Bootstrap analysis of polynomial amplitude and phase signals

In many areas where it is desirable to be able to estimate the form and parameters of an observed AM/FM signal existing procedures require that assumptions must be made of the distribution of the noise or the form of the signal. This paper presents procedures for estimating both the model order and confidence limits for the coefficients of signals whose amplitude and phase are polynomials. The procedures are formulated using minimal assumptions. Simulations run using the presented procedures show that they quite accurately estimate the parameters when the signal to noise ratio is high.

[1]  B. Efron.  Bootstrap Methods: Another Look at the Jackknife , 1979 .

[2]  B. Efron.  Nonparametric standard errors and confidence intervals , 1981 .

[3]  B. Efron.  Better Bootstrap Confidence Intervals , 1987 .

[4]  Petar M. Djuric,et al.  Parameter estimation of chirp signals , 1990, IEEE Trans. Acoust. Speech Signal Process..

[5]  R. Tibshirani,et al.  An introduction to the bootstrap , 1993 .

[6]  D. R. Iskander,et al.  Instantaneous frequency estimation: confidence bounds using the bootstrap , 1994, Proceedings of 1994 28th Asilomar Conference on Signals, Systems and Computers.

[7]  Benjamin Friedlander,et al.  The discrete polynomial-phase transform , 1995, IEEE Trans. Signal Process..

[8]  J. Shao.  Bootstrap Model Selection , 1996 .

[9]  Abdelhak M. Zoubir,et al.  Optimal selection of model order for a class of nonlinear systems using the bootstrap , 1997, 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[10]  Boualem Boashash,et al.  The bootstrap and its application in signal processing , 1998, IEEE Signal Process. Mag..

[11]  Boualem Boashash,et al.  The Bootstrap: Signal Processing Applications , 1998 .