Plot of the frequency response of the average filter:

$ h(k,l)=\frac{1}{16}\left[ \begin{array}{ccc}1& 2 & 1\\ 2 &4 &2 \\ 1 & 2 & 1 \end{array} \right] $

Averagefilterfrequencyresponse.png

Plot of the frequency response of the filter:

$ h(k,l)=\frac{1}{9}\left[\begin{array}{ccc}-1& -1 & -1\\ -1 &8 &-1 \\ -1 & -1 & -1 \end{array} \right] $ with $ \lambda = 0.5 $.

Edgedetectfilterfrequencyresponse.png

Plot of the frequency response of the filter:

$ h(k,l)=\frac{1}{9}\left[\begin{array}{ccc}-\lambda & -\lambda & -\lambda\\ -\lambda &9+8 \lambda & -\lambda \\ -\lambda & -\lambda & -\lambda \end{array} \right] $

Unsharpmaskfrequencyresponse.png

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Basic linear algebra uncovers and clarifies very important geometry and algebra.

Dr. Paul Garrett