TABLE OF CONTENTS The preceding analyses of properties of random signals are focused upon estimating the first- and second-order stochastic characteristics of time series and their spectral density composition. More detailed information about a time series can be obtained if the time series itself can be modeled. In addition, its power spectrum can be obtained from the model. This approach has been given increased emphasis in engineering during the last several decades with new algorithms being developed and many useful applications appearing in books and journal publications.
Basically the concept is to model the signal using the principles of causal and stable discrete time systems as studied in Chapter 6. Recall that in the time domain the input, x( n), and output, y( n), of a system are related by
| (8.1) |  |
In signal modeling the output function is known. From what principle does the input function arise? As was learned in Chapter 6, a system can, when the input is white noise, create an output with properties of other random signals. Thus the properties of y( n) depend on the variance of the white noise, the parameters a(i) and b(l), the autoregressive order p, and the moving average order q. This approach is called parametric signal modeling. Because equation 8.1 also defines an autoregressive-moving average model, the approach is synonymously called ARMA( p,q) modeling. Also recall that if the system's parameters and input are known, the power...
