Let's summarize this way of understanding how a system changes an input
signal into an output signal. First, the input signal can be decomposed into a
set of impulses, each of which can be viewed as a scaled and shifted delta
function. Second, the output resulting from each impulse is a scaled and shifted
version of the impulse response. Third, the overall output signal can be found
by adding these scaled and shifted impulse responses. In other words, if we
know a system's impulse response, then we can calculate what the output will
be for any possible input signal. This means we know every thing about the
system. There is nothing more that can be learned about a linear system's
characteristics. (However, in later chapters we will show that this information
can be represented in different forms).
The impulse response goes by a different name in some applications. If the
system being considered is a filter, the impulse response is called the filter
kernel, the convolution kernel, or simply, the kernel. In image processing,
the impulse response is called the point spread function. While these terms
are used in slightly different ways, they all mean the same thing, the signal
produced by a system when the input is a delta function.