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

Bewley Lattice Diagram

Bewley Lattice Diagram

The Bewley lattice diagram, developed by L. V. Bewley, effectively organizes the reflections occurring during transmission-line transients. It visually represents how voltage waves propagate and reflect within a transmission line, making it easier to understand the complex interactions that occur.

Convolution Properties II

Convolution Properties II

The important convolution properties include width, area, differentiation, and integration properties.
The width property indicates that if the durations of input signals are T1 and T2, then the width of the output response equals the sum of both durations, irrespective of the shapes of the two functions. For instance, convolving two rectangular pulses with durations of 2 seconds and 1 second results in a function with a width of 3 seconds.
The area property asserts that the area under the...

Lattice Centering and Coordination Number

Lattice Centering and Coordination Number

The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
Types of Unit Cells
Imagine taking a large number of identical...

Reconstruction of Signal using Interpolation

Reconstruction of Signal using Interpolation

Signal processing techniques are essential for accurately converting continuous signals to digital formats and vice versa. When a continuous signal is sampled with a period T, the resulting sampled signal exhibits replicas of the original spectrum in the frequency domain, spaced at intervals equal to the sampling frequency. To handle this sampled signal, a zero-order hold method can be applied, which creates a piecewise constant signal by retaining each sample's value until the next sampling...

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...

The Seven Crystal Systems: Overview

The Seven Crystal Systems: Overview

Crystals with various point group symmetries belong to different crystal classes, which are synonymous terms. Despite being in the same class, crystals may have distinct shapes, like cubes and octahedra. There are 32 three-dimensional point groups, all of which are systematically divided into seven crystal systems.The basic cubic crystal system, exemplified by NaCl, features orthogonal vectors (α = β = �� = 90°) of equal lengths (a = b = c). When specific requirements are not imposed on the...

You might also read

Related Articles

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

Sort by

Same journal

Marginal-Aware Framework for 3D Shape Segmentation: Resolving Boundary-Internal Face Imbalance.

IEEE transactions on image processing : a publication of the IEEE Signal Processing Society·2026

Same journal

Semantic Composition via Optimal Transport for Composed Image Retrieval.

IEEE transactions on image processing : a publication of the IEEE Signal Processing Society·2026

Same journal

MultiTaskVIF: Segmentation-oriented visible and infrared image fusion via multi-task learning.

IEEE transactions on image processing : a publication of the IEEE Signal Processing Society·2026

Same journal

DTEA: Degradation-Aware Taylor Expansion Approximation Network for Pansharpening.

IEEE transactions on image processing : a publication of the IEEE Signal Processing Society·2026

Same journal

Noisy Tensor Completion for Sparse-Aperture Microwave Imaging in Distributed MIMO Radar Networks.

IEEE transactions on image processing : a publication of the IEEE Signal Processing Society·2026

Same journal

CGGS: Consistency-Augmented Geometric Gaussian Splatting for Ego-centric 3D Scene Generation.

IEEE transactions on image processing : a publication of the IEEE Signal Processing Society·2026

Search research articles

Related Experiment Video

Updated: Jul 14, 2026

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

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

Published on: January 28, 2019

Algebraic signal processing theory: 2-D spatial hexagonal lattice.

Markus Pünschel¹, Martin Rötteler

¹Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA 15213 USA. pueschel@ece.cmu.edu

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

|June 6, 2007

Summary

We introduce a new framework for signal processing on 2-D hexagonal lattices, extending algebraic signal processing theory. This framework enables advanced analysis for both infinite and finite signal arrays, including a novel discrete triangle transform.

More Related Videos

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials

Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials

Published on: September 26, 2014

Related Experiment Videos

Last Updated: Jul 14, 2026

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

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

Published on: January 28, 2019

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials

Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials

Published on: September 26, 2014

Area of Science:

* Digital signal processing
* Algebraic theory
* Lattice-based signal analysis

Background:

* Existing signal processing frameworks are often limited to Cartesian grids.
* Hexagonal lattices offer advantages in sampling efficiency and symmetry.
* Algebraic signal processing theory provides a structured approach to developing signal processing tools.

Purpose of the Study:

* To develop a comprehensive signal processing framework for 2-D hexagonal lattices.
* To extend algebraic signal processing theory to hexagonal grids.
* To define and analyze transforms and concepts for hexagonal signal sampling.

Main Methods:

* Construction of signal models using polynomial algebras based on hexagonal space shifts.
* Application of algebraic signal processing theory principles.
* Definition of hexagonal z-transform, boundary conditions, filtering, and Fourier transform.

Main Results:

* A unified framework for signal processing on infinite and finite 2-D hexagonal lattices.
* Introduction of the nonseparable discrete triangle transform for finite hexagonal arrays.
* Demonstration of the framework as a natural extension of algebraic signal processing theory.

Conclusions:

* The developed framework provides a robust foundation for hexagonal lattice signal processing.
* The discrete triangle transform is a key component for finite hexagonal signal analysis.
* This work bridges Mersereau's hexagonal lattice work with modern algebraic signal processing.