Fast algorithms for Brownian matrices

Brownian motion is one of the most common models used to represent nonstationary signals. The covariance matrix of a discrete-time Brownian motion has a very particular structure, and is called a Brownian matrix. This note presents a number of results concerning linear problems appearing in digital signal processing with Brownian matrices. In particular, it is shown that fast algorithms used for Toeplitz matrices are simpler and faster for Brownian matrices. Examples are given to illustrate the different results presented in the note.