ABSTRACT
We are interested in constructing a stochastic model for the signal s(t), which represents air pressure as a function of time while music is being played. This relatively simple example will provide a good introduction into the basic ideas of Pattern Theory for variables with continuous values. Except for one digression in Section 2.4, we are not concerned about the mathematical details of modeling stochastic processes of continuous time, so we always assume the sound signal has been discretely sampled. A typical piece of data might be given with a sampling interval Δt = 1/8000 seconds,1 so that if five seconds of data are considered, we have a sequence of real numbers sk = s(kΔt), 1 ≤ k ≤ 40, 000, and we want a stochastic model for this finite-dimensional piece of data.
