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Related Concept Videos

Vector Algebra: Method of Components01:08

Vector Algebra: Method of Components

It is cumbersome to find the magnitudes of vectors using the parallelogram rule or using the graphical method to perform mathematical operations like addition, subtraction, and multiplication. There are two ways to circumvent this algebraic complexity. One way is to draw the vectors to scale, as in navigation, and read approximate vector lengths and angles (directions) from the graphs. The other way is to use the method of components.
In many applications, the magnitudes and directions of...
IR Spectrum Peak Splitting: Symmetric vs Asymmetric Vibrations01:08

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...
Polar and Cylindrical Coordinates01:22

Polar and Cylindrical Coordinates

The Cartesian coordinate system is a very convenient tool to use when describing the displacements and velocities of objects and the forces acting on them. However, it becomes cumbersome when we need to describe the rotation of objects. So, when describing rotation, the polar coordinate system is generally used.
Curvilinear Motion: Polar Coordinates01:27

Curvilinear Motion: Polar Coordinates

In polar coordinates, the motion of a particle follows a curvilinear path. The radial coordinate symbolized as 'r,' extends outward from a fixed origin to the particle, while the angular coordinate, 'θ,' measured in radians, represents the counterclockwise angle between a fixed reference line and the radial line connecting the origin to the particle.
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Polar Coordinates01:24

Polar Coordinates

The polar coordinate system offers an alternative to the Cartesian coordinate system for specifying points in a plane, using a distance and an angle instead of x and y coordinates. This system is particularly advantageous in situations involving circular or rotational symmetry, such as in physics or engineering problems involving waves, oscillations, or orbital paths.Defining Polar CoordinatesIn polar coordinates, a point is represented as P(r, ��), where r is the radial distance from a fixed...
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Vector Components in the Cartesian Coordinate System

Vectors are usually described in terms of their components in a coordinate system. Even in everyday life, we naturally invoke the concept of orthogonal projections in a rectangular coordinate system. For example, if someone gives you directions for a particular location, you will be told to go a few km in a direction like east, west, north, or south, along with the angle in which you are supposed to move. In a rectangular (Cartesian) xy-coordinate system in a plane, a point in a plane is...

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Related Experiment Video

Updated: May 21, 2026

Multimodal Nonlinear Hyperspectral Chemical Imaging Using Line-Scanning Vibrational Sum-Frequency Generation Microscopy
08:49

Multimodal Nonlinear Hyperspectral Chemical Imaging Using Line-Scanning Vibrational Sum-Frequency Generation Microscopy

Published on: December 1, 2023

Simultaneous source localization and polarization estimation via non-orthogonal joint diagonalization with

Xiao-Feng Gong1, Ke Wang, Qiu-Hua Lin

  • 1School of Information and Communication Engineering, Dalian University of Technology, Dalian 116024, China. xfgong@dlut.edu.cn

Sensors (Basel, Switzerland)
|June 28, 2012
PubMed
Summary

This study introduces new algorithms for joint direction-of-arrival (DOA) and polarization estimation using electromagnetic vector-sensors (EMVS). The methods simplify complex optimization problems for improved signal processing accuracy.

Keywords:
LQLUcomplex non-orthogonal joint diagonalizationdirection-of-arrivalelectromagnetic vector-sensorpolarization

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A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
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Last Updated: May 21, 2026

Multimodal Nonlinear Hyperspectral Chemical Imaging Using Line-Scanning Vibrational Sum-Frequency Generation Microscopy
08:49

Multimodal Nonlinear Hyperspectral Chemical Imaging Using Line-Scanning Vibrational Sum-Frequency Generation Microscopy

Published on: December 1, 2023

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
07:56

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

Area of Science:

  • Signal Processing
  • Electromagnetics
  • Array Signal Processing

Background:

  • Electromagnetic vector-sensors (EMVS) enable simultaneous measurement of signal amplitude, phase, and polarization.
  • Direction-of-arrival (DOA) and polarization estimation are crucial for modern wireless communication and radar systems.
  • Existing methods for joint DOA and polarization estimation often involve computationally intensive algorithms.

Purpose of the Study:

  • To develop novel complex-valued non-orthogonal joint diagonalization (CNJD) algorithms for DOA and polarization estimation.
  • To propose a new strategy leveraging the multi-dimensional structure of EMVS data for enhanced estimation.
  • To evaluate the performance of the proposed methods against existing techniques.

Main Methods:

  • Development of two new CNJD algorithms utilizing LU/LQ decompositions and a Jacobi-type scheme.
  • Implementation of a novel strategy to exploit second-order statistics of EMVS outputs.
  • Comparative simulations against tensorial and existing joint diagonalization methods.

Main Results:

  • The proposed CNJD algorithms effectively address the high-dimensional optimization challenges in joint DOA and polarization estimation.
  • The novel strategy demonstrates improved performance in simultaneous DOA and polarization estimation using EMVS.
  • Simulations validate the effectiveness of the new approach compared to prior art.

Conclusions:

  • The presented CNJD algorithms offer efficient solutions for complex optimization problems in EMVS signal processing.
  • The novel strategy provides a robust framework for simultaneous DOA and polarization estimation.
  • This work contributes to advancements in array signal processing for electromagnetic applications.