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Related Concept Videos

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

Time and frequency -Domain Interpretation of Phase-lag Control

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 finite,...
Time and frequency -Domain Interpretation of Phase-lead Control01:24

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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

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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Gain

Gain and phase shift are properties of linear circuits that describe the effect a circuit has on a sinusoidal input voltage or current. The circuit's behavior that contains reactive elements will depend on the frequency of the input sinusoid. As a result, it is observed that the gain and phase shift will all be frequency functions.
Gain:
Suppose Vin is the input and Vout is the output signal to a circuit.
IR Spectrum Peak Splitting: Symmetric vs Asymmetric Vibrations01:08

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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 stretching vibration...
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Properties of Fourier Transform II

The Fourier Transform (FT) is an essential mathematical tool in signal processing, transforming a time-domain signal into its frequency-domain representation. This transformation elucidates the relationship between time and frequency domains through several properties, each revealing unique aspects of signal behavior.
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Related Experiment Video

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Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
08:39

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Published on: January 28, 2019

Spectral analysis of phase shifting algorithms.

M Servin1, J C Estrada, J A Quiroga

  • 1Centro de Investigaciones en Optica A. C., Loma del Bosque 115, Col. Lomas del Campestre, 37150, León Guanajuato, México. mservin@cio.mx

Optics Express
|September 23, 2009
PubMed
Summary
This summary is machine-generated.

A new spectral analysis method for Phase Shifting Interferometry (PSI) algorithms is introduced. This novel approach offers invariance to rotation and time-shifts, overcoming limitations of the standard Freischlad and Koliopoulos (F&K) analysis.

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Area of Science:

  • Optics and Photonics
  • Metrology
  • Signal Processing

Background:

  • Phase Shifting Interferometry (PSI) is a key technique for optical metrology.
  • The Freischlad and Koliopoulos (F&K) method (1990) provides spectral analysis of PSI algorithms.
  • The F&K analysis has drawbacks, being sensitive to algorithm rotation and reference signal time-shifts.

Purpose of the Study:

  • To develop a novel spectral analysis for PSI algorithms.
  • To create an analysis method invariant to common transformations like rotation and time-shifts.
  • To offer advantages over the existing F&K spectral analysis standard.

Main Methods:

  • Development of a new spectral analysis framework for PSI algorithms.
  • Mathematical formulation of the spectral analysis invariant to rotation and time-shifts.
  • Comparative analysis against the established F&K spectral analysis.

Main Results:

  • The proposed spectral analysis is invariant to algorithm rotation and reference signal time-shifts.
  • This invariance preserves the fundamental phase demodulation properties of PSI algorithms.
  • The new method demonstrates advantages over the F&K spectral analysis.

Conclusions:

  • A robust and invariant spectral analysis method for PSI algorithms has been developed.
  • This new method addresses critical limitations of the F&K spectral analysis.
  • The proposed technique enhances the reliability and applicability of PSI spectral analysis.