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Aliasing01:18

Aliasing

Accurate signal sampling and reconstruction are crucial in various signal-processing applications. A time-domain signal's spectrum can be revealed using its Fourier transform. When this signal is sampled at a specific frequency, it results in multiple scaled replicas of the original spectrum in the frequency domain. The spacing of these replicas is determined by the sampling frequency.
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Doppler Effect - I

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Time and frequency -Domain Interpretation of Phase-lag Control01:21

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Phase-lag controllers are widely used in control systems to improve stability and reduce steady-state errors. A dimmer switch controlling the brightness of a light bulb serves as a practical example of phase-lag control, gradually adjusting the bulb's brightness. Mathematically, phase-lag control or low-pass filtering is represented when the factor 'a' is less than 1.
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Related Experiment Video

Updated: Jun 22, 2026

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
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Published on: August 12, 2013

Beam jitter coupling in advanced LIGO.

Guido Mueller

    Optics Express
    |June 6, 2009
    PubMed
    Summary
    This summary is machine-generated.

    Laser beam jitter is a critical noise source in gravitational wave detectors like Advanced LIGO. This study quantifies how beam jitter affects detector sensitivity and sets initial requirements for Advanced LIGO.

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    Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping
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    Area of Science:

    • Astronomy
    • Astrophysics
    • Laser Interferometry

    Background:

    • Laser beam jitter is a significant technical noise source in interferometric gravitational wave detectors.
    • Such fluctuations can cause spurious mirror misalignments, degrading detector sensitivity.

    Purpose of the Study:

    • To calculate the transfer function of beam jitter into the gravitational wave channel for the Advanced LIGO detector.
    • To derive initial requirements for beam jitter in Advanced LIGO.

    Main Methods:

    • Analysis of the transfer function of beam jitter.
    • Modeling the coupling of beam jitter to mirror misalignment in Advanced LIGO.

    Main Results:

    • The transfer function of beam jitter into the gravitational wave channel for Advanced LIGO was calculated.
    • A first expression for beam jitter requirements for Advanced LIGO was derived.

    Conclusions:

    • Beam jitter is a critical noise source that must be controlled for optimal Advanced LIGO performance.
    • The derived requirements provide a quantitative basis for mitigating beam jitter noise in future gravitational wave observations.