Jove
Visualize
Contact Us

Related Concept Videos

Sampling Continuous Time Signal01:11

Sampling Continuous Time Signal

808
In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
In the...
808
NMR Spectrometers: Radiofrequency Pulses and Pulse Sequences01:17

NMR Spectrometers: Radiofrequency Pulses and Pulse Sequences

1.9K
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.
1.9K
Rectangular and Triangular Pulse Function01:19

Rectangular and Triangular Pulse Function

2.1K
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,
2.1K
Sampling Theorem01:15

Sampling Theorem

1.5K
In signal processing, the analysis of continuous-time signals, denoted as x(t), often involves sampling techniques to convert these signals into discrete-time signals. This process is essential for digital representation and manipulation. A critical component in sampling is the train of impulses, characterized by the sampling interval and the sampling frequency. The relationship between these parameters and the original signal's properties dictates the success of the sampling process.
1.5K
Random Variables01:09

Random Variables

18.3K
A random variable is a single numerical value that indicates the outcome of a procedure. The concept of random variables is fundamental to the probability theory and was introduced by a Russian mathematician, Pafnuty Chebyshev, in the mid-nineteenth century.
Uppercase letters such as X or Y denote a random variable. Lowercase letters like x or y denote the value of a random variable. If X is a random variable, then X is written in words, and x is given as a number.
For example, let X = the...
18.3K
Basic Discrete Time Signals01:16

Basic Discrete Time Signals

785
The unit step sequence is defined as 1 for zero and positive values of the integer n. This sequence can be graphically displayed using a set of eight sample points, showing a step function starting from n=0 and remaining constant thereafter.
The unit impulse or sample sequence is mathematically expressed as zero for all n values except at n=0, where it is one. The unit impulse sequence, denoted by δ(n), is the first difference of the unit step sequence, while the unit step sequence u(n) is the...
785

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Generalization of Bandlimited Functions and Applications to Quantum Probability Distributions.

Entropy (Basel, Switzerland)·2026
Same author

Optimal Sedation and Analgesia in Patients with Polytrauma, Excluding Brain Injury.

Critical care clinics·2025
Same author

The role of the United Kingdom national poisons information service (NPIS) in the diagnosis of death according to neurological criteria in poisoned and non-poisoned patients.

Journal of the Intensive Care Society·2024
Same author

Conditional Values in Quantum Mechanics.

Entropy (Basel, Switzerland)·2024
Same author

Computational biomechanics for a standing human body: Modal analysis and simulation.

International journal for numerical methods in biomedical engineering·2024
Same author

Quantum Mechanical Approach to the Khintchine and Bochner Criteria for Characteristic Functions.

Entropy (Basel, Switzerland)·2023
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Video

Updated: Mar 10, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

9.8K

Statistics of a space-time random pulse train.

Leon Cohen1, Affa Ahmad2

  • 1Department of Physics, Hunter College of the City University of New York, New York, NY 10065, USA.

The Journal of the Acoustical Society of America
|December 5, 2016
PubMed
Summary

A new method analyzes pulse train statistics, even for non-uniform, space-time dependent pulses. It introduces a dynamical scintillation index to track stationarity, offering general expressions for moments.

More Related Videos

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
07:56

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

9.0K
Quasi-light Storage for Optical Data Packets
07:45

Quasi-light Storage for Optical Data Packets

Published on: February 6, 2014

11.4K

Related Experiment Videos

Last Updated: Mar 10, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

9.8K
A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
07:56

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

9.0K
Quasi-light Storage for Optical Data Packets
07:45

Quasi-light Storage for Optical Data Packets

Published on: February 6, 2014

11.4K

Area of Science:

  • Physics
  • Wave Phenomena
  • Signal Processing

Background:

  • Pulse trains are fundamental in various scientific fields.
  • Characterizing complex pulse trains with space-time dependence and non-uniform distributions is challenging.
  • Existing methods for scintillation index lack space-time adaptability.

Purpose of the Study:

  • To develop a general framework for analyzing the statistical properties of pulse trains.
  • To derive explicit expressions for moments of pulse trains, considering space and time dependence.
  • To introduce and define a dynamical scintillation index for non-stationary pulse trains.

Main Methods:

  • Development of a general analytical approach for pulse train statistics.
  • Derivation of explicit expressions for moments up to the fourth order.
  • Formulation of the dynamical scintillation index based on raw and central moments.
  • Analysis of moment expansions in terms of the number of elementary signals (1/N).

Main Results:

  • General expressions for pulse train moments derived from elementary signal moments.
  • The dynamical scintillation index is shown to be space and time dependent.
  • Exact expressions for raw moments and their 1/N expansions are obtained.
  • Particularly simple exact expressions for central moments are presented.

Conclusions:

  • The developed approach provides a comprehensive method for analyzing complex pulse trains.
  • The dynamical scintillation index offers new insights into the stationarity of space-time pulse trains.
  • The findings are applicable to uncorrelated elementary wave signals and advance the understanding of wave propagation phenomena.