FFT variants - smoothing

[Nick Draper]

I use FFT for smoothing & derivatives and found them better than other methods. Smoothing The principle is that the data is transformed, truncated to remove noisy points at high x and back transformed. The simple version just truncates to 1/n of the range – this corresponds to n point smoothing. The sophisticated version uses the Weiner filter which chooses the truncation point according to the statistical errors. I found this very reliable for data with peaks. Derivatives By swapping the real & imaginary parts of the transform & back transforming you can get the derivatives. Then by truncating, you can get smoothed versions. Versions of these would be useful if they do not already exist. Sp

[Roman Tolchenov]

(In [3213]) Added FFTSmooth algorithm with a couple of simple filters. re #854

[Roman Tolchenov]

(In [3239]) Improved FFTSmooth. re #854

[Roman Tolchenov]

(In [3245]) Added RealFFT algorithm and changed FFTSmooth to use it. re #854

[Roman Tolchenov]

Needs more filters (e.g. Wiener)

[Nick Draper]

Algorithm appears to do nothing if the workspace does not have regular bins. Output a warning level message to the log and update the wiki documentation to explain that the input must have regular binning.

Also mark the truncation filter as not implemented yet in the documentation.

[Stuart Campbell]

This ticket has been transferred to github issue ​1702