📄 contents.m
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% Dictionaries:Contents -- Fast Analysis/Synthesis operators for various
% dictionaries
%
% The routines in this directory provide an object-oriented way to
% perform fast analysis and fast synthesis transforms for all the
% dictionaries implemented in Atomizer. The top level routines are
% FastA, FastS, FastAA and FastSS. Four arguments
% (NameOfDict, par1, par2, par3) are used to specify a dictionary.
% We define the List data structure, which allows easy access to merged
% dictionaries. The dictionaries implemented are Diracs, Heavisides,
% Jumps(Smoothed Heavisides), Discrete Cosines, Discrete Sines,
% PO(Periodized-Orthogonal) Wavelets, TVPO (PO Wavelets normalized by Total
% Variation), Stationary PO Wavelets, PBS(Periodized-Biorthogonal-Symmetric)
% Wavelets, Splines(Stationary PBS Wavelets), Wavelet Packets and Cosine
% Packets, Multi-Duration Exponentials, or mergers of any dictionaries above.
%
%
%
% Routines for General Dictionaries
%
% MakeDict Make dictionary matrix for a dictionary
% SizeOfDict Cardinality and overcompleteness of a dictionary
% FastA Fast Analysis Operator for a dictionary \Phi
% FastAA Fast Analysis Operator for [\Phi -\Phi]
% FastS Fast Synthesis Operator for a dictionary
% FastSS Fast Synthesis Operator for [\Phi -\Phi]
%
%
% List Data Structure
%
% MakeList Make a List object
% NthList Extract the Nth element from a List object
% LengthList Calculate the # of elements in a List object
%
%
% Documentation
%
% dictionary Documentation for dictionary parameters
%
%
% Fast Analysis/Synthesis Operators for Specific Dictinoiaries
%
% Dictionaries normalized by l^2 norm:
%
% FastDIRACAnalysis Dirac Dictionary
% FastDIRACSynthesis
% FastDCTAnalysis Discrete Cosine Dictioary
% FastDCTSynthesis
% FastDSTAnalysis Discrete Sine Dictionary
% FastDSTSynthesis
% FastPOAnalysis Periodized-Orthogonal Wavelet Dictionary
% FastPOSynthesis
% FastPBSAnalysis Periodized-Biorthogonal-Symmetric Wavelet Dictionary
% FastPBSSynthesis
% FastSTATAnalysis Stationary PO Wavelet Dictionary
% FastSTATSynthesis
% FastSPAnalysis Spline (Stationary PBS Wavelet) Dictionary
% FastSPSynthesis
% FastWPAnalysis Wavelet Packet Dictionary
% FastWPSynthesis
% FastCPAnalysis Cosine Packet Dictionary
% FastCPSynthesis
% FastMDCAnalysis Multi-Duration Cosine Dictionary
% FastMDCSynthesis
%
% Dictionaries normalized by Total Variation:
%
% FastHSAnalysis Heaviside Dictionary
% FastHSSynthesis
% FastJUMPAnalysis Smoothed Heaviside Dictionary
% FastJUMPSynthesis
% FastPOTVAnalysis TV-Periodized-Orthogonal Wavelet Dictionary
% FastPOTVSynthesis
%
%
% Supplement Routines used by Fast Operators
%
% FCPSynthesis.c For FastCPSynthesis
% FCPSynthesis.m
% FCPSynthesis.mex
% FWPSynthesis.c For FastWPSynthesis
% FWPSynthesis.m
% FWPSynthesis.mex
% TIWTAnalysis.c For FastSTATAnalysis
% TIWTAnalysis.m
% TIWTAnalysis.mex
% TIWTSynthesis.c For FastSTATSynthesis
% TIWTSynthesis.m
% TIWTSynthesis.mex
% TIPBSAnalysis.c For FastSPAnalysis
% TIPBSAnalysis.m
% TIPBSAnalysis.mex
% TIPBSSynthesis.c For FastSPSynthesis
% TIPBSSynthesis.m
% TIPBSSynthesis.mex4
%
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