Two-dimensional wavelet families

father2d(x, y, [j, kx, ky], s) Returns the value at (x,y) of the 2D father wavelet packet based on the filter represented by string s at scale j and position (kx,ky).

mother2d(x, y, [j, kx, ky], s, ds) Returns the value at (x,y) of the 2D mother wavelet packet based on the filter represented by string s at scale j and position (kx,ky).

dlfather2d(x, y, [j, kx, ky], s) Returns the value at (x,y) of the 2D dual father wavelet packet based on the filter represented by string s at scale j and position (kx,ky).

dlmother2d(x, y, [j, kx, ky], s, ds) Returns the value at (x,y) of the 2D dual mother wavelet packet based on the filter represented by string s at scale j and position (kx,ky).

Arguments:

• x and y are real scalars.
• j (optional) is an integer. If j is omitted, it is assumed to be 0.
• kx and ky (optional) are integers. If omitted, they are assumed to be 0.

• s is a string representing a wavelet filter. Valid strings consist of a letter(s) followed by a number(s). The following letters, which indicate wavelet filters, are allowed:

  d, daub, daublet, s, symm, symmlet, c, coif, coiflet, bl, bs, Bspline, haar

  The number(s) which follow the letters must be valid for the wavelet filter to which the letters refer.

  For example, valid strings for s are "d4" for daublet(4), "s12" for symmlet(12), and "bs33" for Bspline(3,3).

• ds is a one of the following strings: "H", "V", or "D" which indicate, respectively, a horizontal, vertical, or diagonal mother wavelet.

Mathcad Example