Use convolution to find a reference audio sample in a continuous stream of sound

Here we go for the bounty :)

To find a particular reference signal in a larger audio fragment, you need to use a cross-correlation algorithm. The basic formulae can be found in this Wikipedia article.

Cross-correlation is a process by which 2 signals are compared. This is done by multiplying both signals and summing the results for all samples. Then one of the signals is shifted (usually by 1 sample), and the calculation is repeated. If you try to visualize this for very simple signals such as a single impulse (e.g. 1 sample has a certain value while the remaining samples are zero), or a pure sine wave, you will see that the result of the cross-correlation is indeed a measure for for how much both signals are alike and the delay between them. Another article that may provide more insight can be found here.

This article by Paul Bourke also contains source code for a straightforward time-domain implementation. Note that the article is written for a general signal. Audio has the special property that the long-time average is usualy 0. This means that the averages used in Paul Bourkes formula (mx and my) can be left out. There are also fast implementations of the cross-correlation based on the FFT (see ALGLIB).

The (maximum) value of the correlation depends on the sample values in the audio signals. In Paul Bourke's algorithm however the maximum is scaled to 1.0. In cases where one of the signals is contained entirely within another signal, the maximum value will reach 1. In the more general case the maximum will be lower and a threshold value will have to be determined to decide whether the signals are sufficiently alike.

Instead of a convolution you should use a correlation. The size of the correlation peak tells you how much both signals are alike, the position of the peak their relative position in time, or the delay between both signals.