**Holger Boche**

**Stabilitaetsverhalten der kausalen Variante des idealen Tiefpasses**

**The paper is published:**
Rostocker Mathematisches Kolloquium, Rostock. Math. Kolloq. 53, 111-123 (1999)

**MSC:**- 93A25 Input-output systems
- 93C62 Digital systems
- 94A12 Signal theory (characterization, reconstruction, etc.)

**Abstract:** 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. A construction of 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.

**Keywords:** *Input-output systems, Digital systems, Signal theory (characterization, reconstruction, etc.)*