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Related Concept Videos

State Space Representation01:27

State Space Representation

741
The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
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Transfer Function to State Space01:23

Transfer Function to State Space

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State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
In an...
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State Space to Transfer Function01:21

State Space to Transfer Function

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The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:
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Graphing the Wave Function01:13

Graphing the Wave Function

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Consider the wave equation for a sinusoidal wave moving in the positive x-direction. The wave equation is a function of both position and time. From the wave equation, two different graphs can be plotted.
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Properties of Fourier series I01:20

Properties of Fourier series I

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The Fourier series is a powerful tool in signal processing and communications, allowing periodic signals to be expressed as sums of sine and cosine functions. A foundational property of the Fourier series is linearity. If we consider two periodic signals, their linear combination results in a new signal whose Fourier coefficients are simply the corresponding linear combinations of the original signals' coefficients. This property is crucial in applications like frequency modulation (FM) radio,...
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Properties of Fourier series II01:21

Properties of Fourier series II

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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.
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Nonclassicality phase-space functions: more insight with fewer detectors.

Alfredo Luis1, Jan Sperling2, Werner Vogel2

  • 1Departamento de Óptica, Facultad de Ciencias Físicas, Universidad Complutense, 28040 Madrid, Spain.

Physical Review Letters
|March 28, 2015
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Summary

We introduce a new method using on-off detectors and unbalanced homodyning to visualize quantum effects in radiation fields. This technique efficiently reveals nonclassical signatures without complex data processing, offering insights beyond traditional photon number resolution.

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Area of Science:

  • Quantum Optics
  • Quantum Information Science

Background:

  • On-off detectors are standard for measuring low photon number radiation fields.
  • Photoelectric detection theory uses s-parametrized quasiprobabilities.

Purpose of the Study:

  • To develop a novel method for visualizing nonclassical effects in quantum radiation fields.
  • To introduce a new class of phase-space distributions directly sampled from measurements.

Main Methods:

  • Combining on-off detector systems with unbalanced homodyning and a weak local oscillator.
  • Sampling click-counting statistics to generate phase-space functions.
  • Analyzing negativities in sampled phase-space functions to identify quantum signatures.

Main Results:

  • Generated phase-space functions representing the click counterpart to standard quasiprobabilities.
  • Demonstrated direct visualization of nonclassical effects without post-processing.
  • Showed that fewer on-off detectors can provide more insight than perfect photon number resolution.

Conclusions:

  • The proposed technique efficiently characterizes nonclassicality in quantum radiation fields.
  • This method can uncover quantum signatures in both particle and wave domains, including photon number and squeezed states.
  • Applications are expected in quantum optics and quantum technology.