tailieunhanh - Digital Signal Processing Handbook P16

Linear parametric models of stationary random processes, whether signal or noise, have been found to be useful in a wide variety of signal processing tasks such as signal detection, estimation, filtering, and classification, and in a wide variety of applications such as digital | Tugnait . Validation Testing and Noise Modeling Digital Signal Processing Handbook Ed. Vijay K. Madisetti and Douglas B. Williams Boca Raton CRC Press LLC 1999 1999 by CRC Press LLC 16 Validation Testing and Noise Modeling Jitendra K. Tugnait Auburn University Introduction Gaussianity Linearity and Stationarity Tests Gaussianity Tests Linearity Tests Stationarity Tests Order Selection Model Validation and Confidence Intervals Order Selection Model Validation Confidence Intervals Noise Modeling Generalized Gaussian Noise Middleton Class A Noise Stable Noise Distribution Concluding Remarks References Introduction Linear parametric models of stationary random processes whether signal or noise have been found to be useful in a wide variety of signal processing tasks such as signal detection estimation filtering and classification and in a wide variety of applications such as digital communications automatic control radar and sonar and other engineering disciplines and sciences. A general representation of a linear discrete-time stationary signal x t is given by x t 2 h i e t i i 0 where e t is a zero-mean . independent and identically distributed random sequence with finite variance and h i i 0 is the impulse response of the linear system such that J2 œ h2 i 1. Much effort has been expended on developing approaches to linear model fitting given a single measurement record of the signal or noisy signal . Parsimonious parametric models such as AR autoregressive MA moving average ARMA or state-space as opposed to impulse response modeling have been popular together with the assumption of Gaussianity of the data. Define H q X h i q i where q 1 is the backward shift operator . q lx t x t 1 etc. . If q is replaced with the complex variable z then H z is the Z-transform of h i . it is the system transfer function. 1999 by CRC Press LLC Using maybe rewritten as x t H q e t . Fitting linear models to the .