εsin(ωx) for some very small ε and very large ω).
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