# Is there a two-dimensional sinc interpolation software?

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Jaime De La Mota Sanchis il 30 Set 2021
Risposto: Nikeet Pandit il 10 Mag 2022
Hello everyone. I have found this package of software. I am interested in doing a two-dimensonal sinc interpolation as defined in the diapositives 15 to 18 of this presentation. Unfortunately. I haven't found anything.
Can anybody point me to some code that might work?
Best regards.
Jaime.
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### Risposta accettata

Star Strider il 30 Set 2021
One-dimensional sinc interplation is described in Ideal Bandlimited Interpolation. It may be possible to adapt it to a 2D problem.
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Matt J il 30 Set 2021
Modificato: Matt J il 30 Set 2021
Yes, it is possible, but this is only valid for plaid upsampling, not arbitrary interpolation.
M=length(Image);
t=1:M;
dt=0.2;
ts = -M:dt:2*M;
[Ts,T] = ndgrid(ts,t);
A=sinc(Ts - T);
A([1:M/dt,end+1-M/dt:end],:)=[];
ImageInterpolated = A*Image*A.';
whos Image ImageInterpolated
Name Size Bytes Class Attributes Image 256x256 524288 double ImageInterpolated 1281x1281 13127688 double
imshow(ImageInterpolated,[])
Jaime De La Mota Sanchis il 30 Set 2021
That is great, since I have a grid of size 19*13 with values of temperature and I want to find an equation using this sinc interpolation to have a function to describe said field. Is there a way to adapt this code so that instead of an image, a matrix is introduced and the resulting expressin can be read?

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### Più risposte (2)

Matt J il 30 Set 2021
Since interpolation is commonly approximated by cubic spline interpolation, which you have an option for in interp2.
Vq = interp2(X,Y,V,Xq,Yq,'spline');
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Jaime De La Mota Sanchis il 30 Set 2021
Thanks for the answer. Is there a way to find the equation used to build said interpolation?

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Nikeet Pandit il 10 Mag 2022
We know that Fourier is a seperable transform... so if we want to do a Fourier 2D transform its equivalent to doing 1D transform on rows and then columns. I assume then this property holds for sinc interpolation... So I adapted the 1D example for sinc interpolation they provide on the sinc(x) documentation ... and then I applied the interpolation to the rows and then interpolation to the columns and it seemed to work
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