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)
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:
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:
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