Identification of multivariable stochastic linear systems via spectral analysis given time-domain data

The simplicity of structure of chaotic systems, combined with the richness of their output, inspires their use in modeling efforts. On the other hand, the difficulty of their analysis warrants approximation methods, especially since the absence, by definition, of well-defined limit sets prohibits, in general, a meaningful linearization. In this work we present some results, which can support a methodology founded on spectral analysis for approximating chaotic systems via stochastic linear systems. The main contribution is the use of spectral moments for identifying the location of embedded limit cycles and the spectrum-based validation of approximations.

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Parameterized macromodeling of stochastic linear systems for frequency- and time-domain variability analysis

2018 IEEE 22nd Workshop on Signal and Power Integrity (SPI) ◽

10.1109/sapiw.2018.8401680 ◽

2018 ◽

Cited By ~ 2

Author(s):

Yinghao Ye ◽

Domenico Spina ◽

Giulio Antonini ◽

Tom Dhaene

Keyword(s):

Linear Systems ◽

Time Domain ◽

Variability Analysis ◽

Stochastic Linear Systems

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Investigation of Dispersion-Relation-Preserving Scheme and Spectral Analysis Methods for Acoustic Waves

Journal of Vibration and Acoustics ◽

10.1115/1.2889711 ◽

1997 ◽

Vol 119 (2) ◽

pp. 250-257 ◽

Cited By ~ 3

Author(s):

Florence O. Vanel ◽

Oktay Baysal

Keyword(s):

Spectral Analysis ◽

Boundary Conditions ◽

Time Domain ◽

Acoustic Waves ◽

Acoustic Wave Propagation ◽

Analysis Methods ◽

Time Domain Data ◽

Disturbance Source ◽

The Time Domain ◽

Tukey Method

Important characteristics of acoustic wave propagation are encoded in their dispersion relations. Hence, a computational algorithm, which attempts to preserve these relations, was investigated. Considering the linearized, 2-D Euler equations, simulations were performed to validate this scheme and its boundary conditions. The results were found to agree favorably with the exact solutions. The boundary conditions were transparent to the outgoing waves, except when the disturbance source was close to a corner boundary. The time-domain data generated by such computations were often intractable until their spectra was analyzed. For this purpose, the relative merits of three spectral analysis methods were considered. For simple, periodic waves with steep-sloped spectra, the periodogram method produced better estimates than the Blackman-Tukey method, and the Hanning window was more effective when used with the former. For chaotic waves, however, the weighted-overlapped-segment-averaging and Blackman-Tukey methods were better than the periodogram method. Therefore, it was observed that the spectral representation of time-domain data was significantly dependent on the particular method employed.

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Identification of stochastic linear systems via spectral analysis: reduced-order approximation, performance analysis and transfer function bias

Proceedings of 35th IEEE Conference on Decision and Control ◽

10.1109/cdc.1996.572885 ◽

2002 ◽

Cited By ~ 7

Author(s):

J.K. Tugnait

Keyword(s):

Spectral Analysis ◽

Performance Analysis ◽

Transfer Function ◽

Linear Systems ◽

Order Approximation ◽

Reduced Order ◽

Stochastic Linear Systems

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JOINT INTERPRETATION OF AIRBORNE ELECTROMAGNETIC DATA IN THE TIME DOMAIN AND FREQUENCY DOMAIN

Engineering survey ◽

10.25296/1997-8650-2018-12-7-8-76-83 ◽

2018 ◽

Vol 12 (7-8) ◽

pp. 76-83

Author(s):

E. V. KARSHAKOV ◽

J. MOILANEN

Keyword(s):

Fourier Transform ◽

Frequency Domain ◽

Time Domain ◽

Frequency Interval ◽

Single Spectrum ◽

Simultaneous Inversion ◽

Homogeneous Half Space ◽

Time Domain Data ◽

The Time Domain

Тhe advantage of combine processing of frequency domain and time domain data provided by the EQUATOR system is discussed. The heliborne complex has a towed transmitter, and, raised above it on the same cable a towed receiver. The excitation signal contains both pulsed and harmonic components. In fact, there are two independent transmitters operate in the system: one of them is a normal pulsed domain transmitter, with a half-sinusoidal pulse and a small "cut" on the falling edge, and the other one is a classical frequency domain transmitter at several specially selected frequencies. The received signal is first processed to a direct Fourier transform with high Q-factor detection at all significant frequencies. After that, in the spectral region, operations of converting the spectra of two sounding signals to a single spectrum of an ideal transmitter are performed. Than we do an inverse Fourier transform and return to the time domain. The detection of spectral components is done at a frequency band of several Hz, the receiver has the ability to perfectly suppress all sorts of extra-band noise. The detection bandwidth is several dozen times less the frequency interval between the harmonics, it turns out thatto achieve the same measurement quality of ground response without using out-of-band suppression you need several dozen times higher moment of airborne transmitting system. The data obtained from the model of a homogeneous half-space, a two-layered model, and a model of a horizontally layered medium is considered. A time-domain data makes it easier to detect a conductor in a relative insulator at greater depths. The data in the frequency domain gives more detailed information about subsurface. These conclusions are illustrated by the example of processing the survey data of the Republic of Rwanda in 2017. The simultaneous inversion of data in frequency domain and time domain can significantly improve the quality of interpretation.

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