WAVELET
Wavelet Computations.

WAVELET is a MATLAB library which contains some utilities for computations involving wavelets.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

WAVELET is available in a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

HAAR, a MATLAB library which computes the Haar transform of data.

SFTPACK, a MATLAB library which implements the "slow" Fourier transform, intended as a teaching tool and comparison with the fast Fourier transform.

SINE_TRANSFORM, a MATLAB library which demonstrates some simple properties of the discrete sine transform.

WALSH, a MATLAB library which implements versions of the Walsh and Haar transforms.

Reference:

1. Gilbert Strang, Truong Nguyen,
   Wavelets and Filter Banks,
   Wellesley-Cambridge Press, 1997,
   ISBN: 0-9614088-7-1,
   LC: TK7872.F5S79 / QA403.3.S87.

Source Code:

• cascade.m carries out the cascade algorithm.
• daub_coefficients.m returns a Daubechies coefficient vector for even orders 2 through 20.
• daub2_matrix.m returns the DAUB2 matrix.
• daub2_scale.m recursively evaluates the DAUB2 scaling function.
• daub2_scale_plot.m plots the DAUB2 scaling function.
• daub2_transform.m computes the DAUB2 transform of a vector.
• daub2_transform_inverse.m inverts the DAUB2 transform of a vector.
• daub4_matrix.m returns the DAUB4 matrix.
• daub4_scale.m recursively evaluates the DAUB4 scaling function.
• daub4_scale_plot.m plots the DAUB4 scaling function.
• daub4_transform.m computes the DAUB4 transform of a vector.
• daub4_transform_inverse.m inverts the DAUB4 transform of a vector.
• daub6_matrix.m returns the DAUB6 matrix.
• daub6_scale.m recursively evaluates the DAUB6 scaling function.
• daub6_scale_plot.m plots the DAUB6 scaling function.
• daub6_transform.m computes the DAUB6 transform of a vector.
• daub6_transform_inverse.m inverts the DAUB6 transform of a vector.
• daub8_matrix.m returns the DAUB8 matrix.
• daub8_scale.m recursively evaluates the DAUB8 scaling function.
• daub8_scale_plot.m plots the DAUB8 scaling function.
• daub8_transform.m computes the DAUB8 transform of a vector.
• daub8_transform_inverse.m inverts the DAUB8 transform of a vector.
• daub10_matrix.m returns the DAUB10 matrix.
• daub10_scale.m recursively evaluates the DAUB10 scaling function.
• daub10_scale_plot.m plots the DAUB10 scaling function.
• daub10_transform.m computes the DAUB10 transform of a vector.
• daub10_transform_inverse.m inverts the DAUB10 transform of a vector.
• daub12_matrix.m returns the DAUB12 matrix.
• daub12_transform.m computes the DAUB12 transform of a vector.
• daub12_transform_inverse.m inverts the DAUB12 transform of a vector.
• daub14_transform.m computes the DAUB14 transform of a vector.
• daub14_transform_inverse.m inverts the DAUB14 transform of a vector.
• daub16_transform.m computes the DAUB16 transform of a vector.
• daub16_transform_inverse.m inverts the DAUB16 transform of a vector.
• daub18_transform.m computes the DAUB18 transform of a vector.
• daub18_transform_inverse.m inverts the DAUB18 transform of a vector.
• daub20_transform.m computes the DAUB20 transform of a vector.
• daub20_transform_inverse.m inverts the DAUB20 transform of a vector.
• i4_modp.m returns the nonnegative remainder of I4 division.
• i4_wrap.m forces an I4 to lie between given limits by wrapping.
• r8_uniform_01.m returns a unit pseudorandom R8.
• r8mat_is_identity.m tests how closely a matrix is to the identity matrix.
• r8vec_conjugate.m reverses a vector and negates even-indexed entries.
• r8vec_uniform_01.m returns a unit pseudorandom R8VEC.
• timestamp.m prints the current YMDHMS date as a time stamp.

Examples and Tests:

• wavelet_test.m, a sample calling program.
• wavelet_test01.m, tests DAUB2_TRANSFORM and DAUB2_TRANSFORM_INVERSE.
• wavelet_test02.m, tests DAUB4_TRANSFORM and DAUB4_TRANSFORM_INVERSE.
• wavelet_test03.m, tests DAUB6_TRANSFORM and DAUB6_TRANSFORM_INVERSE.
• wavelet_test04.m, tests DAUB8_TRANSFORM and DAUB8_TRANSFORM_INVERSE.
• wavelet_test05.m, tests DAUB10_TRANSFORM and DAUB10_TRANSFORM_INVERSE.
• wavelet_test06.m, tests DAUB12_TRANSFORM and DAUB12_TRANSFORM_INVERSE.
• wavelet_test07.m, tests DAUB14_TRANSFORM and DAUB14_TRANSFORM_INVERSE.
• wavelet_test08.m, tests DAUB16_TRANSFORM and DAUB16_TRANSFORM_INVERSE.
• wavelet_test09.m, tests DAUB18_TRANSFORM and DAUB18_TRANSFORM_INVERSE.
• wavelet_test10.m, tests DAUB20_TRANSFORM and DAUB20_TRANSFORM_INVERSE.
• wavelet_test11.m, tests DAUB*_MATRIX.
• wavelet_test12.m, tests DAUB*_SCALE.
• wavelet_test_output.txt, the output file.

• cascade_test.m, a sample calling program for the CASCADE algorithm.
• cascade_test01.m, compares 5 one step cascades and one five-step cascade.
• cascade_test01.png, an image of the results.
• cascade_test02.m, approximates a scaling function using multiple cascades.
• cascade_test02.png, an image of the results.
• cascade_test03.m, approximates a wavelet using multiple cascades.
• cascade_test03.png, an image of the results.
• cascade_test_output.txt, the output file.

Functions such as DAUB4_SCALE_PLOT can plot a scaling function approximated using a given recursion level N. Typically a value of N = 4 or 5 is enough.

• daub2_scale_plot_n1.png
• daub2_scale_plot_n2.png
• daub4_scale_plot_n0.png
• daub4_scale_plot_n1.png
• daub4_scale_plot_n2.png
• daub4_scale_plot_n3.png
• daub4_scale_plot_n4.png
• daub4_scale_plot_n5.png
• daub4_scale_plot_n6.png
• daub6_scale_plot_n1.png
• daub6_scale_plot_n2.png
• daub6_scale_plot_n3.png
• daub6_scale_plot_n4.png
• daub6_scale_plot_n5.png
• daub6_scale_plot_n6.png
• daub8_scale_plot_n1.png
• daub8_scale_plot_n2.png
• daub8_scale_plot_n3.png
• daub8_scale_plot_n4.png
• daub8_scale_plot_n5.png
• daub10_scale_plot_n1.png
• daub10_scale_plot_n2.png
• daub10_scale_plot_n3.png
• daub10_scale_plot_n4.png
• daub10_scale_plot_n5.png

You can go up one level to the MATLAB source codes.