# Want to Understand Convolution

Started by July 12, 2003
```I've looked at the equations for convolution and correlation and, yes,
I can work them. And I've heard that common illustration of clapping
your hands in an echo chamber. But I just can't get my brain around
just what it happening there.

Anyone know of a book giving a good intuitive grasp of convolution,
preferably with lots of handwaving, examples, and problems?

Cheers,
Wendell
```
```"Wendell" <wende598@yahoo.com> wrote in message
> I've looked at the equations for convolution and correlation and, yes,
> I can work them. And I've heard that common illustration of clapping
> your hands in an echo chamber. But I just can't get my brain around
> just what it happening there.
>
> Anyone know of a book giving a good intuitive grasp of convolution,
> preferably with lots of handwaving, examples, and problems?

I just found some neat stuff with Google:

http://www.jhu.edu/~signals/index.html

Leon
--
Leon Heller, G1HSM
leon_heller@hotmail.com
http://www.geocities.com/leon_heller

```
```In article c398b566.0307120705.4d47ff86@posting.google.com, Wendell at
wende598@yahoo.com wrote on 07/12/2003 11:05:

> I've looked at the equations for convolution and correlation and, yes,
> I can work them. And I've heard that common illustration of clapping
> your hands in an echo chamber. But I just can't get my brain around
> just what it happening there.

can you or have you gotten your brain around discrete-time convolution?
also, are you okay with the basic definition of a linear system (i.e.
superposition)?  (time-invariancy is actually an option here, but might be
nice to check out.)  that's a lot easier to understand and then to get to
the concept of continuous-time convolution, which requires all that fracas
about the direc impulse.  the impulse function in the discrete-time world is
easiest nontrivial function to get one's brain around:

{ 0     n not = 0
d[n] = {
{ 1     n = 0

now, do you understand how *any* arbitrary discrete-time function can be
constructed from adding up time-shifted and scaled impulses:

+inf
x[n] =  SUM{ x[k] * d[n-k] }
k=-inf

now ram that summation through a linear system and you get the Convolution
Summation which is the discrete-time counterpart to the Convolution Integral
in the continuous-time context.

that wasn't too hard, was it?

r b-j

```
```Hi Wendell,

> a book giving a good intuitive
> grasp of convolution,

I highly recommend "Understanding Digital Signal Processing" by Richard

Also, for less math and some really _good_ handwaving, there's "The
Scientist and Engineer's Guide to Digital Signal Processing" by  Steven W.
Smith. Dr. Smith has very kindly placed his book online at www.dspguide.com.

HTH

Rick Armstrong