Using chaos to characterise tape noise

In a magnetic recording tape, noise due to the medium itself, independent of the level of any signal carried by the tape, is often treated as being random. Such additive (signal-independent) noise will obey Poisson statistics. In order to study complicated time series of dynamical systems it is common practice to reconstruct the phase space of the system. The state of a system may be specified uniquely at any instant in time by a point in F-dimensional phase space, where F is the number of independent variables of the system, and the independent variables form the base vectors of the space. The evolution of the system in time is represented by the evolution of its trajectory in phase space, where each point on the trajectory (or attractor) gives the instantaneous value of each of the independent state variables. The system's attractor may be quantified in a number of ways. For this study we have chosen three measures, for each of which easily-implementable algorithms exist. These measures are: (i) Lyapunov exponent; (ii) entropy; and (iii) fractal dimension. Each of these quantifiers is defined and computed values for a number of tape systems are presented.<>