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

821
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...
821
Difference Equation Solution using z-Transform01:24

Difference Equation Solution using z-Transform

775
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...
775
Interference and Diffraction02:18

Interference and Diffraction

28.7K
Interference is a characteristic phenomenon exhibited by waves. When two electromagnetic waves interact with their peaks and troughs coinciding, a resulting wave with enhanced amplitude is produced. This is known as constructive interference. In this case, the two waves interacting are in phase with each other.
28.7K
Definition of z-Transform01:26

Definition of z-Transform

1.9K
The z-transform is a powerful mathematical tool used in the analysis of discrete-time signals and systems. It is an essential analytical tool, analogous to the Laplace transform used in continuous-time systems. It plays a crucial role in the analysis of signals and systems, complementing the discrete-time Fourier transform. Both the z-transform and the Laplace transform convert differential or difference equations into algebraic equations, simplifying the process of solving complex problems.
1.9K
Real Zeros of Polynomials01:27

Real Zeros of Polynomials

331
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...
331
Properties of the z-Transform I01:17

Properties of the z-Transform I

807
The z-transform is a fundamental tool in digital signal processing, enabling the analysis of discrete-time systems through its various properties. It is an invaluable tool for analyzing discrete-time systems, offering a range of properties that simplify complex signal manipulations. One fundamental property is linearity. For any two discrete-time signals, the z-transform of their linear combination equals the same linear combination of their individual z-transforms. This property is essential...
807

You might also read

Related Articles

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

Sort by
Same author

Efficacy and outcomes of [<sup>177</sup>Lu]Lu-PSMA-617 in patients with mCRPC treated with or without concurrent ARPI: a real-world single-center analysis.

European journal of nuclear medicine and molecular imaging·2026
Same author

Salvage Radiotherapy Confers an Overall Survival Advantage in Biochemical Recurrence of Prostate Cancer: Evidence from the International PROMISE Registry.

Journal of nuclear medicine : official publication, Society of Nuclear Medicine·2026
Same author

Enhancing image retrieval via Siamese network-based hashing with gated residual connections.

Scientific reports·2026
Same author

Dynamics, Pharmacokinetics, and Dosimetry of First-in-Human [<sup>68</sup>Ga]Ga-OncoACP3-DOTA PET in Patients with Prostate Cancer.

Journal of nuclear medicine : official publication, Society of Nuclear Medicine·2026
Same author

FAP-targeted [<sup>68</sup>Ga]BED003-PET in different solid malignancies.

European journal of nuclear medicine and molecular imaging·2026
Same author

Risk Assessment in Large B-Cell Lymphoma Using Metabolic Tumor Volume: Real-World Data from a Multicenter Cohort of Patients Undergoing CAR T-Cell Therapy.

Journal of nuclear medicine : official publication, Society of Nuclear Medicine·2026

Related Experiment Video

Updated: May 5, 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

9.1K

Phase wavefront aberration modeling using Zernike and pseudo-Zernike polynomials.

Kambiz Rahbar, Karim Faez, Ebrahim Attaran Kakhki

    Journal of the Optical Society of America. A, Optics, Image Science, and Vision
    |December 11, 2013
    PubMed
    Summary

    This study models phase wavefront aberrations using Zernike and pseudo-Zernike polynomials. Combining these polynomials enhances the robustness of aberration estimation in optical systems, improving precision despite noise.

    More Related Videos

    High-resolution, High-speed, Three-dimensional Video Imaging with Digital Fringe Projection Techniques
    11:34

    High-resolution, High-speed, Three-dimensional Video Imaging with Digital Fringe Projection Techniques

    Published on: December 3, 2013

    16.3K
    Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping
    09:43

    Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping

    Published on: March 20, 2017

    9.7K

    Related Experiment Videos

    Last Updated: May 5, 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

    9.1K
    High-resolution, High-speed, Three-dimensional Video Imaging with Digital Fringe Projection Techniques
    11:34

    High-resolution, High-speed, Three-dimensional Video Imaging with Digital Fringe Projection Techniques

    Published on: December 3, 2013

    16.3K
    Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping
    09:43

    Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping

    Published on: March 20, 2017

    9.7K

    Area of Science:

    • Optical engineering
    • Applied mathematics
    • Surface metrology

    Background:

    • Orthogonal polynomials are vital for representing complex surfaces.
    • Zernike polynomials are widely used in optics for instrument testing and aberration analysis.
    • Noise in optical surface estimation reduces precision.

    Purpose of the Study:

    • To model phase wavefront aberrations in third-order optics.
    • To investigate the use of combined Zernike and pseudo-Zernike polynomials.
    • To enhance the robustness of aberration estimation in the presence of noise.

    Main Methods:

    • Utilizing Zernike polynomials for surface representation.
    • Incorporating pseudo-Zernike polynomials into the modeling.
    • Applying noise management strategies for estimation refinement.

    Main Results:

    • The combination of Zernike and pseudo-Zernike polynomials effectively models phase wavefront aberrations.
    • This combined approach increases the robustness of the estimation process.
    • Improved precision in estimating phase wavefront aberration distribution was observed.

    Conclusions:

    • Combined Zernike and pseudo-Zernike polynomials offer a robust method for modeling optical aberrations.
    • This technique is beneficial for improving the accuracy of optical surface estimations.
    • The findings contribute to advanced aberration theory and optical testing.