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FourierParameters

FourierParameters
is an option to Fourier and related functions that specifies the conventions to use in computing Fourier transforms.
  • Some common choices for are (default), (data analysis), (signal processing).
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:
Use a nondefault definition of the discrete Fourier transform:
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Out[1]=
Use the same definition to get the inverse:
In[2]:=
Click for copyable input
Out[2]=
 
A nondefault definition used for the continuous Fourier transform:
In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=
A typical pure mathematics or systems-engineering definition of Fourier transform:
Use the same definition for the inverse transform:
A common signal-processing definition of Fourier transform:
Use the same parameter definition for the inverse:
A typical data-analysis definition of discrete Fourier transform:
Use the same definition to get the correct inverse:
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:
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