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DOCUMENTATION CENTER SEARCH
Function Index
InverseDiscreteWaveletTransform
InverseDiscreteWaveletTransform[
coef
,
h
]
is the inverse discrete wavelet transform (IDWT) of
coef
,
using filter
h
.
The argument
coef
must be in the format of a nested list of wavelet coefficients (see
DiscreteWaveletTransform
).
InverseDiscreteWaveletTransform
uses Mallat's algorithm.
The 1D series form of the DWT is given by the following formula:
where
j
denotes the scale and
k
is the vector index. This operation is an upsampling operation followed by linear digital filtering. The coefficients c
_{k}
^{j}
and d
_{k}
^{j}
are known, respectively, as the level
j
scaling and wavelet coefficients. At scale
j
, the scaling and wavelet coefficients are combined to form the level j+1 scaling coefficients. The top-level sequence c
^{J}
represent the original signal. For a signal of length
N
, where
N
is a power of two, we get J=
Log
[
2,N
]. In such a case, the iteration may be repeated
J
times beginning with two one-sample-long sequences and ending with a sequence
N
samples long.
The 2D series formulation of the IDWT is given by
where the filters h
^{0}
, h
^{1}
, h
^{2}
, and h
^{3}
are formed by vector outer products of the quadrature mirror filters
h
and
g
(see
DiscreteWaveletTransform
).
See also User's Guide
8.6
.
Example
This loads the package.
In[1]:=
This creates a list of wavelet coefficients.
In[2]:=
Out[2]=
This computes the inverse wavelet transform and verifies invertibility.
In[3]:=
Out[3]=
THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.