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Fourier Coefficients Analysis: Real and Odd vs Real and Even Signals, Exercises of Signals and Systems Theory

An in-depth analysis of fourier coefficients for real and odd signals versus real and even signals. Topics covered include the relationship between time domain functions and fourier coefficients, time reversal, and time scaling. The document also includes various plots and equations to illustrate the concepts.

Typology: Exercises

2011/2012

Uploaded on 08/09/2012

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Download Fourier Coefficients Analysis: Real and Odd vs Real and Even Signals and more Exercises Signals and Systems Theory in PDF only on Docsity!

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1

1 T

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Replace t–t

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Time reversal applied to a continuous time signal results in a

time reversal of the corresponding sequence of Fourier Coefficients

Consequence of this property:

If x(t) is even i.e. x(-t)=x(t) – then its FS Coeffs are also even a

=a-k

k

If x(t) is odd i.e. x(-t)=-x(t) – then its FS Coeffs are also odd a

=-a-k

k

k

m

jk

T

t

jk

T

t

jk

T

FS

k

t

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T

FS

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x

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t

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o o

o

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 

 

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) (

)

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Taking complex conjugate of a signal the FS coefficients obtained

are time reversed and complex conjugate

Case: x(t) is real.In this case x(t)=x*(t) Then a

=a*-k

k^ i.e. FS coeffs are Conjugate Symmetric