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Related Concept Videos

Sampling Methods: Overview01:06

Sampling Methods: Overview

379
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. 
In analytical chemistry, the choice of...
379
Sampling Methods: Sample Types01:18

Sampling Methods: Sample Types

274
Sampling materials are classified into three main types: solid, liquid, and gas.
Solid samples include a variety of substances, such as sediments from water bodies, soil, metals, and biological tissues. Two standard methods for extracting sediments from water bodies are grab sampling and piston coring. Grab sampling involves using a device to collect a discrete sediment sample from the bottom of a water body with minimal disturbance. Grab samples do not always represent the entire area due to...
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Sampling Plans01:23

Sampling Plans

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Sampling is a crucial step in analytical chemistry, allowing researchers to collect representative data from a large population. Common sampling methods include random, judgmental, systematic, stratified, and cluster sampling.
Random sampling is a method where each member of the population has an equal chance of being selected for the sample. It involves selecting individuals randomly, often using random number generators or lottery-type methods. For example, when analyzing the properties of a...
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Random Sampling Method01:09

Random Sampling Method

11.2K
Sampling is a technique to select a portion (or subset) of the larger population and study that portion (the sample) to gain information about the population. Data are the result of sampling from a population. The sampling method ensures that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest. Among the various sampling methods used by...
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Cluster Sampling Method01:20

Cluster Sampling Method

12.0K
Appropriate sampling methods ensure that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest.
To choose a cluster sample, divide the population into clusters (groups) and then randomly select some of the clusters. All the members from these clusters are in the cluster sample. For example, if you randomly sample four departments from your...
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Stratified Sampling Method01:16

Stratified Sampling Method

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Sampling is a technique to select a portion (or subset) of the larger population and study that portion (the sample) to gain information about the population. The sampling method ensures that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest.
To choose a stratified sample, divide the population into groups called strata and then take a...
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Embracing off-the-grid samples.

Oscar López1, Özgür Yılmaz2

  • 1Harbor Branch Oceanographic Institute, Florida Atlantic University, 5600 US 1 North, Fort Pierce, FL 34946 USA.

Sampling Theory, Signal Processing, and Data Analysis
|August 10, 2023
PubMed
Summary
This summary is machine-generated.

Randomly deviating from a standard grid (off-the-grid sampling) significantly reduces the number of samples needed for accurate signal reconstruction. This technique also improves noise reduction, offering benefits for signal acquisition and anti-aliasing.

Keywords:
Anti-aliasingCompressive sensingDirichlet kernelJitter samplingNonuniform samplingSub-Nyquist sampling

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Area of Science:

  • Signal Processing
  • Information Theory
  • Applied Mathematics

Background:

  • Empirical studies suggest benefits of off-the-grid sampling for signal acquisition, including undersampling and anti-aliasing.
  • Theoretical conditions and explicit advantages for these sampling methods are not well-documented in existing literature.

Purpose of the Study:

  • To provide theoretical insights into the advantages of off-the-grid sampling when sampling positions are known.
  • To demonstrate the effectiveness of nonuniform samples for compressive sampling and noise attenuation.

Main Methods:

  • Utilized a square-root LASSO decoder with an interpolation kernel for compressive sampling analysis.
  • Employed a least squares problem formulation to analyze noise attenuation through oversampling.

Main Results:

  • Showed that a significantly reduced number of random off-the-grid samples suffice for accurate signal reconstruction compared to traditional equispaced sampling.
  • Demonstrated that random off-the-grid samples enhance noise attenuation by a factor of 1/epsilon.

Conclusions:

  • Off-the-grid sampling offers a more efficient approach to signal acquisition, requiring fewer samples for accurate reconstruction.
  • This method provides a robust framework for both undersampling, anti-aliasing, and noise suppression in signal processing.