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