Difference between revisions of "Fourier Transform"
(Created page with "Category:Analytica User Guide <breadcrumbs>Analytica User Guide > More Array Functions > {{PAGENAME}}</breadcrumbs> __TOC__ ==See Also== <footer>Interpolation functions...") |
|||
| Line 4: | Line 4: | ||
__TOC__ | __TOC__ | ||
| + | The Fourier and inverse Fourier transforms convert a time-series into a power spectrum and viseversa. These are well-known transformations that are employed for many applications including | ||
| + | finding and characterizing periodicities in time-series analysis and regression; fast convolution | ||
| + | and de-convolution; transfer function modeling in systems analysis; solving systems of differential | ||
| + | equations; Bayesian analysis using characteristic functions; and signal filtering. | ||
| + | |||
| + | The discrete Fourier transform involves a time domain (corresponding to an index) and a frequency | ||
| + | domain (corresponding to a frequency index). The time points are equally spaced at internals | ||
| + | of Δt, and the frequency points are equally spaced at ΔF . Both index have <code>n</code>points. The intervals spacings are related as | ||
| + | |||
| + | <center> | ||
| + | <math>\Delta t =\frac{1}{n \Delta t}</math> | ||
| + | </center> | ||
==See Also== | ==See Also== | ||
<footer>Interpolation functions / {{PAGENAME}} / Sets - collections of unique elements</footer> | <footer>Interpolation functions / {{PAGENAME}} / Sets - collections of unique elements</footer> | ||
Revision as of 23:43, 13 December 2015
The Fourier and inverse Fourier transforms convert a time-series into a power spectrum and viseversa. These are well-known transformations that are employed for many applications including finding and characterizing periodicities in time-series analysis and regression; fast convolution and de-convolution; transfer function modeling in systems analysis; solving systems of differential equations; Bayesian analysis using characteristic functions; and signal filtering.
The discrete Fourier transform involves a time domain (corresponding to an index) and a frequency
domain (corresponding to a frequency index). The time points are equally spaced at internals
of Δt, and the frequency points are equally spaced at ΔF . Both index have npoints. The intervals spacings are related as
[math]\displaystyle{ \Delta t =\frac{1}{n \Delta t} }[/math]
Enable comment auto-refresher