dwt3
Single-level 3-D discrete wavelet transform
Description
Examples
Define the original 3-D data.
X = reshape(1:64,4,4,4)
X = X(:,:,1) = 1 5 9 13 2 6 10 14 3 7 11 15 4 8 12 16 X(:,:,2) = 17 21 25 29 18 22 26 30 19 23 27 31 20 24 28 32 X(:,:,3) = 33 37 41 45 34 38 42 46 35 39 43 47 36 40 44 48 X(:,:,4) = 49 53 57 61 50 54 58 62 51 55 59 63 52 56 60 64
Perform single-level decomposition of X
using the wavelet "db1"
. Inspect the filters in the output.
wt = dwt3(X,"db1");
wt.filters
ans = struct with fields:
LoD: {[0.7071 0.7071] [0.7071 0.7071] [0.7071 0.7071]}
HiD: {[-0.7071 0.7071] [-0.7071 0.7071] [-0.7071 0.7071]}
LoR: {[0.7071 0.7071] [0.7071 0.7071] [0.7071 0.7071]}
HiR: {[0.7071 -0.7071] [0.7071 -0.7071] [0.7071 -0.7071]}
Decompose X
using the wavelet "db2"
.
[LoD,HiD,LoR,HiR] = wfilters("db2");
wt = dwt3(X,{LoD,HiD,LoR,HiR});
wt.filters
ans = struct with fields:
LoD: {[-0.1294 0.2241 0.8365 0.4830] [-0.1294 0.2241 0.8365 0.4830] [-0.1294 0.2241 0.8365 0.4830]}
HiD: {[-0.4830 0.8365 -0.2241 -0.1294] [-0.4830 0.8365 -0.2241 -0.1294] [-0.4830 0.8365 -0.2241 -0.1294]}
LoR: {[0.4830 0.8365 0.2241 -0.1294] [0.4830 0.8365 0.2241 -0.1294] [0.4830 0.8365 0.2241 -0.1294]}
HiR: {[-0.1294 -0.2241 0.8365 -0.4830] [-0.1294 -0.2241 0.8365 -0.4830] [-0.1294 -0.2241 0.8365 -0.4830]}
Decompose X
using different wavelets, one for each orientation: "db1"
, "db2"
, and again "db1"
. Specify periodic extension.
WS = struct("w1","db1","w2","db2","w3","db1"); wt = dwt3(X,WS,"mode","per"); wt.filters
ans = struct with fields:
LoD: {[0.7071 0.7071] [-0.1294 0.2241 0.8365 0.4830] [0.7071 0.7071]}
HiD: {[-0.7071 0.7071] [-0.4830 0.8365 -0.2241 -0.1294] [-0.7071 0.7071]}
LoR: {[0.7071 0.7071] [0.4830 0.8365 0.2241 -0.1294] [0.7071 0.7071]}
HiR: {[0.7071 -0.7071] [-0.1294 -0.2241 0.8365 -0.4830] [0.7071 -0.7071]}
Decompose X
using the filters given by WF
and set the extension mode to half-point symmetric.
WF = wt.filters; wtBIS = dwt3(X,WF,"mode","sym")
wtBIS = struct with fields:
sizeINI: [4 4 4]
filters: [1×1 struct]
mode: 'sym'
dec: {2×2×2 cell}
Input Arguments
Input data, specified as a 3-D array.
Data Types: double
Analyzing wavelet used to compute the 3-D DWT, specified as a character
vector or string scalar. The analyzing wavelet is from one of the following
wavelet families: Best-localized Daubechies, Beylkin, Coiflets, Daubechies,
Fejér-Korovkin, Haar, Han linear-phase moments, Morris minimum-bandwidth,
Symlets, Vaidyanathan, Discrete Meyer, Biorthogonal, and Reverse
Biorthogonal. See wfilters
for the wavelets
available in each family.
Analyzing wavelets to use in the 3-D wavelet decomposition, one for each
direction, specified as a cell array of character vectors, a string array,
or a structure. w = {'wname1','wname2','wname3'}
, or
w = ["wname1","wname2","wname3"]
, or
w
is a structure with three fields,
"w1"
, "w2"
, and
"w3"
, containing character vectors or string scalars
that are the names of wavelets.
Example: wt =
dwt3(x,["db2","db4","db6"]);
Wavelet filters to use in the 3-D wavelet decomposition, specified as
either a cell array or structure. wf
specifies four
filters, two for decomposition and two for reconstruction, or 3 × 4
filters (one quadruplet by direction). wf
is either a
cell array (1-by-4) or (3-by-4) : {LoD,HiD,LoR,HiR}
or a
structure with the four fields "LoD"
,
"HiD"
, "LoR"
,
"HiR"
.
Extension mode used when performing the wavelet decomposition, specified as:
extmode | DWT Extension Mode |
---|---|
"zpd" | Zero padding |
"sp0" | Smooth extension of order 0 |
"spd" (or "sp1" ) | Smooth extension of order 1 |
"sym" or "symh" | Symmetric extension (half point): boundary value symmetric replication |
"symw" | Symmetric extension (whole point): boundary value symmetric replication |
"asym" or "asymh" | Antisymmetric extension (half point): boundary value antisymmetric replication |
"asymw" | Antisymmetric extension (whole point): boundary value antisymmetric replication |
"ppd" , "per" | Periodized extension If the signal length is odd and
|
The global variable managed by dwtmode
specifies the default extension
mode.
Output Arguments
Single-level 3-D wavelet decomposition, returned as a structure with the following fields:
sizeINI | Size of the three-dimensional array
|
mode | Name of the wavelet transform extension mode. |
filters | Structure with four fields:
|
dec | 2-by-2-by-2 cell array containing the coefficients of the decomposition.
The
|
Version History
Introduced in R2010a
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