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dervast
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Homework Statement
I am reading the book Wiley Signal And Systems-Simon Haykin and at the page 34 i read the followings
Consider the complex exponential e^j*theta. Using Euler's identity we may expand this term as e^j*theta=cos(theta)+jsin(theta)
This result indicates that we may express the continuous time sinusoidal signal x(t)=Acos(wt+f) as the real part of the complex exponential signal Be^jwt (w is the angle like theta) where B itself a complex quantity defined by B=Ae^i*f (f another angle)
that is we may write
Acos(wt+f)=Re{Be^jwt}
I ask this cause i need firstly to understand this part befroe i can understand what
a)is an exponentially damped sinusoidal signal
and b)why these signals can't be ever periodics
Homework Equations
The Attempt at a Solution
I am trying to understand why the author assumes that x(t)=Acos(wt+f) is the real part of Be^jwt and why the B is in exponential form again B=Ae^i*f
I am asking cause i am have to understand this first so i can later on i can understand what an exponentially damped sinusoidal signal is
and why such signals can't ever be periodics
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