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Porblem-1. Barker Spectrum Derive analytically the spectrum of the Barker code (11 chips) Problem-2 . Convolution a.) Define the spectrum Prove that the inverse Fourier Transform of is b) Use...

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Porblem-1. Barker Spectrum
Derive analytically the spectrum of the Barker code (11 chips)


Problem-2 . Convolution
a.) Define the spectrum
Prove that the inverse Fourier Transform of is
b) Use convolution theorem and problem 1 to prove that
(hint: transform to the frequency domain)
Document Preview: Porblem-1. Barker Spectrum Derive analytically the spectrum of the Barker code (11 chips) Problem-2 . Convolution a.) Define the spectrum Prove that the inverse Fourier Transform of is b) Use convolution theorem and problem 1 to prove that (hint: transform to the frequency domain)
Answered Same Day Dec 23, 2021

Solution

Robert answered on Dec 23 2021
130 Votes
Problem-1: Barker Spectrum
Derive analytically the spectrum of the Barker code (11 chips)
Diagram of Barker code for 11chips
Solution: The barker code given in the diagram above is a repetition of a basic pulse
shape
( )
( )
Therefore the given barker code can be written as
( ) ∑[ ( ( ) )]
From the given barker code, we have
1 -1 1 1 -1 1 1 1 -1 -1 -1
Therefore,
( ) [ ( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( )]
The Fourier transform of ( ) is
( ) ∫ ...
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