Chemistry

Properties of the Fourier transform

Properties of the Fourier transform


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Symmetry example 4 of the FT: Purely imaginary even function

F.4(x)=F.4(-x)=i2cos3x=iF.1(x)C.4(k)=iC.1(k)=0+ireC.1(k)

Multiplication by i shifts the real part in example 1 into the imaginary part of the spectrum without reversing the sign. It applies

in theC.4(-3)=in theC.4(3)andreC.4(k)=0

This finding applies to everyone k and because of the linearity for any linear combination of icoskxFunctions.

theorem
For any purely imaginary even function, the spectrum is purely imaginary and straight (symmetrical).


Video: Communication systems 37: Properties of Fourier transforms خصائص تحويل فوريير (May 2022).