2D Shannon Wavelet Decomposition

Hi,

I would like to proceed to a 2D Shannon wavelet decomposition and I am surprised that none of this is implemented (unless I have not found it). May someone help me ?

Answer 1

[Wayne King]

Hi Claire, Currently there is no 2D CWT implementation in the Wavelet Toolbox. The Shannon wavelet is a sinc in time so it does not have compact support. Accordingly, you cannot implement it with FIR filters. Frankly, I'm having difficulty even imagining how you could implement a decent 2D CWT approximation.

However, there is a FIR filter approximation for the Meyer wavelet, which is a similar sinc in time continuous wavelet. You can obtain and use those filters with

[LoD,HiD] = wfilters('dmey');

[Claire]

Actually, I would like to implement at least a 1D discrete wavelet transform, with Shannon's wavelets. I know that I have to treat the Shannon DWT in the Fourier domain, but I only know the continuous form of the wavelet. And my discretization does not give an orthogonal basis.

Once this step will be completed, it will be easy to extend to n-dimensional transform. Any suggestion ?