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Related Concept Videos

Properties of DTFT I01:24

Properties of DTFT I

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...
Discrete Fourier Transform01:15

Discrete Fourier Transform

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...
Discrete-Time Fourier Series01:20

Discrete-Time Fourier Series

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]...
Relation of DFT to z-Transform01:20

Relation of DFT to z-Transform

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 terms of...
Discrete-time Fourier transform01:26

Discrete-time Fourier transform

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...
Properties of DTFT II01:24

Properties of DTFT II

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. Multiplying by j...

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Updated: May 10, 2026

Design and Characterization Methodology for Efficient Wide Range Tunable MEMS Filters
15:25

Design and Characterization Methodology for Efficient Wide Range Tunable MEMS Filters

Published on: February 4, 2018

Optimally Tuned Multiconfigurational Short-Range DFT for Linear Response Properties.

Michal Hapka1, Katarzyna Pernal2, Ewa Pastorczak2

  • 1Faculty of Chemistry, University of Warsaw, ul. L. Pasteura 1, Warsaw 02-093, Poland.

The Journal of Physical Chemistry. A
|May 8, 2026
PubMed
Summary
This summary is machine-generated.

This study introduces an optimal-tuning method for multiconfigurational short-range density functional theory (MC-srDFT). This new approach improves the accuracy of calculating molecular polarizabilities by determining a system-specific parameter.

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Published on: January 25, 2020

Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Theoretical Chemistry

Background:

  • Multiconfigurational short-range density functional theory (MC-srDFT) integrates wave function theory and DFT.
  • MC-srDFT lacks established methods for selecting its range-separation parameter.
  • Existing methods often use a universal parameter, limiting accuracy.

Purpose of the Study:

  • Develop a theoretically grounded protocol for determining the system-specific range-separation parameter in MC-srDFT.
  • Improve the accuracy of static and dynamic dipole polarizability calculations.
  • Provide a more rigorous approach compared to using universal parameters.

Main Methods:

  • Introduced an optimal-tuning scheme based on enforcing correct electron density decay.
  • Determined the range-separation parameter using the Extended Koopmans' Theorem (EKT) and ionization potential.
  • Applied MC-srDFT with full linear response and its extended random phase approximation (ERPA) variant.

Main Results:

  • The optimal-tuning scheme successfully determined system-specific range-separation parameters.
  • Calculated static and dynamic dipole polarizabilities for molecular systems.
  • Demonstrated substantial improvement in polarizability accuracy compared to a universal parameter (μ = 0.4 bohr⁻¹).

Conclusions:

  • The proposed optimal-tuning scheme provides a theoretically sound method for MC-srDFT parameter selection.
  • This approach significantly enhances the accuracy of polarizability predictions.
  • The method offers a more reliable alternative to universal parameters in MC-srDFT calculations.