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Published on: August 19, 2021
Spectral recovery by analytic continuation in crossing-based spectrum analysis.
Applied Optics
|December 4, 2010
Summary
Analytic continuation recovers the true spectrum of undersampled analog signals from aliased Fourier spectra. This method reconstructs accurate signal bandwidth from sinusoid-crossing data, even with noise.
Area of Science:
- Signal Processing
- Fourier Analysis
- Analog-to-Digital Conversion
Background:
- Undersampling analog signals leads to aliasing, corrupting the Fourier spectrum.
- Sinusoid-crossing detection offers an alternative data acquisition method.
- Accurate crossing localization is crucial for reliable spectrum reconstruction.
Purpose of the Study:
- To recover the true spectrum of an undersampled analog signal.
- To overcome limitations of traditional aliasing in Fourier spectrum analysis.
- To demonstrate a novel spectrum recovery technique using analytic continuation.
Main Methods:
- Utilizing analytic continuation to reconstruct the original signal spectrum.
- Computing aliased Fourier spectra from sinusoid-crossing locations.
- Employing a reference sinusoid for signal intersection detection.
Main Results:
- Successfully recovered the true spectrum of an undersampled signal.
- Demonstrated robustness of the method with an interferogram test signal.
- Showed effectiveness in both noise-free and noisy conditions (additive Gaussian noise).
Conclusions:
- Analytic continuation enables accurate spectrum recovery from undersampled signals.
- The technique is viable even with low-accuracy crossing detection if the signal has compact support.
- This method offers a potential solution for signal analysis when traditional sampling is not feasible.
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