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

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.
Convolution: Math, Graphics, and Discrete Signals01:24

Convolution: Math, Graphics, and Discrete Signals

In any LTI (Linear Time-Invariant) system, the convolution of two signals is denoted using a convolution operator, assuming all initial conditions are zero. The convolution integral can be divided into two parts: the zero-input or natural response and the zero-state or forced response, with t0 indicating the initial time.
To simplify the convolution integral, it is assumed that both the input signal and impulse response are zero for negative time values. The graphical convolution process...
Properties of the z-Transform II01:16

Properties of the z-Transform II

The property of Accumulation in signal processing is derived by analyzing the accumulated sum of a discrete-time signal and using the time-shifting property to determine its z-transform. This principle reveals that the z-transform of the summed signal is related to the z-transform of the original signal by a multiplicative factor.
Moreover, the convolution property indicates that the convolution of two signals in the time domain corresponds to the product of their z-transforms in the frequency...
Properties of Laplace Transform-II01:16

Properties of Laplace Transform-II

Time differentiation, convolution, integration, and periodicity are fundamental concepts in analyzing functions and signals over time. Each concept provides a unique perspective on how functions evolve, interact, and repeat, offering essential tools for various scientific and engineering applications.
Time differentiation involves analyzing the rate of change of a function over time. Mathematically, it is the derivative of a function with respect to time. This concept can be likened to tracking...
Linear time-invariant Systems01:23

Linear time-invariant Systems

A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be calculated...
Central Limit Theorem01:14

Central Limit Theorem

The central limit theorem, abbreviated as clt, is one of the most powerful and useful ideas in all of statistics. The central limit theorem for sample means says that if you repeatedly draw samples of a given size and calculate their means, and create a histogram of those means, then the resulting histogram will tend to have an approximate normal bell shape. In other words, as sample sizes increase, the distribution of means follows the normal distribution more closely.
The sample size, n, that...

You might also read

Related Articles

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

Sort by
Same author

Limitations of a class of binary phase-only filters.

Applied optics·2010
Same author

Performance analysis of associative memories with nonlinearities in the correlation domain.

Applied optics·2010
Same author

Synchronous vs asynchronous behavior of Hopfield's CAM neural net.

Applied optics·2010
Same author

Composite matched filter output partitioning.

Applied optics·2010
Same author

Conventional and composite matched filters with error correction: a comparison.

Applied optics·2010
Same author

Class of continuous level associative memory neural nets.

Applied optics·2010
Same journal

Gaussian-modulated continuous-variable quantum key distribution over 60 km fiber using an integrated silicon photonic receiver.

Optics letters·2026
Same journal

E2E-OCT: end-to-end joint learning model using optical coherence tomography images for vocal cord leukoplakia diagnosis.

Optics letters·2026
Same journal

Holographic generation of panoramic 3D scenes by concave ellipsoidal mirror reflection.

Optics letters·2026
Same journal

Dual-pilot phase recovery with pair-wise maximum-ratio combining for coherent PONs.

Optics letters·2026
Same journal

Mapping the whispering gallery modes of a CaF<sub>2</sub> disk resonator with half-tapered fibers to estimate the fundamental mode volume.

Optics letters·2026
Same journal

Quantitative estimation of deep-subwavelength scale via dark-field scattering axial energy concentration decay profiles.

Optics letters·2026
See all related articles

Related Experiment Video

Updated: Jun 20, 2026

A Tactile Automated Passive-Finger Stimulator (TAPS)
19:44

A Tactile Automated Passive-Finger Stimulator (TAPS)

Published on: June 3, 2009

Sampling theory for linear integral transforms.

R J Marks Ii

    Optics Letters
    |August 25, 2009
    PubMed
    Summary
    This summary is machine-generated.

    A new sampling theorem eliminates integration errors in processors by filtering the operation kernel before sampling. This enables integration-error-free processing of discrete linear operations at the Nyquist rate.

    More Related Videos

    X-ray Beam Induced Current Measurements for Multi-Modal X-ray Microscopy of Solar Cells
    10:16

    X-ray Beam Induced Current Measurements for Multi-Modal X-ray Microscopy of Solar Cells

    Published on: August 20, 2019

    Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
    06:45

    Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

    Published on: October 28, 2022

    Related Experiment Videos

    Last Updated: Jun 20, 2026

    A Tactile Automated Passive-Finger Stimulator (TAPS)
    19:44

    A Tactile Automated Passive-Finger Stimulator (TAPS)

    Published on: June 3, 2009

    X-ray Beam Induced Current Measurements for Multi-Modal X-ray Microscopy of Solar Cells
    10:16

    X-ray Beam Induced Current Measurements for Multi-Modal X-ray Microscopy of Solar Cells

    Published on: August 20, 2019

    Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
    06:45

    Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

    Published on: October 28, 2022

    Area of Science:

    • Signal Processing
    • Numerical Analysis

    Background:

    • Discrete processors often introduce integration errors when approximating continuous linear operations.
    • Existing methods may not guarantee error-free processing for sampled data.

    Purpose of the Study:

    • To develop a sampling theorem that minimizes integration error in discrete linear processors.
    • To enable integration-error-free processing of continuous linear operations using sampled inputs.

    Main Methods:

    • A novel sampling theorem is introduced.
    • The theorem involves pre-filtering the operation kernel before sampling.
    • This method is applied to discrete versions of continuous linear operations.

    Main Results:

    • Integration error is significantly reduced or eliminated in matrix-vector and linear multiplexing processors.
    • Processing of inputs sampled at their Nyquist rate becomes integration-error-free.
    • Demonstrated applicability to Laplace and Hilbert transformations.

    Conclusions:

    • The developed sampling theorem provides a method for accurate discrete processing of continuous linear operations.
    • Pre-filtering the kernel is a key technique for achieving integration-error-free results.
    • This approach enhances the precision of digital signal processing applications.