Jove
Visualize
Contact Us
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 Concept Videos

The Phase Rule01:20

The Phase Rule

The phase rule describes the relationship between the variance (degrees of freedom), the number of components, and the number of phases in a system at equilibrium.Variance is a concept that denotes the number of independent intensive properties (properties are those that do not depend on the amount of material in the system), such as temperature, pressure, and composition, that can be altered without impacting the number of phases in equilibrium.In a single-component system, such as pure water,...
Sampling Methods: Overview01:06

Sampling Methods: Overview

A sample refers to a smaller subset representative of a larger population. In analytical chemistry, studying or analyzing an entire population is often impractical or impossible. Therefore, samples are used to draw inferences and generalize the whole population. The sampling method selects individuals or items from a population to create a sample. Standard sampling methods include random, judgemental, systematic, stratified, and cluster sampling. 
In analytical chemistry, the choice of sampling...
Sampling Methods: Sample Types01:18

Sampling Methods: Sample Types

Sampling materials are classified into three main types: solid, liquid, and gas.
Solid samples include a variety of substances, such as sediments from water bodies, soil, metals, and biological tissues. Two standard methods for extracting sediments from water bodies are grab sampling and piston coring. Grab sampling involves using a device to collect a discrete sediment sample from the bottom of a water body with minimal disturbance. Grab samples do not always represent the entire area due to...
Sampling Plans01:23

Sampling Plans

Sampling is a crucial step in analytical chemistry, allowing researchers to collect representative data from a large population. Common sampling methods include random, judgmental, systematic, stratified, and cluster sampling.
Random sampling is a method where each member of the population has an equal chance of being selected for the sample. It involves selecting individuals randomly, often using random number generators or lottery-type methods. For example, when analyzing the properties of a...
Sampling Theorem01:15

Sampling Theorem

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.
Basic Discrete Time Signals01:16

Basic Discrete Time Signals

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...

You might also read

Related Articles

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

Sort by
Same author

A hierarchical cascade of sleep rhythms supports motor memory and is hijacked by epileptic spikes in human epilepsy.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same author

Sleep Microarchitecture, Epileptic Spikes, and Memory in Epilepsy: Implications for Developmental and Epileptic Encephalopathies.

Journal of clinical neurophysiology : official publication of the American Electroencephalographic Society·2026
Same author

Accounting for edge uncertainty in stochastic actor-oriented models for dynamic network analysis.

Network science (Cambridge University Press)·2026
Same author

Leveraging generative AI to enhance Synthea model development.

JAMIA open·2026
Same author

Auditory-evoked changes in slow oscillations and spindles correlate with memory consolidation in children with epilepsy and controls.

Clinical neurophysiology : official journal of the International Federation of Clinical Neurophysiology·2025
Same author

RealtimeDecoder: A Fast Software Module for Online Clusterless Decoding.

eNeuro·2025
Same journal

A Model-Free Reinforcement Learning Implementation of Decision Making Under Uncertainty by Sequential Sampling.

Neural computation·2026
Same journal

DROP: Distributional and Regular Optimism and Pessimism for Reinforcement Learning.

Neural computation·2026
Same journal

Hierarchical Active Inference Using Successor Representations.

Neural computation·2026
Same journal

W-Kernel and Its Principal Space for Frequentist Evaluation of Bayesian Estimators.

Neural computation·2026
Same journal

A Hidden Markov Model-Inspired Sequence Classification Method for Hyperdimensional Computing.

Neural computation·2026
Same journal

Sparse Graphical Modeling for Electrophysiological Phase-Based Connectivity Using Circular Statistics.

Neural computation·2026
See all related articles

Related Experiment Video

Updated: May 14, 2026

Phase-Resolved Functional Lung MRI for Pulmonary Ventilation and Perfusion (V/Q) Assessment
05:56

Phase-Resolved Functional Lung MRI for Pulmonary Ventilation and Perfusion (V/Q) Assessment

Published on: August 9, 2024

Some sampling properties of common phase estimators.

Kyle Q Lepage1, Mark A Kramer, Uri T Eden

  • 1Department of Mathematics, Boston University, Boston, MA 02446, USA. lepage@math.bu.edu

Neural Computation
|January 24, 2013
PubMed
Summary
This summary is machine-generated.

Analyzing neural rhythms requires accurate phase estimation. This study reveals common statistical properties in Hilbert, Morlet, and Fourier transform methods, enabling improved phase estimation in neuroscience.

More Related Videos

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

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

Published on: January 28, 2019

A Method for Tracking the Time Evolution of Steady-State Evoked Potentials
12:03

A Method for Tracking the Time Evolution of Steady-State Evoked Potentials

Published on: May 25, 2019

Related Experiment Videos

Last Updated: May 14, 2026

Phase-Resolved Functional Lung MRI for Pulmonary Ventilation and Perfusion (V/Q) Assessment
05:56

Phase-Resolved Functional Lung MRI for Pulmonary Ventilation and Perfusion (V/Q) Assessment

Published on: August 9, 2024

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

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

Published on: January 28, 2019

A Method for Tracking the Time Evolution of Steady-State Evoked Potentials
12:03

A Method for Tracking the Time Evolution of Steady-State Evoked Potentials

Published on: May 25, 2019

Area of Science:

  • Neuroscience
  • Signal Processing
  • Computational Biology

Background:

  • The instantaneous phase of neural rhythms is crucial for understanding brain function.
  • Accurate phase estimation is essential for analyzing neural oscillatory activity.

Purpose of the Study:

  • To analytically investigate the statistical sampling properties of three common instantaneous phase estimators.
  • To compare the behavior, bias, and variance of Hilbert, complex Morlet, and discrete Fourier transform phase estimators.

Main Methods:

  • Utilized a geometric argument to explore the connection between phase estimators and data likelihood.
  • Analyzed the statistical sampling properties of Hilbert, complex Morlet, and discrete Fourier transform methods.
  • Investigated the temporal dependence and effect of model misspecification on phase estimates.

Main Results:

  • All three phase estimators (Hilbert, complex Morlet, discrete Fourier transform) maximize data likelihood under different neural signal assumptions.
  • Identified common statistical sampling properties across these estimators.
  • Characterized the bias, variance, and temporal dependence of each estimator.

Conclusions:

  • Understanding the shared properties of phase estimators allows for analytical investigation of their behavior.
  • Prior knowledge of rhythmic signals can enhance the accuracy of phase estimates.
  • The findings provide insights for selecting and applying phase estimation techniques in neuroscience research.