FourierParameters
✖
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 allclose allBasic Examples (2)Summary of the most common use cases
Use a nondefault definition of the discrete Fourier transform:

https://wolfram.com/xid/0b0kl78yxlv-bx8i6q

Use the same definition to get the inverse:

https://wolfram.com/xid/0b0kl78yxlv-blntkx

A nondefault definition used for the continuous Fourier transform:

https://wolfram.com/xid/0b0kl78yxlv-er3uq3


https://wolfram.com/xid/0b0kl78yxlv-nffxwk

Scope (3)Survey of the scope of standard use cases
A typical pure mathematics or systems-engineering definition of Fourier transform:

https://wolfram.com/xid/0b0kl78yxlv-d56p7l

Use the same definition for the inverse transform:

https://wolfram.com/xid/0b0kl78yxlv-cc82ej

A typical data-analysis definition of discrete Fourier transform:

https://wolfram.com/xid/0b0kl78yxlv-ceciga

Use the same definition to get the correct inverse:

https://wolfram.com/xid/0b0kl78yxlv-ltygg7

A common signal-processing definition of Fourier transform:

https://wolfram.com/xid/0b0kl78yxlv-mdpqu8


https://wolfram.com/xid/0b0kl78yxlv-ci12q2

Discrete-time Fourier transform:

https://wolfram.com/xid/0b0kl78yxlv-y6msu

Possible Issues (2)Common pitfalls and unexpected behavior
The same FourierParameters values need to be used for both forward and inverse transforms:

https://wolfram.com/xid/0b0kl78yxlv-i7jjak

Here the inverse uses a different choice of FourierParameters:

https://wolfram.com/xid/0b0kl78yxlv-dsnfhj

The second parameter needs to be relatively prime to the data length to guarantee invertibility:

https://wolfram.com/xid/0b0kl78yxlv-bmtnm4


https://wolfram.com/xid/0b0kl78yxlv-i9xzsm


Wolfram Research (1999), FourierParameters, Wolfram Language function, https://reference.wolfram.com/language/ref/FourierParameters.html.
Text
Wolfram Research (1999), FourierParameters, Wolfram Language function, https://reference.wolfram.com/language/ref/FourierParameters.html.
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.
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
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: 06-June-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: 06-June-2025
]}