Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Q.2 Consider the decaying exponential signal f(t) = Ae¯"u(t);a>0 -at 1 where r=- is caled the time constant of f(t). a a) Show that at time t= Nr x(Nr) =: e x(0) , ie., x(Nr)_ 1 x(1 + Nr) - and x(0) x(t) b) Now consider the sinusoidal signal with decaying exponential envelope: x(1) = {Ae" cos(2,f +9)}u(t) ; a>0. Give the relationship between the time period To of the sinusoidal signal and the time constant t of the exponential signal if x(T,) _ 1 x(107,) x(0) =0.01 . %3D x(0)

Q.2 Consider the decaying exponential signal f(t) = Ae¯"u(t);a>0 -at 1 where r=- is caled the time constant of f(t). a a) Show that at time t= Nr x(Nr) =: e x(0) , ie., x(Nr)_ 1 x(1 + Nr) - and x(0) x(t) b) Now consider the sinusoidal signal with decaying exponential envelope: x(1) = {Ae" cos(2,f +9)}u(t) ; a>0. Give the relationship between the time period To of the sinusoidal signal and the time constant t of the exponential signal if x(T,) _ 1 x(107,) x(0) =0.01 . %3D x(0)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
See similar textbooks
icon
Related questions
icon
Concept explainers
Question
Q.2 Consider the decaying exponential signal f (t) = Ae¯“u(t);a>0 where 7=- is called the time constant of f(t). a a) Show that at time t= NT x(Nt)=- x(0) x(Nr) 1 and eN , ie., x(t + N7) 1 %3D %3D e x(0) x(t) eN b) Now consider the sinusoidal signal with decaying exponential envelope: x(1) = {Ae¯" cos(t +p)}u(t) ; a>0. -at Give the relationship between the time period To of the sinusoidal signal and the time constant t of the exponential signal if 1 x(107,) x(T,) x(0) - = 0.01 . x(0) %3D e"
Transcribed Image Text:Q.2 Consider the decaying exponential signal f (t) = Ae¯“u(t);a>0 where 7=- is called the time constant of f(t). a a) Show that at time t= NT x(Nt)=- x(0) x(Nr) 1 and eN , ie., x(t + N7) 1 %3D %3D e x(0) x(t) eN b) Now consider the sinusoidal signal with decaying exponential envelope: x(1) = {Ae¯" cos(t +p)}u(t) ; a>0. -at Give the relationship between the time period To of the sinusoidal signal and the time constant t of the exponential signal if 1 x(107,) x(T,) x(0) - = 0.01 . x(0) %3D e"
Expert Solution
steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Ellipses
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
SEE MORE TEXTBOOKS