Sampling dynamical systems

Linear dynamical systems are widely used in many different fields from engi neering to economics. One simple but important class of such systems is cal led the single-input transfer function model, Suppose that: all variables o f the system are sampled for a period using a fixed sample rate. The centra l issue of this paper is the determination of the smallest sampling rate th at will yield a sample that will allow the investigator to identify the dis crete-time representation of the system. A critical sampling rate exists th at will identify the model, This rate, called the Nyquist rate, is twice th e highest frequency component of the system. Sampling at a lower rate will result in an identification problem that is serious. The standard assumptio ns made about the model and the unobserved innovation errors in the model p rotect the investigators from the identification problem and resulting bias es of undersampling. The critical assumption that is needed to identify an undersampled system is that at least one of the exogenous time series be wh ile noise.