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, Rθ, 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

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  1. R. L. Pickholtz, D. L. Schilling, and L. B. Milstein, “Theory of spread-spectrum communications: a tutorial,” IEEE Trans. Commun. 30, 855–884 (1982).
    [CrossRef]
  2. I. Marson and J. E. Faller, “g-the acceleration of gravity: its measurement and its importance,” J. Phys. E 19, 22–32 (1986).
    [CrossRef]
  3. T. M. Niebauer, “The effective measurement height of free-fall absolute gravimeters,” Metrologia 26, 115–118 (1989).
    [CrossRef]
  4. T. M. Niebauer, G. S. Sasagawa, J. E. Faller, R. Hilt, and F. Klopping, “A new generation of absolute gravimeters,” Metrologia 32, 159–180 (1995).
    [CrossRef]
  5. I. Murata, “A transportable apparatus for absolute measurement of gravity,” Bulletin of the Earthquake Research Institute 53, 49–130 (1978).
  6. P. R. Parker, M. A. Zumberge, and R. L. Parker, “A new method forfringe-signal processing in absolute gravity meters,” Manuscripta Geodaetica 20, 173–181 (1995).
  7. T. Tsubokawa and S. Svitlov, “New method of digital fringe processing in an absolute gravimeter,” IEEE Trans. Instrum. Meas. 48, 488–491 (1999).
    [CrossRef]
  8. T. M. Niebauer, A. Schiel, and D. van Westrum, “Complex heterodyne for undersampled chirped sinusoidal signals,” Appl. Opt. 45, 8322–8330 (2006).
    [CrossRef]
  9. E. Bedrosian, “The analytic signal representation of modulated waveforms,” Proc. IRE 50, 2071–2076 (1962).
    [CrossRef]

2006 (1)

1999 (1)

T. Tsubokawa and S. Svitlov, “New method of digital fringe processing in an absolute gravimeter,” IEEE Trans. Instrum. Meas. 48, 488–491 (1999).
[CrossRef]

1995 (2)

P. R. Parker, M. A. Zumberge, and R. L. Parker, “A new method forfringe-signal processing in absolute gravity meters,” Manuscripta Geodaetica 20, 173–181 (1995).

T. M. Niebauer, G. S. Sasagawa, J. E. Faller, R. Hilt, and F. Klopping, “A new generation of absolute gravimeters,” Metrologia 32, 159–180 (1995).
[CrossRef]

1989 (1)

T. M. Niebauer, “The effective measurement height of free-fall absolute gravimeters,” Metrologia 26, 115–118 (1989).
[CrossRef]

1986 (1)

I. Marson and J. E. Faller, “g-the acceleration of gravity: its measurement and its importance,” J. Phys. E 19, 22–32 (1986).
[CrossRef]

1982 (1)

R. L. Pickholtz, D. L. Schilling, and L. B. Milstein, “Theory of spread-spectrum communications: a tutorial,” IEEE Trans. Commun. 30, 855–884 (1982).
[CrossRef]

1978 (1)

I. Murata, “A transportable apparatus for absolute measurement of gravity,” Bulletin of the Earthquake Research Institute 53, 49–130 (1978).

1962 (1)

E. Bedrosian, “The analytic signal representation of modulated waveforms,” Proc. IRE 50, 2071–2076 (1962).
[CrossRef]

Bedrosian, E.

E. Bedrosian, “The analytic signal representation of modulated waveforms,” Proc. IRE 50, 2071–2076 (1962).
[CrossRef]

Faller, J. E.

T. M. Niebauer, G. S. Sasagawa, J. E. Faller, R. Hilt, and F. Klopping, “A new generation of absolute gravimeters,” Metrologia 32, 159–180 (1995).
[CrossRef]

I. Marson and J. E. Faller, “g-the acceleration of gravity: its measurement and its importance,” J. Phys. E 19, 22–32 (1986).
[CrossRef]

Hilt, R.

T. M. Niebauer, G. S. Sasagawa, J. E. Faller, R. Hilt, and F. Klopping, “A new generation of absolute gravimeters,” Metrologia 32, 159–180 (1995).
[CrossRef]

Klopping, F.

T. M. Niebauer, G. S. Sasagawa, J. E. Faller, R. Hilt, and F. Klopping, “A new generation of absolute gravimeters,” Metrologia 32, 159–180 (1995).
[CrossRef]

Marson, I.

I. Marson and J. E. Faller, “g-the acceleration of gravity: its measurement and its importance,” J. Phys. E 19, 22–32 (1986).
[CrossRef]

Milstein, L. B.

