ndwt performs a multilevel
1-D nondecimated wavelet decomposition using either a particular
wavelet ('wname') or the wavelet filters
you specify. The decomposition also uses the specified DWT extension
mode (see dwtmode).

WT = ndwt(X,N,'wname') returns
a structure which contains the non-decimated wavelet transform of
the vector X at the level N.N is
a positive integer, and 'wname' is a string
containing the wavelet name. The default default extension mode is'sym'.
For more information on wname, see wfilters.

WT = ndwt(X,N,'wname','mode','ExtM') uses
the extension mode specified in the string 'ExtM'.

WT is a structure with the fields shown in
the table.

Instead of a wavelet you can specify four filters (two for decomposition
and two for reconstruction).

WT = ndwt(X,N,WF,...) specifies four filters
(two for decomposition and two for reconstruction) instead of a wavelet
name. WF is a 1-by-4 cell array {LoD,HiD,LoR,HiR} or
a structure with the four fields 'LoD', 'HiD', 'LoR', 'HiR'.

rowvect

Logical value which is true if X is
a row vector

level

Level of the decomposition

mode

Name of the wavelet transform extension mode

filters

Structure with 4 fields, LoD, HiD, LoR,
and HiR, which contain the filters used for DWT

dec

1 by (level+1) cell array containing
the coefficients of the decomposition. dec{1} contains
the coefficients of the approximation and dec{j} (j
= 2 to level+1), contains the coefficients
of the detail of level (level+1-j)

longs

1 by (level+2) vector containing the
lengths of the components. longs is defined as
(where N is the level)

Use fine-scale nondecimated wavelet transform
coefficients to localize a discontinuity.

Create signal consisting of a 1/2–hz sine wave
sampled at 1 kHz with discontinuities at 0.3 and 0.72 seconds.

t = linspace(0,1,1000);
x = 4*sin(4*pi*t);
x = x - sign(t - .3) - sign(.72 - t);
plot(t,x); xlabel('t'); ylabel('x');
grid on;

Obtain the nondecimated wavelet transform of the input
signal down to level 4 using the Daubechies extremal phase wavelet
with 2 vanishing moments and the default whole-point symmetric extension
mode. Reconstruct a signal approximation based on the level-one wavelet
coefficients.

W = ndwt(x,4,'db2','mode','per');
d1 = indwt(W,'d',1);

Plot the original signal and the signal approximation
to visualize how the wavelet coefficients localize the discontinuities.

Specify an extension mode different from the
default whole-point symmetric extension.

Load the freqbrk signal and obtain
the nondecimated wavelet transform down to level 4 using the Daubechies
extremal phase wavelet with 2 vanishing moments. Use the periodic
extension mode.

load freqbrk;
W = ndwt(freqbrk,4,'db2','mode','per');

Specify the decomposition and reconstruction
filters as a cell or structure array.

Obtain the decomposition and reconstruction filters for
the biorthogonal spline wavelet with 3 vanishing moments in the reconstruction
wavelet and 5 vanishing moments in the decomposition wavelet. Create
a cell array with the scaling and wavelet filters and analyze the freqbrk signal.