The Fourier Transforms: Difference between revisions

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==== Shifting the function changes the phase of the spectrum ===
==== Shifting the function changes the phase of the spectrum ===


<math>\mathcal{F}[x(t-a)] = X(t)e^{-j2\pi f a}</math>
<math>\mathcal{F}[x(t-a)] = X(t)e^{j2\pi f a}</math>


==== Frequency and amplitude are affected when changing spatial scale inversely ====
==== Frequency and amplitude are affected when changing spatial scale inversely ====

Revision as of 09:56, 12 October 2007

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

   


frac{x(t) - x(-t)}{2}</math>