pseudiff

Return the 2D pseudo differential operator kⁿ wavelet

Syntax

out = pseudiff(kx, ky, mode [, alpha])

Description

Return the 2D pseudiff wavelet or scaling function packets based on the recursive filter

  phi_n(k) = 0.5*k^(n-2) + 0.5*(n-2)*phi_(n-2)(k)

(implemented in phin.m) So, the wavelet packet is

  wpck = \sqrt(phi_n(k) - phi_n(alpha*k))

and the scaling function

  wphi = \sqrt(phi_n(k))

Input Data

kx, ky

[REAL MATRIX] the frequency plane

mode

['infinit'|'scaling'|'wavelet'|'dscaling'|'dwavelet']: specify the function to return through out. So, you can have the integrated scaling function ('scaling'), the wavelet packet ('wavelet'), the duals of these (respectively 'dscaling' and 'dwavelet') useful for the reconstruction, and finally the infinitesimal wavelet ('infinit'), that is the 2D mexican hat.

alpha

[REAL]: the scale ratio defining the packet wavelet.

n

[INTEGER]: the order of the pseudiff wavelet packet.

Output Data

out

The frequency mask of the returned function.

Example(s)

References

P. Vandergheynst, "Ondelettes directionnelles et Ondelettes sur la Sphère", PhD Thesis, Louvain-la-Neuve, 1998.

See Also

gaussian2d iwpck2d mexican2d mexican2d_ctr phin pmexican2d wpck2d wpck2d_yashow

Location

discrete/frames/2d/wpck_defs/pseudiff.m