A convolution formula for time-invariant linear communication systems

For every linear and time-invariant time-discrete (communication) system T : l(infinity) --> l(infinity), formally, the following convolution formula can be derived: (Tf)(n) = Sigma(k is an element of Z) h(n - k)f(k), n is an element of Z, f is an element of l(infinity), where h = T delta is the delta impulse response. This paper is concerned with the question under which assumptions linear an d time-invariant time-discrete systems T : l(infinity) --> l(infinity) can be characterized by this formula. For this purpose we derive a convolution formula in a more general situatio n which also leads to a well-known convolution formula in the time-continuo us case. Copyright (C) 1999 John Wiley & Sons, Ltd.