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

Inverse z-Transform by Partial Fraction Expansion01:20

Inverse z-Transform by Partial Fraction Expansion

The inverse z-transform is a crucial technique for converting a function from its z-domain representation back to the time domain. One effective method for finding the inverse z-transform is the Partial Fraction Method, which involves decomposing a function into simpler fractions with distinct coefficients. These fractions correspond to known z-transform pairs, facilitating the inverse transformation process.
To begin the process, the poles of the function are identified and the function is...
Binomial Expansion Using Pascal's Triangle01:30

Binomial Expansion Using Pascal's Triangle

Expanding a binomial expression such as (a + b)n results in a predictable sequence of terms that can be systematically derived using Pascal’s Triangle. This triangular array of numbers plays a central role in understanding and computing the coefficients of binomial expansions.Pascal’s Triangle is constructed such that each row corresponds to the coefficients of a binomial raised to a power. The topmost row, known as the zeroth row, corresponds to (a + b)0, and each successive row gives the...
Complex Zeros01:29

Complex Zeros

Complex zeros are the solutions to polynomial equations that include imaginary numbers, specifically, numbers of the form a + bi, where a and b are real numbers and i is the imaginary unit defined by i2=-1. These zeros satisfy the equation P(x) = 0, where P(x) is a polynomial with real or complex coefficients. Since the complex number system includes all real numbers, it provides a complete framework for analyzing all possible roots of a polynomial.Every polynomial of degree n≥1 can be...
Real Zeros of Polynomials01:27

Real Zeros of Polynomials

Polynomials are algebraic expressions of terms with variables raised to non-negative integer powers. A central aspect of analyzing polynomial functions is determining their real zeros—values of the variable for which the polynomial evaluates to zero. These values represent the x-intercepts of the polynomial’s graph.The Rational Zeros Theorem lists possible rational solutions for a polynomial equation with integer coefficients. If f(x)=anxn+....+a0​, then every rational zero is of the form p/q​,...
Routh-Hurwitz Criterion II01:19

Routh-Hurwitz Criterion II

In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first column of the Routh...
Difference Equation Solution using z-Transform01:24

Difference Equation Solution using z-Transform

The z-transform is a powerful tool for analyzing practical discrete-time systems, often represented by linear difference equations. Solving a higher-order difference equation requires knowledge of the input signal and the initial conditions up to one term less than the order of the equation.
The z-transform facilitates handling delayed signals by shifting the signal in the z-domain, which corresponds to delaying the signal in the time domain, and advancing signals by similarly shifting in the...

You might also read

Related Articles

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

Sort by
Same author

126&#x2003;ReBreed21, a rapid reinsemination program: fertility in <i>Bos indicus</i> cattle of different parities.

Reproduction, fertility, and development·2022
Same author

Pulmonary ventilation/perfusion single photon emission tomography--Initial experience of a Nuclear Medicine Department.

Revista portuguesa de pneumologia·2015
Same author

Heart rate variability in chronic Chagas patients before and after treatment with benznidazole.

Autonomic neuroscience : basic & clinical·2010
Same author

Assessment of salivary gland function in Sjögren's syndrome: the role of salivary gland scintigraphy.

Autoimmunity reviews·2009
Same author

[Salivary gland scintigraphy in the evaluation of patients with sicca complaints].

Acta reumatologica portuguesa·2008
Same author

Mixed inflammatory/regulatory cytokine profile marked by simultaneous raise of interferon-gamma and interleukin-10 and low frequency of tumour necrosis factor-alpha(+) monocytes are hallmarks of active human visceral Leishmaniasis due to Leishmania chagasi infection.

Clinical and experimental immunology·2006
Same journal

Multifunctional reconfigurable terahertz metasurface based on vanadium dioxide phase transition: achieving broadband absorption and efficient polarization conversion.

Applied optics·2026
Same journal

High-Q-factor electromagnetically induced transparency utilizing quasi-bound states in the continuum in an all-dielectric terahertz metasurface.

Applied optics·2026
Same journal

Automated stitching interferometry for high-precision metrology of X-ray mirrors.

Applied optics·2026
Same journal

Experimental demonstration of an approach to designing a metal-dielectric DBR resonant cavity structure.

Applied optics·2026
Same journal

High-precision wavefront reconstruction from a single-shot interferogram using a physics-driven hybrid feature calibration network.

Applied optics·2026
Same journal

Ultra-high-Q Fano resonance based on coupled topological corner states in Kagome photonic crystals.

Applied optics·2026
See all related articles

Related Experiment Video

Updated: Jun 12, 2026

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture
09:04

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture

Published on: February 23, 2018

Algorithm for computation of Zernike polynomials expansion coefficients.

A Prata, W V Rusch

    Applied Optics
    |June 16, 2010
    PubMed
    Summary
    This summary is machine-generated.

    A new algorithm efficiently expands functions using Zernike polynomials, offering a faster and more accurate method for computational optics. This numerical technique significantly speeds up calculations compared to traditional integration rules.

    Related Experiment Videos

    Last Updated: Jun 12, 2026

    Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture
    09:04

    Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture

    Published on: February 23, 2018

    Area of Science:

    • Optics and Photonics
    • Computational Science
    • Numerical Analysis

    Background:

    • Zernike polynomials are crucial for describing optical aberrations and wavefronts.
    • Accurate and efficient computation of Zernike expansion coefficients is vital in optical metrology and adaptive optics.

    Purpose of the Study:

    • To present a numerically efficient algorithm for function expansion in Zernike polynomials.
    • To improve computational speed and accuracy in Zernike coefficient evaluation.

    Main Methods:

    • Developed an algorithm utilizing standard 2-D integration formulas based on Zernike polynomial orthogonality.
    • Employed quadratic approximations to mitigate integration challenges posed by oscillatory Zernike functions.

    Main Results:

    • The proposed algorithm demonstrates significant numerical efficiency.
    • Achieved at least a fourfold improvement in computational speed compared to nested 2-D Simpson's integration rules.
    • The method is both fast and numerically accurate.

    Conclusions:

    • The novel algorithm provides a computationally advantageous approach for Zernike polynomial expansions.
    • This advancement is expected to benefit practical applications in optical system analysis and design.