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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.


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