Abstract
An identification procedure is proposed for a nonGaussian white-noise-driven, linear, time-invariant, nonminimum-phase FIR (finite-impulse response) system. The method is based on parametric modeling of the third moments of the output sequence and uses causal and anticausal autoregressive moving-average (ARMA) models. The magnitude and phase response of the system are expressed in terms of the AR parameters of the ARMA models. In particular, the AR part of the causal ARMA model captures the minimum-phase component of the system, and the AR part of the anticausal ARMA captures the maximum-phase component. Both sets of parameters are obtained by solving overdetermined linear systems of equations. A model-order-selection criterion based on third-order moments is proposed. The ARMA bispectrum approach is compared to more conventional approaches for magnitude and phase reconstruction. It is demonstrated that the proposed identification procedure exhibits improved modeling performance. The method does not require knowledge of the non-Gaussian noise distribution.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
Keywords
BispectrumOverdetermined systemAutoregressive–moving-average modelAutoregressive modelMathematicsSystem identificationWhite noiseParametric statisticsImpulse responseMoving averageAlgorithmApplied mathematicsComputer scienceStatisticsMathematical analysisData modeling
Affiliated Institutions
Related Publications
On estimating noncausal nonminimum phase ARMA models of non-Gaussian processes
The authors address the problem of estimating the parameters of non-Gaussian ARMA (autoregressive moving-average) processes using only the cumulants of the noisy observation. Th...
A unifying maximum-likelihood view of cumulant and polyspectral measures for non-Gaussian signal classification and estimation
Classification and estimation of non-Gaussian signals observed in additive Gaussian noise of unknown covariance are addressed using cumulants or polyspectra. By integrating idea...
Asymptotically optimal estimation of MA and ARMA parameters of non-Gaussian processes from high-order moments
A description is given of an asymptotically-minimum-variance algorithm for estimating the MA (moving-average) and ARMA (autoregressive moving-average) parameters of non-Gaussian...
Semiparametric ARCH Models
This article introduces a semiparametric autoregressive conditional heteroscedasticity (ARCH) model that has conditional first and second moments given by autoregressive moving ...
New criteria for blind deconvolution of nonminimum phase systems (channels)
A necessary and sufficient condition for blind deconvolution (without observing the input) of nonminimum-phase linear time-invariant systems (channels) is derived. Based on this...
Publication Info
- Year
- 1988
- Type
- article
- Volume
- 36
- Issue
- 4
- Pages
- 513-524
- Citations
- 72
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
72
OpenAlex
Cite This
C.L. Nikias
(1988).
ARMA bispectrum approach to nonminimum phase system identification.
IEEE Transactions on Acoustics Speech and Signal Processing
, 36
(4)
, 513-524.
https://doi.org/10.1109/29.1555
Identifiers
- DOI
- 10.1109/29.1555