# Convolution in Contious Linear Time Invariant System

1. Jan 21, 2010

### N.Saravanan

Dear Experts,
For convolution to work any input signal we should be able to represent the input signal in terms of appropriately scaled and shifted unit impulses. This one holds good for discrete time system in which the input signal can be represented as sum of scaled shifted unit impulses. But is it possible to represent an analog input signal as sum of scaled and shifted unit impulse. If so how? Why I ask is unlike in discrete system for which the unit impulse has no width, the practical unit impulse in analog system has negligible width. The unit impulse signal raises to value 1 from 0 in a very short time interval and falls back to zero again. Sum of scaled and shifted unit impulses repeat this action at a faster rate. So if we represent an analog input signal by scaled and shifted unit impulses the representation is actually a signal which touches the zero axis at intermediate intervals. But the original input analog signal need not touch the zero axis. So won't the signal approximation in continuous time produce a distorted input signal. So if we convolve this distorted zero touching input signal will we get the actual response of a system to any input? Kindly please explain the concept.

Thank You,
N.Saravanan.

Last edited by a moderator: Jan 21, 2010