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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.
Phase-lag controllers do not place a pole at zero, but instead influence the steady-state error by amplifying any...
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Phase-lead controllers are commonly used in various control systems to enhance response speed and stability. Adjusting the brightness on a television screen offers a practical example of phase-lead control. When contrast is enhanced, a phase-lead controller is employed. Mathematically, phase-lead control is identified when the first parameter is smaller than the second.
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Aliasing01:18

Aliasing

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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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Linear Approximation in Frequency Domain01:26

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Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
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IR Frequency Region: X–H Stretching01:24

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In IR spectroscopy, signals produced by the X−H bonds (such as C−H, O−H, or N−H) can be observed in the frequency range of  2700–4000 cm–1. The C−H stretching vibration forms sharp bands in the region 2850–3000 cm–1. The presence of the O−H stretching vibration leads to the forming of an absorption band in the frequency range 3650–3200 cm−1. At the same time, N−H stretching can be confirmed by absorption bands in...
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Identical bonds within a polyatomic group can stretch symmetrically (in-phase) or asymmetrically (out-of-phase). Similar to hydrogen bonding, these vibrations also influence the shape of the IR peak. Generally, asymmetric stretching frequencies are higher than symmetric stretching frequencies. For example, primary amines exhibit two distinct IR peaks between 3300–3500 cm−1 corresponding to the symmetric and asymmetric N-H stretching, while secondary amines exhibit a single...
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Carrier-frequency estimation for digital holograms of phase objects.

Nishant Goyal, Kedar Khare

    Applied Optics
    |March 4, 2024
    PubMed
    Summary
    This summary is machine-generated.

    Accurate carrier fringe frequency estimation is crucial for off-axis digital hologram demodulation. A new definition using the power spectrum centroid improves accuracy, especially for phase objects, and enhances noise robustness.

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    Area of Science:

    • Optics and Photonics
    • Digital Holography
    • Signal Processing

    Background:

    • Off-axis digital holography requires precise carrier fringe frequency estimation for accurate object wave demodulation.
    • Current methods often rely on amplitude peaks in Fourier transforms, which are insufficient for phase objects.
    • The carrier-envelope representation is key to understanding hologram demodulation fidelity.

    Purpose of the Study:

    • To investigate and propose a more robust definition for carrier fringe frequency in digital holograms.
    • To address the limitations of existing methods, particularly for phase objects.
    • To provide a definition that is applicable across various hologram types and robust to noise.

    Main Methods:

    • Analysis of digital holograms using the carrier-envelope representation.
    • Application of Mandel's criterion for evaluating hologram quality.
    • Comparison of traditional amplitude peak-based frequency estimation with a proposed centroid-based method.
    • Validation using simulated and experimental off-axis holograms.

    Main Results:

    • The amplitude peak definition of carrier frequency is shown to be inadequate for phase objects.
    • The centroid of the cross-term's power spectrum is identified as a more appropriate carrier frequency definition.
    • This new definition demonstrates uniform applicability to phase objects.
    • The centroid method offers improved robustness against noise and results in a smoother envelope representation.

    Conclusions:

    • A novel, centroid-based definition of carrier fringe frequency is proposed for off-axis digital holograms.
    • This method overcomes limitations of previous approaches, particularly for phase objects.
    • The proposed definition enhances demodulation accuracy, noise resilience, and overall wave representation quality.