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DiscreteConvolve

The option Circular→True (the default) returns a circular convolution result that has the same dimensions as img.
The option Circular→False returns a linear convolution result. The dimensions of the result are larger than the dimensions of original data. Assuming img is of dimensions Nr × Nc and h is of dimensions Mr × Mc, the returned result is of dimensions Nr+Mr-1 × Nc+Mc-1.
TransientSamples → False returns the steady-state samples only.
The option Centered positions the steady-state output values in the output array.
The option Centered only takes effect if Circular → True.
The option Centered → False places all the transient samples at the beginning of the output array. Specifically, element {1,1,...} of the result contains img1,1,... h1,1,..., and element {-1,-1,...} of the result contains img-1,-1,... h1,1,....
The option Centered → True (default) evenly distributes the transient samples at the beginning and end of the output array. Specifically, element {1,1,...} of the result contains , and element {-1,-1,...} of the result contains .
The argument img may be a vector, matrix, or ImageData expression.
The argument ker may be a vector or matrix.
The ArrayDepth of ker and the raw image data in img must be equal.
See also User's Guide 5.2.

Examples

This loads the package.
In[1]:=
This defines a 1D signal sig and an impulse response ker.
In[2]:=
This returns a circular convolution result.
In[3]:=
Out[3]//TableForm=Out[3]//TableForm=
This returns a linear convolution result.
In[4]:=
Out[4]//TableForm=Out[4]//TableForm=
This returns the steady-state values only (note that this result is independent of option Circular).
In[5]:=
Out[5]//TableForm=Out[5]//TableForm=
Here we blur a picture by convolving with a moving average filter. First we define the filter and load an example image.
In[6]:=
In[7]:=
Here we display the original and blurred images.
In[8]:=
Out[8]=Out[8]=


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