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A frequency averaging framework for the solution of complex dynamic systems.

Lecomte C - Proc. Math. Phys. Eng. Sci. (2014)

Bottom Line: A frequency averaging framework is proposed for the solution of complex linear dynamic systems.It is remarkable that, while the mid-frequency region is usually very challenging, a smooth transition from low- through mid- and high-frequency ranges is possible and all ranges can now be considered in a single framework.An interpretation of the frequency averaging in the time domain is presented and it is explained that the average may be evaluated very efficiently in terms of system solutions.

View Article: PubMed Central - PubMed

Affiliation: Associate Member, Southampton Statistical Sciences Research Institute , University of Southampton , Southampton, UK.

ABSTRACT
A frequency averaging framework is proposed for the solution of complex linear dynamic systems. It is remarkable that, while the mid-frequency region is usually very challenging, a smooth transition from low- through mid- and high-frequency ranges is possible and all ranges can now be considered in a single framework. An interpretation of the frequency averaging in the time domain is presented and it is explained that the average may be evaluated very efficiently in terms of system solutions.

No MeSH data available.


Comparison of the exact impulse response with its ‘Averaged’ estimation through frequency average, inverse Fourier transform and scaling as described in (g). Three averaging width, a=1, 0.1 and 0.01 rad Hz, are considered in plots (a), (b) and (c), respectively, and the corresponding relative errors are presented in plots (d), (e) and (f). The inverse Fourier transforms of the discretized transfer functions were evaluated through an explicit trapezoidal integral. The real Gaussian scaling functions affecting the impulse response when the inverse of the frequency average is taken are presented in (h).
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RSPA20130743F5: Comparison of the exact impulse response with its ‘Averaged’ estimation through frequency average, inverse Fourier transform and scaling as described in (g). Three averaging width, a=1, 0.1 and 0.01 rad Hz, are considered in plots (a), (b) and (c), respectively, and the corresponding relative errors are presented in plots (d), (e) and (f). The inverse Fourier transforms of the discretized transfer functions were evaluated through an explicit trapezoidal integral. The real Gaussian scaling functions affecting the impulse response when the inverse of the frequency average is taken are presented in (h).

Mentions: Comparison of the average, variance and impulse response functions for a constant, original, averaging width a=0.1 rad Hz and an averaging width that has been refined in the interval (0.1,1.1) rad Hz. The approximate and exact impulse responses are, respectively, the inverse Fourier transforms of the exact transfer function and that of its average. Both were evaluated through an explicit trapezoidal integral as for the results of figure 5.


A frequency averaging framework for the solution of complex dynamic systems.

Lecomte C - Proc. Math. Phys. Eng. Sci. (2014)

Comparison of the exact impulse response with its ‘Averaged’ estimation through frequency average, inverse Fourier transform and scaling as described in (g). Three averaging width, a=1, 0.1 and 0.01 rad Hz, are considered in plots (a), (b) and (c), respectively, and the corresponding relative errors are presented in plots (d), (e) and (f). The inverse Fourier transforms of the discretized transfer functions were evaluated through an explicit trapezoidal integral. The real Gaussian scaling functions affecting the impulse response when the inverse of the frequency average is taken are presented in (h).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4042715&req=5

RSPA20130743F5: Comparison of the exact impulse response with its ‘Averaged’ estimation through frequency average, inverse Fourier transform and scaling as described in (g). Three averaging width, a=1, 0.1 and 0.01 rad Hz, are considered in plots (a), (b) and (c), respectively, and the corresponding relative errors are presented in plots (d), (e) and (f). The inverse Fourier transforms of the discretized transfer functions were evaluated through an explicit trapezoidal integral. The real Gaussian scaling functions affecting the impulse response when the inverse of the frequency average is taken are presented in (h).
Mentions: Comparison of the average, variance and impulse response functions for a constant, original, averaging width a=0.1 rad Hz and an averaging width that has been refined in the interval (0.1,1.1) rad Hz. The approximate and exact impulse responses are, respectively, the inverse Fourier transforms of the exact transfer function and that of its average. Both were evaluated through an explicit trapezoidal integral as for the results of figure 5.

Bottom Line: A frequency averaging framework is proposed for the solution of complex linear dynamic systems.It is remarkable that, while the mid-frequency region is usually very challenging, a smooth transition from low- through mid- and high-frequency ranges is possible and all ranges can now be considered in a single framework.An interpretation of the frequency averaging in the time domain is presented and it is explained that the average may be evaluated very efficiently in terms of system solutions.

View Article: PubMed Central - PubMed

Affiliation: Associate Member, Southampton Statistical Sciences Research Institute , University of Southampton , Southampton, UK.

ABSTRACT
A frequency averaging framework is proposed for the solution of complex linear dynamic systems. It is remarkable that, while the mid-frequency region is usually very challenging, a smooth transition from low- through mid- and high-frequency ranges is possible and all ranges can now be considered in a single framework. An interpretation of the frequency averaging in the time domain is presented and it is explained that the average may be evaluated very efficiently in terms of system solutions.

No MeSH data available.