Difference between revisions of "Frequency Domain Problem"
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This is closely connected with the [[Fourier Transform in Time]]. Essentially after this | This is closely connected with the [[Fourier Transform in Time]]. Essentially after this | ||
| − | we are left with a problem in which all time dependence is proportional to <math>\exp (i\omega t)</math> | + | we are left with a problem in which all time dependence is proportional to |
| + | <center><math>\exp (i\omega t)</math></center> | ||
and the resultant problem (for complex valued potential, displacement, etc.) | and the resultant problem (for complex valued potential, displacement, etc.) | ||
is said to be in the frequency domain (as opposed to the time domain). | is said to be in the frequency domain (as opposed to the time domain). | ||
In many practical applications this is the only solution required, i.e. engineers simply want | In many practical applications this is the only solution required, i.e. engineers simply want | ||
a table of force as a function of frequency. Often the dependence is taken as | a table of force as a function of frequency. Often the dependence is taken as | ||
| − | <math>\exp (-i\omega t)</math> | + | <center><math>\exp (-i\omega t)</math></center> |
[[Category:Linear Water-Wave Theory]] | [[Category:Linear Water-Wave Theory]] | ||
Revision as of 23:45, 10 September 2008
This is closely connected with the Fourier Transform in Time. Essentially after this we are left with a problem in which all time dependence is proportional to
and the resultant problem (for complex valued potential, displacement, etc.) is said to be in the frequency domain (as opposed to the time domain). In many practical applications this is the only solution required, i.e. engineers simply want a table of force as a function of frequency. Often the dependence is taken as
