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Related Concept Videos

Fast Fourier Transform01:10

Fast Fourier Transform

The Fast Fourier Transform (FFT) is a computational algorithm designed to compute the Discrete Fourier Transform (DFT) efficiently. By breaking down the calculations into smaller, manageable sections, the FFT significantly reduces the computational complexity involved. Direct computation of an N-point DFT requires N2 complex multiplications, whereas the FFT algorithm needs only (N/2)log⁡2N multiplications, offering a much faster performance.
The computational efficiency of the FFT becomes...
Time and frequency -Domain Interpretation of Phase-lag Control01:21

Time and frequency -Domain Interpretation of Phase-lag Control

Phase-lag controllers are widely used in control systems to improve stability and reduce steady-state errors. A dimmer switch controlling the brightness of a light bulb serves as a practical example of phase-lag control, gradually adjusting the bulb's brightness. Mathematically, phase-lag control or low-pass filtering is represented when the factor 'a' is less than 1.
Phase-lag controllers do not place a pole at zero, but instead influence the steady-state error by amplifying any finite,...
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...
Continuous -time Fourier Transform01:11

Continuous -time Fourier Transform

The Fourier series is instrumental in representing periodic functions, offering a powerful method to decompose such functions into a sum of sinusoids. This technique, however, necessitates modification when applied to nonperiodic functions. Consider a pulse-train waveform consisting of a series of rectangular pulses. When these pulses have a finite period, they can be accurately represented by a Fourier series. Yet, as the period approaches infinity, resulting in a single, isolated pulse, the...
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
Time and frequency -Domain Interpretation of Phase-lead Control01:24

Time and frequency -Domain Interpretation of Phase-lead Control

Phase-lead controllers are commonly used in various control systems to enhance response speed and stability. Adjusting the brightness on a television screen offers a practical example of phase-lead control. When contrast is enhanced, a phase-lead controller is employed. Mathematically, phase-lead control is identified when the first parameter is smaller than the second.
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Related Experiment Video

Updated: Jun 15, 2026

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
08:39

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

Published on: January 28, 2019

Ultrafast 2D COSY with constant-time phase-modulated spatial encoding.

Can Wu1, Mingfang Zhao, Shuhui Cai

  • 1Department of Physics, Fujian Key Laboratory of Plasma and Magnetic Resonance, State Key Laboratory of Physical Chemistry of Solid Surfaces, Xiamen University, Xiamen 361005, China.

Journal of Magnetic Resonance (San Diego, Calif. : 1997)
|March 6, 2010
PubMed
Summary
This summary is machine-generated.

New ultrafast 2D COSY methods (g-COSY and gDQF-COSY) offer improved signal-to-noise ratio and resolution. These techniques enhance the ease of obtaining high-quality 2D COSY spectra in a single scan.

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Blood Flow Imaging with Ultrafast Doppler
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Blood Flow Imaging with Ultrafast Doppler

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Last Updated: Jun 15, 2026

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
08:39

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

Published on: January 28, 2019

Blood Flow Imaging with Ultrafast Doppler
05:57

Blood Flow Imaging with Ultrafast Doppler

Published on: October 14, 2020

Area of Science:

  • Nuclear Magnetic Resonance (NMR) Spectroscopy
  • Analytical Chemistry

Background:

  • Ultrafast techniques allow for rapid acquisition of 2D NMR spectra, including COSY, TOCSY, DOSY, HMQC, and J-resolved.
  • These methods are crucial for molecular structure elucidation and characterization.

Purpose of the Study:

  • To propose and validate two novel ultrafast 2D COSY methods: gradient-COSY (g-COSY) and gradient-double-quantum-filtered-COSY (gDQF-COSY).
  • To theoretically derive signal expressions and experimentally verify the performance of these new techniques.

Main Methods:

  • Development of g-COSY and gDQF-COSY based on continuous constant-time phase-modulated spatial encoding.
  • Theoretical analysis of signal formation and experimental validation using NMR spectroscopy.
  • Comparative analysis against previous real-time phase-modulated spatial encoding methods.

Main Results:

  • Experimental verification of the theoretical models for g-COSY and gDQF-COSY.
  • Demonstrated improvement in signal-to-noise ratio (SNR) and spectral resolution for 2D COSY spectra.
  • Easier achievement of high-quality 2D COSY spectra compared to existing methods.

Conclusions:

  • The proposed g-COSY and gDQF-COSY methods represent a significant advancement in ultrafast 2D COSY spectroscopy.
  • These methods offer enhanced spectral quality and efficiency for molecular analysis.
  • The findings facilitate more accessible and robust 2D NMR data acquisition.