dlmodwt
Deep learning maximal overlap discrete wavelet transform and multiresolution analysis
Since R2022a
Syntax
Description
returns
the maximal overlap discrete wavelet transform (MODWT) of w
= dlmodwt(x
)x
using the
lowpass (scaling) and highpass (wavelet) filters associated with the Daubechies
least-asymmetric wavelet with four vanishing moments ("sym4"
). By
default, dlmodwt
uses periodic boundary extension and computes the
MODWT to the maximum level. dlmodwt
requires Deep Learning Toolbox™.
[___] = dlmodwt(___,
specifies options using one or more name-value arguments in addition to the input arguments
in previous syntaxes. For example, Name=Value
)BOUNDARY="periodic"
specifies periodic
extension at the boundary.
Examples
Deep Learning Maximal Overlap Discrete Wavelet Transform
Load the 23 channel Espiga3 EEG data set. The data is sampled at 200 Hz. There are 995 samples in each channel. The data set is arranged as a 995-by-23(-by-1) array.
load Espiga3
Store the signal in an unformatted deep learning array.
x = dlarray(Espiga3);
Obtain the MODWT and MRA of the data. Specify the data format as 'TCB'
.
[wt,mra] = dlmodwt(x,DataFormat='TCB');
Confirm that both wt
and mra
are unformatted dlarray
objects.
whos wt mra
Name Size Bytes Class Attributes mra 10x23x1x995 1830800 dlarray wt 10x23x1x995 1830800 dlarray
dims(wt)
ans = 0x0 empty char array
dims(mra)
ans = 0x0 empty char array
Plot the reconstruction based on the MRA. Compare with the original data set.
xrec = sum(mra); subplot(2,1,1) plot(Espiga3) title("Original EEG Dataset") subplot(2,1,2) plot(extractdata(squeeze(xrec))') title("MODWT MRA Reconstruction")
Input Arguments
x
— Input array
dlarray
object | numeric array
Input array, specified as an unformatted dlarray
(Deep Learning Toolbox), a
formatted dlarray
in 'CBT'
format, or a numeric
array.
If x
is a numeric array or an unformatted
dlarray
, x
must be compatible with the
'CBT'
format. You must specify the
'DataFormat'
as some permutation of 'CBT'
.
x
must have at least two samples along the time dimension.
Example: dlarray(cos(pi./[4;2]*(0:159)),'CTB')
and
dlarray(cos(pi./[4;2]*(0:159))','TCB')
both specify one batch
observation of a two-channel sinusoid in the 'CBT'
format.
Data Types: single
| double
Complex Number Support: Yes
Lo,Hi
— Orthogonal wavelet filters
numeric vectors |
dlarray
objects
Orthogonal wavelet filters used in the MODWT computation, specified as a pair of
even-length real-valued numeric vectors or unformatted dlarray
objects.
Lo
is the scaling (lowpass) filter, and Hi
is
the wavelet (highpass) filter. The wavelet manager wavemngr
designates orthogonal wavelets as type 1 wavelets.
Valid built-in orthogonal wavelet families are: Best-localized Daubechies
("bl"
), Beylkin ("beyl"
), Coiflets
("coif"
), Daubechies ("db"
), Fejér-Korovkin
("fk"
), Haar ("haar"
), Han linear-phase moments
("han"
), Morris minimum-bandwidth ("mb"
),
Symlets ("sym"
), and Vaidyanathan ("vaid"
). For a
list of wavelets in each family, see wfilters
. You can also use waveinfo
with the wavelet family short name. For example,
waveinfo("db")
. Use wavemngr("type",wn)
to
determine if the wavelet wn
is orthogonal (returns 1). For example,
wavemngr("type","db6")
returns 1.
If you have Lo
and Hi
as numeric vectors,
you can use isorthwfb
to determine orthogonality: [tf,checks] = isorthwfb(Lo,Hi)
.
If unspecified, Lo
and Hi
default to:
[~,~,Lo,Hi] = wfilters("sym4")
.
Note
You can specify a pair of empty inputs for Lo
and
Hi
. In this case, the dlmodwt
function
uses the default filters. For example, dlmodwt(x,[],[])
is
equivalent to dlmodwt(x)
. For more information, see Version
History.
