Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Properties of Fourier series II

Properties of Fourier series II

Time scaling of signals is a crucial concept in signal processing that affects the Fourier series representation without altering its coefficients. The process modifies the fundamental frequency, thereby changing how the series represents the signal over time. This principle is essential in various applications, including audio and image processing, where signal manipulation is frequent. Understanding function symmetries is fundamental to simplifying the Fourier series.
A function f(t) is...

Basic signals of Fourier Transform

Basic signals of Fourier Transform

The Fourier Transform is a pivotal mathematical tool in signal processing, enabling the transformation of time-domain signals into their frequency-domain representations. Among the numerous elements within this domain, certain functions like the sinc function, delta function, and exponential signals hold significant importance due to their unique properties and implications.
The sinc function, defined as sinc(x) = sin(πx)/(πx), is particularly notable for its symmetry and behavior at zero. It...

Curvilinear Motion: Rectangular Components

Curvilinear Motion: Rectangular Components

Curvilinear motion characterizes the movement of a particle or object along a curved path, notably evident when envisioning a car navigating a winding road. If the car starts at point A, its position vector is established within a fixed frame of reference, where the ratio of the position vector to its magnitude signifies the unit vector pointing in the position vector's direction.
As the car advances, its position evolves over time. Quantifying the car's velocity involves computing the time...

Rectangular and Triangular Pulse Function

Rectangular and Triangular Pulse Function

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,

Crystallographic Point Groups

Crystallographic Point Groups

Crystallographic point groups represent the various symmetry operations that can occur within crystals. They are unique in that at least one point will always remain unchanged during these actions. For instance, consider the triclinic system. This system, devoid of any axis or plane of symmetry, aligns with the C1 and Ci point groups.where Cᵢ is characterized solely by a center of inversion.Contrastingly, the monoclinic system introduces an element of symmetry. This system with one plane and...

IR Spectrum Peak Splitting: Symmetric vs Asymmetric Vibrations

IR Spectrum Peak Splitting: Symmetric vs Asymmetric Vibrations

Identical bonds within a polyatomic group can stretch symmetrically (in-phase) or asymmetrically (out-of-phase). Similar to hydrogen bonding, these vibrations also influence the shape of the IR peak. Generally, asymmetric stretching frequencies are higher than symmetric stretching frequencies. For example, primary amines exhibit two distinct IR peaks between 3300–3500 cm−1 corresponding to the symmetric and asymmetric N-H stretching, while secondary amines exhibit a single stretching vibration...

You might also read

Related Articles

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

Sort by

Same author

An Effective Video Transformer With Synchronized Spatiotemporal and Spatial Self-Attention for Action Recognition.

IEEE transactions on neural networks and learning systems·2022

Same author

FIR filter banks for hexagonal data processing.

IEEE transactions on image processing : a publication of the IEEE Signal Processing Society·2008

See all related articles

Search research articles

Related Experiment Video

Updated: Jun 29, 2026

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

Compactly supported orthogonal and biorthogonal square root 5-refinement wavelets with 4-fold symmetry.

Qingtang Jiang¹

¹Department of Mathematics and Computer Science, University of Missouri-St. Louis, St. Louis, MO 63121, USA. jiangq@umsl.edu

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society

|October 16, 2008

Summary

This study introduces the construction of orthogonal and biorthogonal wavelets for square root 5-refinement, a novel approach for multiresolution data processing and geometry rendering. These new wavelets utilize unique filter banks with 4-fold rotational symmetry.

Related Experiment Videos

Last Updated: Jun 29, 2026

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

Area of Science:

Digital Signal Processing
Computer Graphics
Applied Mathematics

Background:

Square root 5-refinement offers unique properties for adaptive geometry representation and rendering.
Existing research on wavelets primarily focuses on dyadic or quincunx refinements.
The construction of wavelets for square root 5-refinement remains an underexplored area.

Purpose of the Study:

To construct compactly supported orthogonal and biorthogonal wavelets tailored for square root 5-refinement.
To develop novel filter banks and wavelet constructions for this specific refinement method.

Main Methods:

Derivation of block structures for orthogonal and biorthogonal square root 5-refinement FIR filter banks.
Incorporation of 4-fold rotational symmetry into the filter bank design.
Construction of wavelets based on the derived block structures.

Main Results:

Successfully obtained block structures for orthogonal and biorthogonal square root 5-refinement FIR filter banks.
Achieved 4-fold rotational symmetry in the designed filter banks.
Developed compactly supported orthogonal and biorthogonal wavelets utilizing square root 5-refinement.

Conclusions:

The study successfully addresses the gap in wavelet construction for square root 5-refinement.
The developed wavelets and filter banks are suitable for multiresolution data processing and complex geometry rendering.
This work opens new avenues for applying square root 5-refinement in advanced signal and image processing applications.