If I have a 2D signal (say a 2D image) thats defined on $[-1,1]^2$.
I sample the 2D signal on discrete Chebyshev Points (Chebyshev-Legendre Points), say there is 60 grid points per side.
The highest frequency number $k$, such that $k$ is defined as $\cos(k\pi x)$ that could be represented by this algorithm is probably $floor(60/\pi)$. Or something like this.
I want to get rid of the two fastest oscillating modes from this signal. Can I do a low pass filtering if I want to use Chebyshev Filters? Is this exactly what Chebyshev filters do?
If you could refer me to a reference that would be good too. Somehow wikipedia's explanation is very `engineering'– it eludes me.
What I want to do is simply decompose the signal to 2D Chebyshev polynomials and kick out the fastest oscillating two modes. Simple as that.
Thanks for your help in advance. I would illustrate my question if you have doubts.
Best Answer
I think this question warrant an answer.
Chebyshev Filter means something else. If you are looking for the low order approximation of a function, you are in the right place.
First apply the Chebyshev Transform to get the Chebyshev coefficients; then kick out the fastest oscillating modes by hand.
This could be done automatically using chebfun or could be done manually, following the direction of Wikipedia page for Chebyshev Transform. Will probably take one half a day of work to get everything clicking. Take extra care for the ordering. But it works!