Stationary Processes Made Simple (and Audible)
Author: Alex Ness
Faculty Supervisor: Anandamayee Majumdar
Department: Mathematics
A stationary process is a special type of random function, in which the randomness is "shift invariant." Informally, if you extract slices of a stationary process at different times, each slice will show the same average value, spread, and interdependence of the process. Stationary processes are fundamental models in applied mathematics, in fields as diverse as econometrics, geostatistics, and audio signal processing.
In our project, we develop a fully discrete, algebraic model for stationary process theory. Our model is simple. It is accessible to students with some background in matrix algebra, Fourier transforms, and probability, without requiring graduate-level mathematics. Our model is also useful, especially as a foundation for simulation algorithms. We demonstrate its utility with audio simulations of stationary processes. We show that the property of stationarity is not just symbolic and graphical, but also audible.
Our project is designed to appeal to students who are curious about random processes. It may also interest scientists and engineers whose work involves the spectral analysis of stationary signals. Last but not least, the audio demonstrations will interest anyone who wants to hear how a random function sounds.