Wavelet families

father(x,[j,k],s) Returns the value at x of the father wavelet packet based on the filter represented by string s at scale j and position k.

mother(x,[j,k],s) Returns the value at x of the mother wavelet packet based on the filter represented by string s at scale j and position k.

dlfather(x,[j,k],s) Returns the value at x of the dual father wavelet packet based on the filter represented by string s at scale j and position k.

dlmother(x,[j,k],s) Returns the value at x of the dual mother wavelet packet based on the filter represented by string s at scale j and position k.

Arguments:

• x is a real scalar.
• j (optional) is an integer. If j is omitted, it is assumed to be 0.
• k (optional) is an integer. If k is omitted, it is 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).

Mathcad Example