Data Types: single
| double
level
— Transform level
floor(log2(T))
, where T
is the
size of x
along the time dimension (default) | positive integer
Transform level of the MODWT, specified as a positive integer less than or equal to
floor(log2(T))
, where T
is the size of
x
along the time dimension. If unspecified,
dlmodwt
computes the MODWT down to level
floor(log2(T))
.
Data Types: single
| double
Name-Value Arguments
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.
Example: w = dlmodwt(x,DataFormat='TCB')
specifies the data format as
'TCB'
.
BOUNDARY
— Extension method
"periodic"
(default) | "reflection"
Extension method to apply at the boundary in the computation of the MODWT, specified as one of these:
"periodic"
— Extend signal periodically"reflection"
— Extend signal by reflection. The function computes the MODWT using a reflected signal along theT
dimension twice the original length ofx
. The MODWT transform coefficients are also twice the length of the input.
Example: w = dlmodwt(x,DataFormat="TCB",BOUNDARY="reflection")
extends the signal by reflection.
DataFormat
— Data format of input
character vector | string scalar
Data format of input x
, specified as some permutation of
'CBT'
. This argument is valid only if x
is
unformatted.
Each character in this argument must be one of these labels:
C
— ChannelB
— BatchT
— Time
The dlmodwt
function accepts any permutation of
'CBT'
. Each element of the argument labels the matching dimension
of x
.
Example: w = dlmodwt(x,DataFormat="BCT")
specifies the data
format of the unformatted dlarray
object as
"BCT"
.
Data Types: char
| string
Output Arguments
w
— Maximal overlap discrete wavelet transform
formatted dlarray
object | unformatted dlarray
object
Maximal overlap discrete wavelet transform of x
, returned as a
'SCBT'
formatted dlarray
. w
contains the wavelet coefficients and final-level scaling coefficients of
x
. The MODWT partitions the energy of the signal across the
various scales and scaling coefficients. For more information, see modwt
.
The size of w
depends on the boundary extension method used in
the computation of the MODWT.
If the signal is extended periodically, then
w
islevel
+1-by-C
-by-B
-by-T
.If the signal is extended by reflection, then
w
islevel
+1-by-C
-by-B
-by-2×T
.
level
is the transform level of the MODWT.
C
and B
correspond to the channel and batch
dimensions, respectively. The kth row of w
contains the wavelet coefficients for the kth level. The
(level
+1)th row of w
contains the
approximation coefficients.
If you specify 'DataFormat'
, w
is an
unformatted dlarray
.
mra
— Multiresolution analysis
formatted dlarray
object | unformatted dlarray
object
Multiresolution analysis of the MODWT of x
, returned as a
'SCBT'
formatted dlarray
. mra
contains the projections of x
onto wavelet subspaces and a scaling
space. For more information, see modwtmra
.
mra
is
level
+1-by-C
-by-B
-by-T
,
where level
is the transform level of the MODWT. The
kth row of mra
contains the details for the
kth level. The (level
+1)th row of
mra
contains the level
th level
smooth.
If you specify 'DataFormat'
, mra
is an
unformatted dlarray
compatible with 'SCBT'
format.
To learn more about the differences between the MODWT and the MRA, see Comparing MODWT and MODWTMRA.
Extended Capabilities
GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.
The dlmodwt
function
fully supports GPU arrays. To run the function on a GPU, specify the input data as a gpuArray
(Parallel Computing Toolbox). For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).
Version History
Introduced in R2022aR2022b: dlmodwt
behavior change
You can now specify a pair of empty inputs for the lowpass and highpass filters. The
dlmodwt
function continues to generate an error if one filter input
is empty and the other filter input is nonempty.
Functionality | Previous Behavior | New Behavior |
---|---|---|
w = dlmodwt(x,[],[])
| Errors | w = dlmodwt(x,[],[]) is equivalent to w = dlmodwt(x) |
w = dlmodwt(x,[],[],level) | Errors | w = dlmodwt(x,[],[],level) is equivalent to w =
dlmodwt(x,Lo,Hi,level) ,where [~,~,Lo,Hi] =
wfilters('sym4') |
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