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Definitions:
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\textit{Transfer function}: \ \ \ H 
\newline f(x,y) \ \ \ \ \ is the picture 
\newline h(x,y) \ \ \ \ is linear invariant operator on f 
\newline H(u,v) \ \ \ is Fourier transform of h

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$g=h\ast f$ \qquad $G=H\circ F$ \qquad g is processed picture

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\textit{Impulse Response Function}:

h(x,y) = response when picture is a delta function

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\textit{Point Spread function}

Fourier transform of impulse response

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FIR: finite impulse response filter

delta function $\rightarrow $ finite number of points

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IIR: infinite impulse response filter

delta function $\rightarrow $ all the pixels of the picture.

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e.g.

Fourier space

recursive filter

$g_{n}^{\prime}=(1-\alpha )g_{n-1}^{\prime} +\alpha g_n$

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