The Fourier Transform and its applications goals: present the Fourier ...

or, for symmetry, define: �F ���= 1
� 2� ∫ ∞
−∞
f �t � e −i�t dt and back-transform f �t�= 1
�2� ∫ ∞
−∞
The Fourier Transform and its Applications, Jürgen Stutzki, Sommersemester 2007
�F ��� e i�t d � .
All 1 , 2 , and 3
are common notations, used in different fields and contexts; we prefer the first one.
Other notations often used:
● instead of F �s� : �f �s� or � f �s� .
This is useful to note down certain relations, e.g.� f ⋅g= � f ∗�g (FT of convolution, see below)
● F �s� = FT � f � x �� , operator FT generates Fourier-Trafo of function f �x �
3
math_ground_2.odt
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