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Related Concept Videos

Rectangular and Triangular Pulse Function01:19

Rectangular and Triangular Pulse Function

The unit rectangular pulse function is mathematically represented by a rectangular function centered at the origin with a height of one unit. This function is defined by two parameters: T, which specifies the center location of the pulse along the time axis, and τ, which determines the pulse duration.
For example, consider a rectangular pulse with a 5V amplitude, a 3-second duration, and centered at t=2 seconds. This pulse can be expressed using the rectangular function, written as,
Impulse Response01:17

Impulse Response

The impulse response is the system's reaction to an input impulse. In an RC circuit, the voltage source is the input, and the capacitor's voltage is the output. The system's state and output response before and after input excitation are distinctly defined.
Kirchhoff's law forms an input signal equation, with the capacitor's current and voltage providing the output. Substituting the current and dividing by RC yields a differential equation. The output for an impulse input is the impulse...
Parseval's Theorem for Fourier transform01:15

Parseval's Theorem for Fourier transform

Parseval's theorem is a fundamental principle in signal processing that enables the calculation of a signal's energy in either the time domain or the frequency domain. This theorem is pivotal in demonstrating energy conservation between these two domains, ensuring that the computed energy value remains consistent regardless of the domain of analysis.
To understand Parseval's theorem, it is essential to first comprehend how signal energy is typically calculated. When considering a signal's...
IR Spectroscopy: Hooke's Law Approximation of Molecular Vibration01:16

IR Spectroscopy: Hooke's Law Approximation of Molecular Vibration

A covalently bonded heteronuclear diatomic molecule can be modeled as two vibrating masses connected by a spring. The vibrational frequency of the bond can be expressed using an equation derived from Hooke's law, which describes how the force applied to stretch or compress a spring is proportional to the displacement of the spring. In this case, the atoms behave like masses, and the bond acts like a spring.
According to Hooke's law, the vibrational frequency is directly proportional to the...
NMR Spectrometers: Radiofrequency Pulses and Pulse Sequences01:17

NMR Spectrometers: Radiofrequency Pulses and Pulse Sequences

A pulse is a short burst of radio waves distributed over a range of frequencies that simultaneously excites all the nuclei in the sample. Upon passing a radio frequency pulse along the x-axis, the nuclei absorb energy corresponding to their Larmor frequencies and achieve resonance. This shifts the net magnetization vector from the z-axis toward the transverse plane. This angle of rotation of the magnetization vector, or the flip angle, is proportional to the duration and intensity of the pulse.
Impulse-Momentum Theorem00:49

Impulse-Momentum Theorem

The total change in the motion of an object is proportional to the total force vector acting on it and the time over which it acts. This product is called impulse, a vector quantity with the same direction as the total force acting on the object.
By writing Newton's second law of motion in terms of the momentum of an object and the external force acting on it, and simultaneously using the definition of the impulse vector, it can be shown that the total impulse on an object is equal to its net...

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Related Experiment Video

Updated: Jun 20, 2026

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
12:14

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

Published on: August 12, 2013

Optical pulse modeling with Hermite-Gaussian functions.

H J da Silva, J J O'Reilly

    Optics Letters
    |September 15, 2009
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces an asymptotic method using Hermite-Gaussian functions for optical pulse analysis. The technique allows for analytical study of pulse distortion in optical fibers, even with light source chirping.

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    Patterning via Optical Saturable Transitions - Fabrication and Characterization
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    Patterning via Optical Saturable Transitions - Fabrication and Characterization

    Published on: December 11, 2014

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    Last Updated: Jun 20, 2026

    The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
    12:14

    The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

    Published on: August 12, 2013

    Patterning via Optical Saturable Transitions - Fabrication and Characterization
    08:19

    Patterning via Optical Saturable Transitions - Fabrication and Characterization

    Published on: December 11, 2014

    Area of Science:

    • Optics and Photonics
    • Fiber Optics Communications
    • Mathematical Physics

    Background:

    • Accurate modeling of optical pulses is crucial for understanding signal distortion in monomode fibers.
    • Existing methods may struggle with analytical tractability, especially when considering light source chirping.

    Purpose of the Study:

    • To present an asymptotic method for the synthesis and analysis of optical pulses.
    • To enable analytical study of arbitrary pulse waveform distortion in monomode fibers.
    • To provide a flexible platform for optimizing optical systems.

    Main Methods:

    • Utilizes Hermite-Gaussian functions for pulse representation.
    • Employs asymptotic analysis for mathematical tractability.
    • Applies the method to study pulse distortion, including effects of light source chirping.

    Main Results:

    • The method allows for analytical investigation of pulse distortion in monomode fibers.
    • It effectively models arbitrary pulse waveforms, incorporating light source chirping.
    • Demonstrates suitability for synthesizing analytically tractable representations of realistic pulse shapes.

    Conclusions:

    • The proposed asymptotic method offers a powerful tool for optical pulse analysis and synthesis.
    • It provides a flexible and effective platform for analytical system optimization in fiber optics.
    • This technique facilitates a deeper understanding of pulse behavior under various conditions, including chirping.