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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Joseph N. Mait
  • Vol. 52, Iss. 9 — Mar. 20, 2013
  • pp: 1838–1846

Analytic signal demodulation of phase-modulated frequency-chirped signals

T. M. Niebauer  »View Author Affiliations


Applied Optics, Vol. 52, Issue 9, pp. 1838-1846 (2013)
http://dx.doi.org/10.1364/AO.52.001838


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Abstract

Both interferometers and frequency-modulated (FM) radios create sinusoidal signals with phase information that must be recovered. Often these two applications use narrow band signals but some applications create signals with a large bandwidth. For example, accelerated mirrors in an interferometer naturally create a chirped frequency that linearly increases with time. Chirped carriers are also used for spread-spectrum, FM transmission to reduce interference or avoid detection. In both applications, it is important to recover the underlying phase modulations that are superimposed on the chirped carrier. A common way to treat a chirped waveform is to fit zero crossings of the signal. For lower signal-to-noise applications, however, it is helpful to have a technique that utilizes data over the entire waveform (not just at zero crossings). We present a technique called analytic signal demodulation (ASD), which employs a complex heterodyne of the analytic signal to fully demodulate the chirped waveform. ASD has a much higher sensitivity for recovering phase information than is possible using a chirp demodulation on the raw data. This paper introduces a phase residual function, R θ , that forms an analytic signal and provides a complex demodulation from the received signal in one step. The function defines a phase residual at each point on the chirped waveform, not just at the zero crossings. ASD allows sensitive detection of phase-modulated signals with a very small modulation index (much less than 0.01) that would otherwise be swamped by noise if the raw signal were complex demodulated. The mathematics used to analyze a phase-modulated chirped signal is quite general and can easily be extended for frequency profiles more complicated than a simple chirp.

© 2013 Optical Society of America

OCIS Codes
(060.4080) Fiber optics and optical communications : Modulation
(060.5060) Fiber optics and optical communications : Phase modulation
(120.2650) Instrumentation, measurement, and metrology : Fringe analysis
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.5050) Instrumentation, measurement, and metrology : Phase measurement
(120.5060) Instrumentation, measurement, and metrology : Phase modulation

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: January 3, 2013
Manuscript Accepted: February 5, 2013
Published: March 13, 2013

Citation
T. M. Niebauer, "Analytic signal demodulation of phase-modulated frequency-chirped signals," Appl. Opt. 52, 1838-1846 (2013)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-52-9-1838


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References

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