Optimization of spectrum extrapolation for causal impulse...

Details Optimization of spectrum extrapolation for causal impulse... Optimization of spectrum extrapolation for causal impulse...

2011-06-14

2011-06-14

Malzahn, David H (Department: 2193)

Electrical computers: arithmetic processing and calculating

Electrical digital calculating computer

Particular function performed

Reexamination Certificate

active

07962541

ABSTRACT:
A causal impulse response function is calculated from a truncated spectrum by extending the real part of the spectrum beyond the truncation frequency and computing the imaginary part with the Hilbert transform to enforce causality. The out of band extrapolation is optimized to reduce the discrepancy between the computed and the original imaginary part in the in band frequency range so that the causal impulse response accurately represents the original spectrum. The technique can be applied to spectral with the delay phase subtracted to enforce delay causality. The Hilbert transform may be employed to maintain causality in S-parameter passivity violation correction. At frequencies where violation happens, the S-parameter matrix is scaled down by the inverse of the magnitude of the largest eigenvalue. Magnitudes at other frequencies are unchanged. An additional phase calculated by the magnitude phase Hilbert transform is added to the scaled spectrum to maintain the causality.

REFERENCES:
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Thomas J. Brazil—“Causal-Convolution—A New Method For The Transient Analysis Of Linear Systems At Microwave Frequencies”; IEEE Transactions On Microwave Theory And Techniques, vol. 43, No. 2, Feb. 1995; pp. 315-323.
Philip A. Perry and Thomas J. Brazil—“Forcing Causality On S-Parameter Data Using The Hilbert Transform”; IEEE Microwave And Guided Wave Letters, vol. 8, No. 11, Nov. 1998; pp. 378-380.

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