Two-dimensional wavelet interpolation

waveterp2d(x,y,v,j,m,n,f,[o,[i]]) Returns the value at (x,y) of the periodic multiresolution approximation of v corresponding to subband (m,n) at level j, based on the filter f. f can have an offset o and negation i.

swaveterp2d(x,y,v,j,m,n,f) Returns the value at (x,y) of the symmetric multiresolution approximation of v corresponding to subband (m,n) at level j, based on the filter f.

Arguments:

• x and y are real scalars.
• v is a matrix. For waveterp2d, the rows(v) and cols(v) must be divisible by 2^j. For swaveterp2d, rows(v) ≥ 2^j and cols(v) ≥ 2^j.
• j is an integer.
• m and n are integers less than 2^j giving the indices of the desired subband in sequential order.

• f is a vector of low pass filter coefficients for an orthonormal filter. Alternatively, for a biorthogonal filter, f is a 2-column matrix whose first column contains the low pass filter coefficients and whose second column contains the inverse low pass filter coefficients.

  • For waveterp2d, f is the result from a function, such as daublet or Bspline, that creates the filter coefficients for a particular wavelet or f is an array of user-defined filter coefficients.

  • For swaveterp2d, f is bl, Bspline, or daublet(2).

• o (optional) is a real scalar, for an orthonormal filter, or a 1 × 2 matrix of real scalars for a biorthogonal filter. o is the offset(s) corresponding to the filter f. If not specified, o is a default offset.
• i (optional) is zero or one for an orthonormal filter or, for a biorthogonal filter, i is a 1 × 2 matrix whose elements are zero or one. i = 0 specifies no negation of the default high pass coefficients; i = 1 specifies negation. If not specified, i = 0.

Mathcad Example