[Scilab-users] circshift() : Scilab Enhancement Proposal

[Rafael Guerra]

Hi Samuel,

There might be an advantage of using the suggested DFT approach for fractional circular shifting of continuous/bandlimited input signals. This is a restrictive but quite useful class of signals.

For the more general case of input series, other interpolation schemes should perform better.

PS:
I could not find a good reference on this topic so far.

Regards,
Rafael

From: users [mailto:users-bounces at lists.scilab.org] On Behalf Of Samuel Gougeon
Sent: Sunday, June 17, 2018 8:19 PM
To: Users mailing list for Scilab <users at lists.scilab.org>
Subject: Re: [Scilab-users] circshift() : Scilab Enhancement Proposal

Hello Rafael,

Le 07/06/2018 à 15:04, Rafael Guerra a écrit :

Hi Samuel,



Fyi, many DFT references recommend averaging the values at endpoints and discontinuities in general. See for instance:



Briggs, W. L. and V. E. Henson [1005] The DFT: an owner's manual for the Discrete Fourier Transform, SIAM, Philadelphia.

>and discontinuities in general

Yes, that's a point. If a specific processing is used for the edges, it would look strange to not implement it as well in the body of the initial signal. From here, a criteria (and likely some threshold) must be set to decide what's a discontinuity, and what's not.
I did not go into any reading -- and frankly, if there is a summarized performances comparison and a standard published procedure --, it would be easier just to implement it, instead of reinventing the wheel with external tests. Then, i am afraid that it will come either with some choices with respect to the type of input signal, or with a bunch of processing options (making circshift a signal processing function rather than just a general matrix handling operation).

Anyway, no damping window could process inner discontinuities.

To me, the main advantage of the DFT was to avoid local interpolations, in order to stay simple.
If the algo then implements some interpolations, why not performing the fractional part of the shift
only by interpolation, instead of in addition to the DFT?
If you can provide some quantified rationale and possibly some finalized algo, it would be fine.

Best regards
Samuel
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