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‎wmtsa-matlab-0.2.6/wmtsa/dwt/DWT_Structures.m‎

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%****s* WMTSA-DWT/Structures
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%
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% NAME
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% WMTSA DWT Structures -- structs used in WMTSA DWT toolbox.
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%
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% DESCRIPTION
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% MATLAB structures used in WMTSA DWT toolbox.
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%
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% TOOLBOX
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% wmtsa/dwt
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%
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% CATEGORY
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%
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%
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%***
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%****s* Structures/wtf_s
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%
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% NAME
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% wtf_s -- wavelet transform filter struct.
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%
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% DESCRIPTION
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% wtf_s struct has fields:
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% * g -- scaling (low-pass) filter coefficients (vector).
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% * h -- wavelet (high-pass) filter coefficients (vector).
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% * L -- filter length (= number of coefficients) (integer).
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% * Name -- name of wavelet filter (character string).
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% * Class -- class of wavelet filters (character string).
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% * Transform -- name of transform (character string).
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%
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% Possible values for transform are: DWT, MODWT.
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%
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% SEE ALSO
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%
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%***
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%****s* Structures/w_att_s
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%
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% NAME
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% w_att_s -- wavelet transform attributes struct.
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%
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% DESCRIPTION
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% w_att_s struct has fields:
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% * Transform -- name of transform ('MODWT') (string).
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% * WTF -- name of wavelet transform filter or a wtf_s struct (string or struct).
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% * NX -- number of observations in original series (= length(X)) (integer).
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% * NW -- number of wavelet coefficients (integer).
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% * J0 -- number of levels of partial decompsition (integer).
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% * NChan -- number of channels in a multivariate dataset (integer).
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% * Boundary -- boundary conditions applied (string).
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% * Aligned -- Boolean flag indicating whether coefficients are aligned
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% with original series (1 = true) or not (0 = false) (boolean).
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% * RetrainVJ -- Boolean flag indicating whether VJ scaling coefficients at all
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% levels have been retained (1= true) or not (0 = false) (boolean).
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%
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% Possible values for transform are: DWT, MODWT.
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%
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% SEE ALSO
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%
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%***
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% AUTHOR
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% Charlie Cornish
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%
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% CREATION DATE
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% 2005-03-03
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%
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% COPYRIGHT
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% (c) Charles R. Cornish 2005
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%
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% REVISION
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% $Revision: 630 $
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%
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% $Id: DWT_Structures.m 630 2006-05-02 20:47:17Z ccornish $
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‎wmtsa-matlab-0.2.6/wmtsa/dwt/advance_scaling_filter.m‎

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function nuGj = advance_scaling_filter(wtfname, j)
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% advance_scaling_filter -- Calculate the value to advance scaling filter at jth level for a given wavelet.
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%
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%****f* wmtsa.dwt/advance_scaling_filter
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%
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% NAME
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% advance_scaling_filter -- Calculate the value to advance scaling filter at jth level for a given wavelet.
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%
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% SYNOPSIS
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% nuGj = advance_scaling_filter(wtfname, level)
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%
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% INPUTS
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% wtfname = string containing name of WMTSA-supported wavelet filter.
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% j = jth level (index) of scale or a range of j levels of scales
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% (integer or vector of integers).
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%
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% OUTPUTS
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% nuGj = advance of scaling filter at specified levels.
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%
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% SIDE EFFECTS
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% wavelet is a WMTSA-supported scaling filter; otherwise error.
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%
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% DESCRIPTION
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%
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%
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% EXAMPLE
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%
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%
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% ALGORITHM
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% nuGj = (2^j - 1) * nu
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%
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% For details, see equation 114a of WMTSA.
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%
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% REFERENCES
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% Percival, D. B. and A. T. Walden (2000) Wavelet Methods for
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% Time Series Analysis. Cambridge: Cambridge University Press.
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%
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% SEE ALSO
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% advance_time_series_filter, dwt_filter
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%
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% AUTHOR
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% Charlie Cornish
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%
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% CREATION DATE
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% 2003-05-08
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%
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% COPYRIGHT
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%
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%
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% REVISION
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% $Revision: 612 $
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%
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%***
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% $Id: advance_scaling_filter.m 612 2005-10-28 21:42:24Z ccornish $
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usage_str = ['Usage: nuGj = ', mfilename, ...
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' (wtfname, j)'];
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%% Check input arguments and set defaults.
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error(nargerr(mfilename, nargin, [2:2], nargout, [0:1], 1, usage_str, 'struct'));
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% Check for valid wavelet and get wavelet filter coefficients
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try
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wtf_s = dwt_filter(wtfname);
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catch
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rethrow(lasterror);
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end
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h = wtf_s.h;
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g = wtf_s.g;
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L = wtf_s.L;
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error(argterr(mfilename, j, 'int0', [], 1, '', 'struct'));
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nuGj = NaN;
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switch lower(wtfname)
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case 'haar'
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nuGj = advance_wavelet_filter('haar', j);
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otherwise
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nu = advance_time_series_filter(wtfname);
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nuGj = (2.^j - 1) * nu;
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end
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return
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‎wmtsa-matlab-0.2.6/wmtsa/dwt/advance_time_series_filter.m‎

