Mathematica 9 is now available
Wolfram Mathematica Documentation Center
DOCUMENTATION CENTER SEARCH
Function Index /
Previous section-----Next section

InverseDiscreteWaveletTransform

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 ckj and dkj 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 cJ 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 h0, h1, h2, and h3 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]=Out[2]=
This computes the inverse wavelet transform and verifies invertibility.
In[3]:=
Out[3]=Out[3]=


Any questions about topics on this page? Click here to get an individual response.Buy NowMore Information
THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.