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

[Rafael Guerra]

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.



I think my solution is simple and it looks harmless to me. At least the results look reasonable for different amounts of fractional shifts tested.

But I will keep studying the subject.

Maybe some expert on the matter can jump in.



Note sure about your last question as many scenarios can be thought of, of continuous functions with discontinuities and their sampled versions.

I can think of cases where the slope can be < |u($)-u(1)|/1



Regards,

Rafael



-----Original Message-----
From: users [mailto:users-bounces at lists.scilab.org] On Behalf Of sgougeon at free.fr
Sent: Thursday, June 07, 2018 2:32 PM
To: Users mailing list for Scilab <users at lists.scilab.org>
Subject: Re: [Scilab-users] circshift() : Scilab Enhancement Proposal



>Samuel,

>

>The idea and the implementation of the end-points interpolation is that

>this is done on the input data (big slope), not on the FFT output.



This is clear



>Maybe be it needs some further work. Tbc.



I don't think so.



>Noting also that between the endpoints of the DFT periodic input, there is the interval of one sample.



That is to say: Let u(1:$) be the original signal.

Since it is virtually periodic, the FFT sees u($+1)=u(1).

Do we agree about this?



Then: Do we agree on that the |slope| across the shifted edges of u is necessarily greater or equal to |u($)-u(1)|/1 ?


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