R. L. Pickholtz, D. L. Schilling, and L. B. Milstein, “Theory of spread-spectrum communications: a tutorial,” IEEE Trans. Commun. 30, 855–884 (1982).
[CrossRef]

Murata, I.

I. Murata, “A transportable apparatus for absolute measurement of gravity,” Bulletin of the Earthquake Research Institute 53, 49–130 (1978).

Niebauer, T. M.

T. M. Niebauer, A. Schiel, and D. van Westrum, “Complex heterodyne for undersampled chirped sinusoidal signals,” Appl. Opt. 45, 8322–8330 (2006).
[CrossRef]

T. M. Niebauer, G. S. Sasagawa, J. E. Faller, R. Hilt, and F. Klopping, “A new generation of absolute gravimeters,” Metrologia 32, 159–180 (1995).
[CrossRef]

T. M. Niebauer, “The effective measurement height of free-fall absolute gravimeters,” Metrologia 26, 115–118 (1989).
[CrossRef]

Parker, P. R.

P. R. Parker, M. A. Zumberge, and R. L. Parker, “A new method forfringe-signal processing in absolute gravity meters,” Manuscripta Geodaetica 20, 173–181 (1995).

Parker, R. L.

P. R. Parker, M. A. Zumberge, and R. L. Parker, “A new method forfringe-signal processing in absolute gravity meters,” Manuscripta Geodaetica 20, 173–181 (1995).

Pickholtz, R. L.

R. L. Pickholtz, D. L. Schilling, and L. B. Milstein, “Theory of spread-spectrum communications: a tutorial,” IEEE Trans. Commun. 30, 855–884 (1982).
[CrossRef]

Sasagawa, G. S.

T. M. Niebauer, G. S. Sasagawa, J. E. Faller, R. Hilt, and F. Klopping, “A new generation of absolute gravimeters,” Metrologia 32, 159–180 (1995).
[CrossRef]

Schiel, A.

Schilling, D. L.

R. L. Pickholtz, D. L. Schilling, and L. B. Milstein, “Theory of spread-spectrum communications: a tutorial,” IEEE Trans. Commun. 30, 855–884 (1982).
[CrossRef]

Svitlov, S.

T. Tsubokawa and S. Svitlov, “New method of digital fringe processing in an absolute gravimeter,” IEEE Trans. Instrum. Meas. 48, 488–491 (1999).
[CrossRef]

Tsubokawa, T.

T. Tsubokawa and S. Svitlov, “New method of digital fringe processing in an absolute gravimeter,” IEEE Trans. Instrum. Meas. 48, 488–491 (1999).
[CrossRef]

van Westrum, D.

Zumberge, M. A.

P. R. Parker, M. A. Zumberge, and R. L. Parker, “A new method forfringe-signal processing in absolute gravity meters,” Manuscripta Geodaetica 20, 173–181 (1995).

Appl. Opt. (1)

Bulletin of the Earthquake Research Institute (1)

I. Murata, “A transportable apparatus for absolute measurement of gravity,” Bulletin of the Earthquake Research Institute 53, 49–130 (1978).

IEEE Trans. Commun. (1)

R. L. Pickholtz, D. L. Schilling, and L. B. Milstein, “Theory of spread-spectrum communications: a tutorial,” IEEE Trans. Commun. 30, 855–884 (1982).
[CrossRef]

IEEE Trans. Instrum. Meas. (1)

T. Tsubokawa and S. Svitlov, “New method of digital fringe processing in an absolute gravimeter,” IEEE Trans. Instrum. Meas. 48, 488–491 (1999).
[CrossRef]

J. Phys. E (1)

I. Marson and J. E. Faller, “g-the acceleration of gravity: its measurement and its importance,” J. Phys. E 19, 22–32 (1986).
[CrossRef]

Manuscripta Geodaetica (1)

P. R. Parker, M. A. Zumberge, and R. L. Parker, “A new method forfringe-signal processing in absolute gravity meters,” Manuscripta Geodaetica 20, 173–181 (1995).

Metrologia (2)

T. M. Niebauer, “The effective measurement height of free-fall absolute gravimeters,” Metrologia 26, 115–118 (1989).
[CrossRef]

T. M. Niebauer, G. S. Sasagawa, J. E. Faller, R. Hilt, and F. Klopping, “A new generation of absolute gravimeters,” Metrologia 32, 159–180 (1995).
[CrossRef]

Proc. IRE (1)

E. Bedrosian, “The analytic signal representation of modulated waveforms,” Proc. IRE 50, 2071–2076 (1962).
[CrossRef]

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