Matrix Representation of Linear Systems Relationship

Considering the 1D linear shift-invariant system for simplicity, we have the input-output relationship given by the convolution integral.

• The limits depend upon causality, the nature of h (IIR, FIR), and whether the convolution desired is linear or circular.

• While causality is an inherent property of physical 1D signal processing systems, it is not always relevant in the 2D case as blurring typically occurs in all directions.

• The limits also depend on the reference origin chosen, whether at the sample or at the center of the signal.

h

f

g

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