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Related Concept Videos

Properties of DTFT I01:24

Properties of DTFT I

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In signal processing, Discrete-Time Fourier Transforms (DTFTs) play a critical role in analyzing discrete-time signals in the frequency domain. Various properties of the DTFTs such as linearity, time-shifting, frequency-shifting, time reversal, conjugation, and time scaling help understand and manipulate these signals for different applications.
The linearity property of DTFTs is fundamental. If two discrete-time signals are multiplied by constants a and b respectively, and then combined to...
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Discrete-Time Fourier Series01:20

Discrete-Time Fourier Series

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The Discrete-Time Fourier Series (DTFS) is a fundamental concept in signal processing, serving as the discrete-time counterpart to the continuous-time Fourier series. It allows for the representation and analysis of discrete-time periodic signals in terms of their frequency components. Unlike its continuous counterpart, which utilizes integrals, the calculation of DTFS expansion coefficients involves summations due to the discrete nature of the signal.
For a discrete-time periodic signal x[n]...
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Properties of DTFT II01:24

Properties of DTFT II

205
In the study of discrete-time signal processing, understanding the properties of the Discrete-Time Fourier Transform (DTFT) is crucial for analyzing and manipulating signals in the frequency domain. Several properties, including frequency differentiation, convolution, accumulation, and Parseval's relation, offer powerful tools for signal analysis.
The frequency differentiation property is illustrated by considering a DTFT pair and differentiating both sides with respect to ω.
205
Discrete-time Fourier transform01:26

Discrete-time Fourier transform

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The Discrete-Time Fourier Transform (DTFT) is an essential mathematical tool for analyzing discrete-time signals, converting them from the time domain to the frequency domain. This transformation allows for examining the frequency components of discrete signals, providing insights into their spectral characteristics. In the DTFT, the continuous integral used in the continuous-time Fourier transform is replaced by a summation to accommodate the discrete nature of the signal.
One of the notable...
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Discrete Fourier Transform01:15

Discrete Fourier Transform

303
The Discrete Fourier Transform (DFT) is a fundamental tool in signal processing, extending the discrete-time Fourier transform by evaluating discrete signals at uniformly spaced frequency intervals. This transformation converts a finite sequence of time-domain samples into frequency components, each representing complex sinusoids ordered by frequency. The DFT translates these sequences into the frequency domain, effectively indicating the magnitude and phase of each frequency component present...
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Relation of DFT to z-Transform01:20

Relation of DFT to z-Transform

400
The Discrete Fourier Transform (DFT) is a crucial tool for analyzing the frequency content of discrete-time signals. It converts a sequence of N samples from the time domain into its corresponding sequence in the frequency domain, where each sample represents a specific frequency component.
To understand how the DFT works, it's helpful to consider the z-transform, which is a method for representing discrete sequences in the complex frequency domain. The z-transform involves summing the...
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Related Experiment Video

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Author Spotlight: Exploring Light-Driven Chemical Reactions and Energy-Harnessing Devices in Photochemical Research
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Real-Time Extension of TAO-DFT.

Hung-Yi Tsai1, Jeng-Da Chai1,2,3

  • 1Department of Physics, National Taiwan University, Taipei 10617, Taiwan.

Molecules (Basel, Switzerland)
|November 14, 2023
PubMed
Summary
This summary is machine-generated.

We introduce real-time Thermally Assisted Occupation Density Functional Theory (RT-TAO-DFT) for calculating time-dependent electronic properties. This new method accurately models high-order harmonic generation in molecular hydrogen, offering an alternative to existing techniques.

Keywords:
RT-TAO-DFTTAO-DFThigh-order harmonic generationmulti-reference characterreal-time electron dynamicstime-dependent properties

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Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Electronic Structure Theory

Background:

  • Thermally assisted occupation density functional theory (TAO-DFT) is effective for ground-state properties of complex electronic systems.
  • Studying time-dependent (TD) properties, especially under intense laser fields, requires advanced computational methods.
  • Existing methods may have limitations in accurately describing TD phenomena in multi-reference systems.

Purpose of the Study:

  • To develop a real-time (RT) extension of TAO-DFT, termed RT-TAO-DFT, for calculating time-dependent electronic properties.
  • To investigate the high-order harmonic generation (HHG) spectra and TD properties of molecular hydrogen (H2) using RT-TAO-DFT.
  • To compare the performance of RT-TAO-DFT with the established time-dependent Kohn-Sham (TDKS) method and discuss spin-symmetry breaking effects.

Main Methods:

  • Development of the real-time extension of TAO-DFT (RT-TAO-DFT).
  • Application of RT-TAO-DFT to simulate high-order harmonic generation (HHG) spectra of H2.
  • Calculations performed at equilibrium and stretched H2 geometries under intense laser fields.
  • Comparison of RT-TAO-DFT results with time-dependent Kohn-Sham (TDKS) calculations.

Main Results:

  • RT-TAO-DFT successfully calculates TD properties, including HHG spectra, for molecular hydrogen.
  • The method provides insights into the electronic dynamics of H2 under intense laser irradiation.
  • Comparisons reveal the strengths and potential differences between RT-TAO-DFT and TDKS for these systems.
  • Analysis of spin-symmetry breaking effects in TD properties was conducted.

Conclusions:

  • RT-TAO-DFT is a viable and efficient method for studying time-dependent electronic properties of systems with multi-reference character.
  • The developed method offers a valuable alternative for simulating phenomena like HHG, particularly for challenging electronic systems.
  • Further investigation into spin-symmetry breaking in TD calculations is warranted.