Title :
Sample cumulants of stationary processes: asymptotic results
Author :
Fonollosa, José A R
Author_Institution :
ETSE Telecomunicacio, Univ. Politecnica de Catalunya, Barcelona, Spain
fDate :
4/1/1995 12:00:00 AM
Abstract :
In this paper, we present the formulas of the covariances of the second-, third-, and fourth-order sample cumulants of stationary processes. These expressions are then used to obtain the analytic performance of FIR system identification methods as a function of the coefficients and the statistics of the input sequence. The lower bound in the variance is also compared for different sets of sample statistics to provide insight about the information carried by each sample statistic. Finally, the effect that the presence of noise has on the accuracy of the estimates is studied analytically. The results are illustrated graphically with plots of the variance of the estimates as a function of the parameters or the signal-to-noise ratio. Monte Carlo simulations are also included to compare their results with the predicted analytic performance
Keywords :
Gaussian noise; covariance analysis; higher order statistics; parameter estimation; sequences; signal sampling; transient response; FIR system identification methods; Gaussian noise; Monte Carlo simulations; analytic performance; asymptotic results; coefficients; covariances; fourth-order sample cumulants; input sequence; lower bound; parametric methods; sample statistics; second-order sample cumulants; signal processing; signal-to-noise ratio; stationary processes; statistics; third-order sample cumulants; variance; Finite impulse response filter; Gaussian noise; Higher order statistics; Performance analysis; Performance evaluation; Phase estimation; Predictive models; Signal to noise ratio; Statistical analysis; System identification;
Journal_Title :
Signal Processing, IEEE Transactions on
