Convolution helps to determine the effect a system has on an
input signal. It can be shown that a linear, time-invariant system is
completely characterized by its impulse response. At first
glance, this may appear to be of little use, since impulse
functions are not well defnied in real applications. however,
the sifting property of impulses tells us
that a signal can be decomposed into an infinite sum
(integral) of scaled and shifted impulses. By knowing how a
system affects a single impulse, and by understanding the way
a signal is comprised of scaled and summed impulses, it seems
reasonable that it should be possible to scale and sum the
impulse responses of a system in order to deteremine what
output signal will results from a particular input. This is
precisely what convolution does - * convolution
determines the system's output from knowledge of the input
and the system's impulse response*.

In the rest of this module, we will examine exactly how convolution is defined from the reasoning above. This will result in the convolution integral (see the next section) and its properties. These concepts are very important in Electrical Engineering and will make any engineer's life a lot easier if the time is spent now to truly understand what is going on.

In order to fully understand convolution, you may find it useful to look at the discrete-time convolution as well. It will also be helpful to experiment with the applets available on the internet. These resources will offer different approaches to this crucial concept.