### Citations

643 |
Linear prediction: A tutorial review,”
- Makhoul
- 1975
(Show Context)
Citation Context ... a formidable task, due to the presence of the non-linear parameters sk. Of course this depends on the explicit functional form of y(s; c), but even in the relatively simple exponential modeling case =-=[15]-=- (yt(s; c) = cest ,) the algorithms – which are necessarily iterative in nature — are plagued with convergence problems and yield local minima rather than the global one. This explains the need for an... |

450 |
Interpolation and Approximation,
- Davis
- 1975
(Show Context)
Citation Context ...ll sk are different iii) linear independence i.e. if all sk are different then ∑ nk=1 y(sk; ck) = 0 implies that all ck are vanishing. Requirement iii is closely related to the concept of unisolvency =-=[14]-=-. The assumption of noiseless data is highly unrealistic and therefore a better formulation is : n∑ v = y(sk; ck) + η (2) k=1 with η representing the noise vector, which is supposed to be white, zero-... |

149 |
Spectrum analysis – a modern perspective”,
- Kay, Marple
- 1981
(Show Context)
Citation Context ...matically with the advent of the Singularity Expansion Method (SEM) [2] and Prony’s method was in some sense rediscovered [3]. Of course, the modern versions of the technique, called ’extended Prony’ =-=[4]-=- or ’semi least-squares’ [5] method,bear little resemblance to Prony’s original approach. In addition, numerous other rational modeling techniques, iterative or non-iterative, in time or frequency do... |

30 |
Fast Algorithms for Multivariable Systems
- Morf
- 1974
(Show Context)
Citation Context ...endix B) to be equivalent with the Cholesky decomposition of the inverse of the Grammian G, what makes it possible to consider the use of such tools as fast Cholesky decomposition and lattice filters =-=[16]-=-. 9Minimization with quadratic constraint The solution vector is the normalized eigenvector corresponding with the minimum eigenvalue of the Grammian G. Note that the explicit functional form of y(s;... |

27 |
A Technique for Extracting the Poles and Residues of a System Directly from its Transient Response
- Blaricum, Mittra
- 1975
(Show Context)
Citation Context ...resenting the impulse response. Interest in rational modeling schemes rose dramatically with the advent of the Singularity Expansion Method (SEM) [2] and Prony’s method was in some sense rediscovered =-=[3]-=-. Of course, the modern versions of the technique, called ’extended Prony’ [4] or ’semi least-squares’ [5] method,bear little resemblance to Prony’s original approach. In addition, numerous other rat... |

18 |
Design of a Self-Optimizing Control System
- Kalman
- 1958
(Show Context)
Citation Context ...function, but on the implicitly defined form expressed by this functional equation. In order to carry out this programme, a formulation in terms of the Kalman equation error concept is necessary [12]-=-=[13]-=-. Section 2 formulates the modeling problem and introduces the error and Mean Squared Error (MSE) concept. Section 3 introduces the basic functional equation, the Kalman equation error and the Mean Sq... |

13 | Best Least-Squares Representation of Signals by Exponentials - McDonough, Huggins - 1968 |

10 |
Emerging technology for transient and broad-band analysis and synthesis ol antennas and scatterers
- BAUM
- 1976
(Show Context)
Citation Context ...a weighted sum of exponentials in the time domain, representing the impulse response. Interest in rational modeling schemes rose dramatically with the advent of the Singularity Expansion Method (SEM) =-=[2]-=- and Prony’s method was in some sense rediscovered [3]. Of course, the modern versions of the technique, called ’extended Prony’ [4] or ’semi least-squares’ [5] method,bear little resemblance to Pron... |

6 |
Parametric Modeling of Transient Electromagntic Systems
- Dudley
- 1979
(Show Context)
Citation Context ...y’s original approach. In addition, numerous other rational modeling techniques, iterative or non-iterative, in time or frequency domain, exist and have been extensively treated in the literature [6]-=-=[10]-=-. The final justification of the rational modeling approach is the fact that the SEM-poles or natural frequencies of a given scatterer are aspect and illumination independent, which makes them highly ... |

3 |
Essai experimental et analytique, etc
- Prony
(Show Context)
Citation Context ...INTRODUCTION Modeling a waveform by a linear combination of basis functions containing a variable parameter, is not a new problem. Already by the end of the 18th century Gaspard Riche, Baron de Prony =-=[1]-=- was led to investigate the modeling of a function in terms of a linear combination of exponentials with different exponents, and proposed his celebrated method. One could say that this was the first ... |

3 |
Suboptimal approximation/identification of transient -wave forms from electromagnetic systems by pencil-of-function method
- Sarkar, Nebat, et al.
(Show Context)
Citation Context ...Prony’s original approach. In addition, numerous other rational modeling techniques, iterative or non-iterative, in time or frequency domain, exist and have been extensively treated in the literature =-=[6]-=--[10]. The final justification of the rational modeling approach is the fact that the SEM-poles or natural frequencies of a given scatterer are aspect and illumination independent, which makes them hi... |

2 |
Filter analysis by use of pencil of functions
- Jain
(Show Context)
Citation Context ... operator K has no evident nice properties, such as self-adjoint or unitary, which could reduce the computational burden associated with the Grammian G. However, introducing the reverse time integral =-=[17]-=-, we can reformulate the problem in a more appropriate manner : Ω = [0, ∞] (71) Kx = 1 (∫ t x(t 2 ′ )dt ′ ∫ t + x(t ′ )dt ′ ) (72) 0 ∞ K † = −K (73) u = Ku0 (74) s = 1/α (75) c = −d/α (76) The fact th... |

1 |
A discussion of various approaches to the identification/approximation problem
- Sarkar, Weiner, et al.
- 1982
(Show Context)
Citation Context ... the Singularity Expansion Method (SEM) [2] and Prony’s method was in some sense rediscovered [3]. Of course, the modern versions of the technique, called ’extended Prony’ [4] or ’semi least-squares’ =-=[5]-=- method,bear little resemblance to Prony’s original approach. In addition, numerous other rational modeling techniques, iterative or non-iterative, in time or frequency domain, exist and have been ex... |

1 | Equivalent circuit representation of radiation systems - Sharpe, Roussi - 1979 |

1 |
Waveform feature extraction based on Tauberian approximation
- Figueredo, Hu
- 1982
(Show Context)
Citation Context .... But not all waveforms can be interpreted as transients, and hence, depending on the physical content of any given problem, other than rational parametric models may be appropriate. For instance, in =-=[11]-=- a feature extraction procedure based on a Tauberian approximation is applied to a wide bandwidth radar return signal. By Tauberian approximation is meant a linear combination of shifted versions of a... |

1 |
A discussion of various approaches to the linear system identification problem
- Sarkar, Dianat, et al.
- 1984
(Show Context)
Citation Context ...asis function, but on the implicitly defined form expressed by this functional equation. In order to carry out this programme, a formulation in terms of the Kalman equation error concept is necessary =-=[12]-=--[13]. Section 2 formulates the modeling problem and introduces the error and Mean Squared Error (MSE) concept. Section 3 introduces the basic functional equation, the Kalman equation error and the Me... |