The Fourier Transforms

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The Fourier transform was named after Joseph Fourier, a French mathematician. A Fourier Transform takes a function to its frequency components.


Properties of a Fourier Transform:

Properties of a Fourier Transform:

Linearity

   


= Shifting the function changes the phase of the spectrum

   

Frequency and amplitude are affected when changing spatial scale inversely

   

Symmetries =

   * if x(t) is real, then
   * if x(t) is imaginary, then 
   * if x(t) is even, then 
   * if x(t) is odd, then