Primal scaling function:

Primal wavelet function:

Dual scaling function:

Dual wavelet function:

Primal filter coefficients:

Dual filter coefficients:

ReverseBiorthogonalSplineWavelet[1,1] is equivalent to HaarWavelet:

ReverseBiorthogonalSplineWavelet is equivalent to BiorthogonalSplineWavelet :

ReverseBiorthogonalSplineWavelet is equivalent to BiorthogonalSplineWavelet :

ReverseBiorthogonalSplineWavelet is equivalent to BiorthogonalSplineWavelet :

ReverseBiorthogonalSplineWavelet is equivalent to BiorthogonalSplineWavelet :

Lowpass filter coefficients sum to unity; :

Highpass filter coefficients sum to zero; :

Dual filter coefficients sum to unity; :

Dual highpass filter coefficients sum to zero; :

Scaling function integrates to unity; :

Dual scaling function integrates to unity; :

Wavelet function integrates to zero; :

Dual wavelet function integrates to zero; :

Scaling function has compact support {n₁,n₂}:

Dual scaling function has compact support {nd₁,nd₂}:

Corresponding wavelet function has support {(n₁– nd₂+1)/2, (n₂– nd₁+1)/2}:

Dual wavelet function has support {(nd₁– n₂+1)/2, (nd₂– n₁+1)/2}:

satisfies the recursion equation :

Plot the components and the sum of the recursion:

satisfies the recursion equation :

Plot the components and the sum of the recursion:

satisfies the recursion equation :

Plot the components and the sum of the recursion:

satisfies the recursion equation :

Plot the components and the sum of the recursion:

Frequency response for is given by :

The filter is a lowpass filter:

Fourier transform of is given by :

Frequency response for is given by :

The filter is a dual lowpass filter:

Fourier transform of is given by :

Frequency response for is given by :

The filter is a lowpass filter:

Fourier transform of is given by :

Frequency response for is given by :

The filter is a lowpass filter:

Fourier transform of is given by :

Plot translates and dilations of scaling function:

Plot translates and dilations of wavelet function: