is an option to Fourier and related functions that specifies the conventions to use in computing Fourier transforms.
FourierParameters
is an option to Fourier and related functions that specifies the conventions to use in computing Fourier transforms.
Details
- A typical setting is FourierParameters->{a,b}.
- Some common choices for {a,b} are {0,1} (default), {-1,1} (data analysis), {1,-1} (signal processing).
Examples
open all close allBasic Examples (2)
Use a nondefault definition of the discrete Fourier transform:
Use the same definition to get the inverse:
A nondefault definition used for the continuous Fourier transform:
Scope (3)
A typical pure mathematics or systems-engineering definition of Fourier transform:
Use the same definition for the inverse transform:
A typical data-analysis definition of discrete Fourier transform:
Use the same definition to get the correct inverse:
A common signal-processing definition of Fourier transform:
Discrete Fourier transform:
Discrete-time Fourier transform:
Possible Issues (2)
The same FourierParameters values need to be used for both forward and inverse transforms:
Here the inverse uses a different choice of FourierParameters :
The second parameter needs to be relatively prime to the data length to guarantee invertibility:
See Also
Related Guides
History
Introduced in 1999 (4.0)
Text
Wolfram Research (1999), FourierParameters, Wolfram Language function, https://reference.wolfram.com/language/ref/FourierParameters.html.
CMS
Wolfram Language. 1999. "FourierParameters." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/FourierParameters.html.
APA
Wolfram Language. (1999). FourierParameters. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FourierParameters.html
BibTeX
@misc{reference.wolfram_2025_fourierparameters, author="Wolfram Research", title="{FourierParameters}", year="1999", howpublished="\url{https://reference.wolfram.com/language/ref/FourierParameters.html}", note=[Accessed: 05-December-2025]}
BibLaTeX
@online{reference.wolfram_2025_fourierparameters, organization={Wolfram Research}, title={FourierParameters}, year={1999}, url={https://reference.wolfram.com/language/ref/FourierParameters.html}, note=[Accessed: 05-December-2025]}