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Feature #782

spectral differentiation of odd order (operator MULOMEGA)

Added by Peter Schmidt over 8 years ago.

Status:
New
Priority:
Normal
Assignee:
-
Start date:
02/12/2016
Due date:
% Done:

0%

Estimated time:
Resolution:

Description

Hi

The operator MULOMEGA is stated to perform differentiation in the frequency domain. While this is true for spectral data whose corresponding time domain data is of un-even length, it is strictly not true if the time-domain data vector is of even length in which case the Nyquist frequency should be set to zero. For a mathematical proof of this please see the excellent note by Steven G. Johnson (author of the fftw3 package) currently available at: http://math.mit.edu/~stevenj/fft-deriv.pdf

As the SAC operator FFT operates on even length data vectors (automatically padding any vector to closest power of 2) this seems to be worth mentioning in the description of the MULOMEGA operator (whether or not this actually is of practical importance can of course be discussed...)

regards Peter

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