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function nu = advance_time_series_filter(wtfname)
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% advance_time_series_filter -- Calculate the advance of the time series or filter for a given wavelet.
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%
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%****f* wmtsa.dwt/advance_time_series_filter
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%
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% NAME
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% advance_time_series_filter -- Calculate the advance of the time series or filter for a given wavelet.
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%
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% SYNOPSIS
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% nu = advance_time_series_filter(wtfname)
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%
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% INPUTS
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% wtfname - string containing name of WMTSA-supported wavelet filter.
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%
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% OUTPUTS
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% nu - advance of time series for specified wavelet filter.
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%
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% SIDE EFFECTS
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% wavelet is a WMTSA-supported wavelet filter; otherwise error.
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%
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% DESCRIPTION
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%
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%
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% EXAMPLE
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%
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%
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% ALGORITHM
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%
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% For Least Asymmetric filters, equation 112e of WMTSA:
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% nu = -L/2 + 1, for L/2 is even;
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% = -L/2, for L = 10 or 18;
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% = -L/2 + 2, for L = 14.
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%
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% For Best Localized filter, page 119 of WMTSA.
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% nu = -5, for L = 14;
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% = -11, for L = 18;
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% = -9, for L = 20.
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%
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% For Coiflet filters, page 124 and equation 124 of WMTSA:
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% nu = -2*L/3 + 1
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%
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% REFERENCES
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% Percival, D. B. and A. T. Walden (2000) Wavelet Methods for
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% Time Series Analysis. Cambridge: Cambridge University Press.
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%
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% SEE ALSO
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% dwt_filter
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%
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% AUTHOR
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% Charlie Cornish
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%
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% CREATION DATE
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% 2003-05-08
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%
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% COPYRIGHT
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%
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%
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% REVISION
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% $Revision: 612 $
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%
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%***
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% $Id: advance_time_series_filter.m 612 2005-10-28 21:42:24Z ccornish $
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usage_str = ['Usage: nu = ', mfilename, ...
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' (wtfname)'];
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%% Check input arguments and set defaults.
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error(nargerr(mfilename, nargin, [1:1], nargout, [0:1], 1, usage_str, 'struct'));
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% Check for valid wavelet and get wavelet filter coefficients
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try
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wtf_s = dwt_filter(wtfname);
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catch
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rethrow(lasterror);
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end
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h = wtf_s.h;
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g = wtf_s.g;
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L = wtf_s.L;
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nu = NaN;
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switch lower(wtfname)
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% Haar filter
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case {'haar'}
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nu = 0;
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% Haar filter
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% Value from Figure 115
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case {'d4'}
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nu = -1;
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% Extremal Phase filters
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% case {'haar', 'd4', 'd6', 'd8', 'd12', 'd14', 'd16', 'd18', 'd20'}
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case { 'd6', 'd8', 'd12', 'd14', 'd16', 'd18', 'd20'}
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error('Need to determine nu for Extremal Phase filters - Is it -1 for all filters?.');
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% Least Asymmetric filters
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case { 'la8', 'la10', 'la12', 'la14', 'la18', 'la16', 'la20'}
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nu = advance_least_asymetric_filter(L);
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% Best Localized filters
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case {'bl14', 'bl18', 'bl20'}
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nu = advance_best_localized_filter(L);
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% Coiflet filters
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case {'c6', 'c12', 'c18', 'c24', 'c30'}
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nu = advance_coiflet_filter(L);
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otherwise
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% Do nothing
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end
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return
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function nu = advance_least_asymetric_filter(L)
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% Equation 112c of WMTSA.
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if (mod(L/2, 2) == 0)
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% L/2 is even, i.e. L = 8, 12, 16, 20
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nu = -(L/2) + 1;
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else
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switch (L)
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case {10, 18}
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nu = -(L/2);
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case {14}
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nu = -(L/2) + 2;
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otherwise
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error(['Invalid filter length (L = ', int2str(L), ') ' ...
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'specified.']);
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end
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end
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return
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function nu = advance_best_localized_filter(L)
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% Page 119 of WMTSA.
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switch L
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case 14
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nu = -5;
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case 18
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nu = -11;
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case 18
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nu = -9;
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otherwise
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% Do nothing
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end
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return
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function nu = advance_coiflet_filter(L)
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% Page 124 and equation 124 of WMTSA:
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nu = -(2 * L / 3) + 1;
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return
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