FRACTIONAL SPLINE WAVELET SOFTWARE FOR MATLAB
Thierry Blu and Michael Unser
Biomedical Imaging group
Swiss Federal Institute of Technology Lausanne (EPFL), Switzerland.
October 1999
A. TEST PROGRAM
DEMOFRACT: Demonstration program that generates fBm-like noise using
orthogonal symmetrical fractional spline wavelets. For example, try J=12,
alpha=0.3, beta=1.3. You can modify this file to use non-symmetrical
fractional splines, or also semi-orthonormal fractional splines (modify the
'type' variable: type = '+ortho', or '-ortho', or '*ortho', or '+bspline', or
'-bspline', or '*bspline', or '-dual', or '+dual', or '*dual')
DEMOFRACT2: Generates a series of fBm-like noises.
B. BASIC WAVELET TRANSFORM FUNCTIONS
FFTFRACTSPLINEFILTERS: Computes the frequency responses of the wavelet
analysis and synthesis filters (lowpass and highpass) for various types
('+ortho','-ortho','*ortho','+bspline','-bspline','*bspline','-dual','+dual','*dual')
of orthonormal or semi-orthonormal fractional spline wavelet transforms.
The type "*ortho" is a continuous-order generalization of the
Battle-Lemarié transform.
FFTWAVELETANALYSIS: Performs a FFT-based computation of the wavelet
transform of a signal to a given depth J.
FFTWAVELETSYNTHESIS: Performs a FFT-based computation of the inverse
wavelet transform.
C. OTHER ROUTINES
WEXTRACT: Extraction of a component (or band) of the wavelet
transform.
FRACTSPLINEAUTOCORR: Frequency domain computation of fractional spline
autocorrelation function.