Convolution principles:

- A signal can be decomposed into a group of components called impulses.

- An impulse is a signal composed of all zeros, except a single non-zero point.

- The delta function is a normalized impulse, that is, sample number zero has a value of one, while all other samples have a value of zero.

- The input signal can be decomposed into a set of impulses, each of which can be viewed as a scaled and shifted delta function.

- The output resulting from each impulse is a scaled and shifted version of the impulse response.

- The overall output signal can be found by adding these scaled and shifted impulse responses.
 

Filtering by convolution:

If the system being considered is a filter, the impulse response is called the filter kernel.

Here are examples using a 3k, 1k and 300Hz Low Pass filter kernels.
Notice (especially in the 300Hz example) how steep the slope of the filter can be using filtering by convolution.

3k LP kernel:           sonogram          soundfile

1k LP kernel:           sonogram          soundfile

300Hz LP kernel:      sonogram          soundfile
 

Here are these filter kernels convolved with an example soundfile:              sonogram          soundfile

3k LP convolved with voice:                   sonogram          soundfile

1k LP convolved with voice:                   sonogram          soundfile

300Hz LP convolved with voice:            sonogram          soundfile
 

"Stealing" Reverbs:

Being convolution a complete "inprint" of a system, we can give the properties of a certain system to any signal we want by simply convolving it with the impulse response of the system.
Using this idea we can very simply obtain impulse responses from all kinds of commercial digital processors no matter how sofisticated those devices might be.
By doing so we literally "steal" the most complex and expensive algorithms and apply them to the sound we are interested in.
Convolution does all that for us.

In these examples I took the impulse responses of a pretty popular digital reverberator called Alesis Quadraverb:

Quadraverb (small room) impulse response:                sonogram          soundfile

Quadraverb (large room) impulse response:                 sonogram          soundfile
 

Here are these impulse responses convolved with our example soundfile:

Quadraverb (small room) convolved with voice:             sonogram         soundfile

Quadraverb (large room) convolved with voice:             sonogram          soundfile
 

More creative and uncommon uses of convolution:

By taking impulses from natural occurring sounds around us we can really push the boundaries of convolution and create sounds that would not be possible
to be generated in reality but that don't sound synthetic and still have resemblance with the real phenomenon.
A bell, a door slam or a hit on a metal surface are all sounds that would fit succesfully the technique of convolution given their sharp attacks that make them very close to an impulse.

Bell:                                                  sonogram          soundfile

Bell convolved with voice:              sonogram          soundfile
 

String:                                              sonogram          soundfile

String convolved with voice:          sonogram          soundfile
 

Metal hit:                                         sonogram          soundfile

Metal hit convolved with voice:      sonogram          soundfile
 

Crash cymbal:                                            sonogram           soundfile

Crash cymbal convolved with voice:       sonogram           soundfile
 

In these last examples it's very difficult to think about convolution like we defined it at the beginning in terms of scaling shifting and adding delat functions, because the signals are very complex.
It's a lot easier to go to the frequency domain and think in terms of spectral intersection where the spectral characteristics of two sound are superimposed  one on the other.
By thinking in these terms it's easier to understand why the sonic results of a convolution process depends very much on the source sounds.
Impulses or impulse-like sounds work very well because they tend to have energy across the whole spectrum.
 
 

A wider library of sound and examples is available.
Please contact castelli@ccrma.stanford.edu if interested.