### Abstract

Given (n + 1) consecutive autocorrelations of a stationary discrete-time stochastic process, one interesting question is how to extend this finite sequence so that the power spectral density associated with the resulting infinite sequence of correlations is nonnegative everywhere. It is well known that when the Hermitian Toeplitz matrix generated from the given correlations is positive-definite the problem has an infinite number of solutions and the particular solution that maximizes entropy results in a stable all-pole model of order n. Since maximization of entropy is equivalent to maximization of the minimum mean square error associated with one-step predictors, the problem of obtaining admissible extensions that maximize the minimum mean square error associated with k-step (k ≤ n) predictors, which are compatible with the given correlations, is studied. It is shown that the resulting spectrum corresponds to that of a stable ARMA (n, k-1) process. The details of this particular extension method are worked out for a two-step predictor.

Original language | English (US) |
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Title of host publication | ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings |

Publisher | Publ by IEEE |

Pages | 2619-2622 |

Number of pages | 4 |

Volume | 5 |

State | Published - 1990 |

Event | 1990 International Conference on Acoustics, Speech, and Signal Processing: Speech Processing 2, VLSI, Audio and Electroacoustics Part 2 (of 5) - Albuquerque, New Mexico, USA Duration: Apr 3 1990 → Apr 6 1990 |

### Other

Other | 1990 International Conference on Acoustics, Speech, and Signal Processing: Speech Processing 2, VLSI, Audio and Electroacoustics Part 2 (of 5) |
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City | Albuquerque, New Mexico, USA |

Period | 4/3/90 → 4/6/90 |

### Fingerprint

### ASJC Scopus subject areas

- Signal Processing
- Electrical and Electronic Engineering
- Acoustics and Ultrasonics

### Cite this

*ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings*(Vol. 5, pp. 2619-2622). Publ by IEEE.

**Generalization of maximum entropy spectrum extension method.** / Pillai, Unnikrishna.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings.*vol. 5, Publ by IEEE, pp. 2619-2622, 1990 International Conference on Acoustics, Speech, and Signal Processing: Speech Processing 2, VLSI, Audio and Electroacoustics Part 2 (of 5), Albuquerque, New Mexico, USA, 4/3/90.

}

TY - GEN

T1 - Generalization of maximum entropy spectrum extension method

AU - Pillai, Unnikrishna

PY - 1990

Y1 - 1990

N2 - Given (n + 1) consecutive autocorrelations of a stationary discrete-time stochastic process, one interesting question is how to extend this finite sequence so that the power spectral density associated with the resulting infinite sequence of correlations is nonnegative everywhere. It is well known that when the Hermitian Toeplitz matrix generated from the given correlations is positive-definite the problem has an infinite number of solutions and the particular solution that maximizes entropy results in a stable all-pole model of order n. Since maximization of entropy is equivalent to maximization of the minimum mean square error associated with one-step predictors, the problem of obtaining admissible extensions that maximize the minimum mean square error associated with k-step (k ≤ n) predictors, which are compatible with the given correlations, is studied. It is shown that the resulting spectrum corresponds to that of a stable ARMA (n, k-1) process. The details of this particular extension method are worked out for a two-step predictor.

AB - Given (n + 1) consecutive autocorrelations of a stationary discrete-time stochastic process, one interesting question is how to extend this finite sequence so that the power spectral density associated with the resulting infinite sequence of correlations is nonnegative everywhere. It is well known that when the Hermitian Toeplitz matrix generated from the given correlations is positive-definite the problem has an infinite number of solutions and the particular solution that maximizes entropy results in a stable all-pole model of order n. Since maximization of entropy is equivalent to maximization of the minimum mean square error associated with one-step predictors, the problem of obtaining admissible extensions that maximize the minimum mean square error associated with k-step (k ≤ n) predictors, which are compatible with the given correlations, is studied. It is shown that the resulting spectrum corresponds to that of a stable ARMA (n, k-1) process. The details of this particular extension method are worked out for a two-step predictor.

UR - http://www.scopus.com/inward/record.url?scp=0025593241&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0025593241&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0025593241

VL - 5

SP - 2619

EP - 2622

BT - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings

PB - Publ by IEEE

ER -