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Related Concept Videos

Downsampling01:20

Downsampling

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When considering a sampled sequence with zero values between sampling instants, one can replace it by taking every N-th value of the sequence. At these integer multiples of N, the original and sampled sequences coincide. This process, known as decimation, involves extracting every N-th sample from a sequence, thereby creating a more efficient sequence.
The Fourier transform of the decimated sequence reveals a combination of scaled and shifted versions of the original spectrum. This...
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Upsampling01:22

Upsampling

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Managing signal sampling rates is essential in digital signal processing to maintain signal integrity. A decimated signal, characterized by a reduced frequency range due to its lower sampling rate, can be upsampled by inserting zeros between each sample. This upsampling process expands the original spectrum and introduces repeated spectral replicas at intervals dictated by the new Nyquist frequency. To refine this zero-inserted sequence, it is passed through a lowpass filter with a cutoff...
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Sampling Methods: Overview01:06

Sampling Methods: Overview

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A sample refers to a smaller subset representative of a larger population. In analytical chemistry, studying or analyzing an entire population is often impractical or impossible. Therefore, samples are used to draw inferences and generalize the whole population. The sampling method selects individuals or items from a population to create a sample. Standard sampling methods include random, judgemental, systematic, stratified, and cluster sampling. 
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Reducing Line Loss01:18

Reducing Line Loss

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In a three-phase circuit, line loss is an indicator of energy dissipated as heat due to the resistance of transmission lines. To address this, incorporating transformers into the system—a step-up transformer at the source and a step-down transformer at the load—is a strategic solution. Two three-phase transformers are introduced to improve this.
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Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

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Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
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Sample Preparation for Analysis: Advanced Techniques01:08

Sample Preparation for Analysis: Advanced Techniques

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Accurate analysis of complex samples often requires advanced preparation techniques to achieve reliable and reproducible results. Samples containing inorganic or organic materials can be challenging to dissolve or decompose effectively. Standard sample preparation methods include acid digestion, fusion, dry ashing, and wet digestion.
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Related Experiment Video

Updated: May 6, 2026

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis
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Improve GRAPPA with cross-sampled ACS lines and nonlinear kernel model.

Xiaoyan Wang1, Haifeng Wang, Jing Zhou

  • 1Department of Educational Technology, Yuxi Normal University, Yunnan, China.

Bio-Medical Materials and Engineering
|November 12, 2013
PubMed
Summary
This summary is machine-generated.

A new cross-sampled nonlinear (CSNL) GRAPPA method enhances parallel magnetic resonance imaging (PMRI) by using orthogonal calibration data and a nonlinear model to reduce artifacts and noise during high acceleration.

Keywords:
GRAPPAcross-samplednonlinearparallel MRI

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Area of Science:

  • Medical Imaging
  • Magnetic Resonance Imaging
  • Image Reconstruction

Background:

  • Parallel magnetic resonance imaging (PMRI) accelerates data acquisition.
  • Generalized Auto-calibrating Partially Parallel Acquisitions (GRAPPA) is a common PMRI technique.
  • GRAPPA reconstructs missing k-space data using weights derived from auto-calibration signal (ACS) lines.

Purpose of the Study:

  • To introduce a novel hybrid method for enhanced GRAPPA reconstruction.
  • To improve artifact and noise reduction in PMRI, especially at high acceleration factors.
  • To combine the advantages of cross-sampling ACS data and nonlinear modeling.

Main Methods:

  • Proposed a novel hybrid reconstruction method for GRAPPA.
  • Utilized cross-sampling of ACS lines orthogonal to the reduced acquisition lines.
  • Employed a second-order nonlinear model for estimating reconstruction weights.

Main Results:

  • The proposed cross-sampled nonlinear (CSNL) GRAPPA method was evaluated using in vivo experiments.
  • CSNL GRAPPA effectively reduced aliasing artifacts.
  • CSNL GRAPPA demonstrated significant noise reduction, particularly under high acceleration conditions.

Conclusions:

  • The CSNL GRAPPA method offers improved performance over standard GRAPPA.
  • This technique is effective for achieving high acceleration in PMRI with reduced artifacts.
  • The hybrid approach successfully integrates cross-sampling and nonlinear modeling benefits.