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On the convolution of signals with finite energy and relations to the behaviour of the low pass

: Boche, H.; Schreiber, H.


Electrical engineering 81 (1998), Nr.4, S.263-270
ISSN: 0003-9039
ISSN: 0948-7921
Fraunhofer HHI ()
convolution; low-pass filters; signals convolution; finite energy; low pass behaviour; causal variant; energy norm; finite energy input signal; infinite energy output signal; low pass filter

In this paper the behaviour of the causal variant of the ideal low-pass is investigated. It is shown that this system is not stable with respect to the energy norm. An input signal with finite energy is given in the paper such that the output signal has an infinite energy. This result solves a problem proposed by Professor Mathis.