Insufficiencies of the practical BIBO stability concept with regard to signal processing systems

In this paper the practical BIBO stability concept introduced by Agathoklis and Bruton is analyzed with respect to its applicability in the field of signal processing applications. In the field of n-D signal processing signals are often bounded to all but one dimension like be the time-direction of a spatio-temporal signal, for instance. This property makes the use of systems which meet the conditions of practical BIBO stability, mainly known from the field of control theory, appear to be feasible. However, it can be shown hat practical stability in its original form is not sufficient in signal processing if not further conditions are supposed. This is done by comparing the 2D Fourier transform of the actually measured impulse response of exemplary systems to the frequency response expected on basis of the transfer function. Additionally, an application example is given to verify the presented observations.