Want to Understand Convolution

Started by Wendell 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
news:c398b566.0307120705.4d47ff86@posting.google.com...
> 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 Lyons. It's a fun read. 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 (reply address is bogus)