The Fourier Transforms: Difference between revisions
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| Line 7: | Line 7: | ||
==== Linearity ==== | ==== Linearity ==== | ||
<math>\mathcal{F}[a*x(t) + b*y(t)] = a*X(f) + b*Y(f)</math> | <math>\mathcal{F}[a*x(t) + b*y(t)] = a*X(f) + b*Y(f)</math> | ||
==== Shifting the function changes the phase of the spectrum ==== | |||
<math>\mathcal{F}[x(a*t)] = \frac{1}{a}X(\frac{f}{a})</math> | |||
frac{x(t) - x(-t)}{2}</math> | |||
Revision as of 10:46, 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
frac{x(t) - x(-t)}{2}</math>