Wavelet Toolbox

One-Dimensional Wavelet Capabilities

Basic one-dimensional objects.   

	Objects	Description
Signal in original time	s Ak, 0 k j Dk, 1 k j	Original signal Approximation at level k Detail at level k
Coefficients in scale-related time	cAk, 1 k j cDk, 1 k j [cAj, cDj, ..., cD1]	Approximation coefficients at level k Detail coefficients at level k Wavelet decomposition at level j, j 1

Analysis-decomposition capabilities.   

Purpose	Input	Output	M-File
Single-level decomposition	s	cA1, cD1	dwt
Single-level decomposition	cAj	cAj+1, cDj+1	dwt
Decomposition	s	[cAj, cDj, ..., cD1]	wavedec

Synthesis-reconstruction capabilities.   

Purpose	Input	Output	M-File
Single-level reconstruction	cA1, cD1	s or A0	idwt
Single-level reconstruction	cAj+1, cDj+1	cAj	idwt
Full reconstruction	[cAj, cDj, ..., cD1]	s or A0	waverec
Selective reconstruction	[cAj, cDj, ..., cD1]	Al, Dm	wrcoef

Decomposition structure utilities.   .

Purpose	Input	Output	M-File
Extraction of detail coefficients	[cAj, cDj, ..., cD1]	cDk, 1 k j	detcoef
Extraction of approximation coefficients	[cAj, cDj, ..., cD1]	cAk, 0 k j	appcoef
Recomposition of the decomposition structure	[cAj, cDj, ..., cD1]	[cAk, cDk, ..., cD1] 1 k j	upwlev

To illustrate the command line mode for one-dimensional capabilities, see the section One-Dimensional Analysis Using the Command Line.

Why Does Such an Algorithm Exist?

Two-Dimensional Wavelet Capabilities