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Related Concept Videos

Sampling Theorem01:15

Sampling Theorem

In signal processing, the analysis of continuous-time signals, denoted as x(t), often involves sampling techniques to convert these signals into discrete-time signals. This process is essential for digital representation and manipulation. A critical component in sampling is the train of impulses, characterized by the sampling interval and the sampling frequency. The relationship between these parameters and the original signal's properties dictates the success of the sampling process.
Upsampling01:22

Upsampling

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...
Bandpass Sampling01:17

Bandpass Sampling

In signal processing, bandpass sampling is an effective technique for sampling signals that have most of their energy concentrated within a narrow frequency band. This type of signal is known as a bandpass signal. The key principle of bandpass sampling involves sampling the signal at a rate that is greater than twice the signal's bandwidth to prevent aliasing.
A bandpass signal has a spectrum with a lower frequency limit, denoted as ω1, and an upper frequency limit, denoted as ω2. The spectrum...
Aliasing01:18

Aliasing

Accurate signal sampling and reconstruction are crucial in various signal-processing applications. A time-domain signal's spectrum can be revealed using its Fourier transform. When this signal is sampled at a specific frequency, it results in multiple scaled replicas of the original spectrum in the frequency domain. The spacing of these replicas is determined by the sampling frequency.
If the sampling frequency is below the Nyquist rate, these replicas overlap, preventing the original signal...
Sampling Continuous Time Signal01:11

Sampling Continuous Time Signal

In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
In the...
Sampling Methods: Overview01:06

Sampling Methods: Overview

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 sampling...

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Estimating the optimal sampling rate using wavelet transform: an application to optical turbulence.

Gustavo Funes1, Angel Fernández, Darío G Pérez

  • 1Centro de Investigaciones Ópticas (CONICET La Plata - CIC), C.C. 3, 1897 Gonnet, Argentina. gfunes@ciop.unlp.edu.ar

Optics Express
|July 12, 2013
PubMed
Summary
This summary is machine-generated.

This study introduces a practical experimental method using discrete wavelet transform to determine optimal sampling rates for optical turbulence measurements, avoiding information loss and oversampling without prior turbulence knowledge.

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Area of Science:

  • Optics and Photonics
  • Signal Processing
  • Atmospheric Science

Background:

  • Determining appropriate sampling rates is crucial for accurately measuring optical quantities affected by light propagation through turbulence.
  • Current methods for estimating sampling rates often rely on ad hoc assumptions or require prior knowledge of optical turbulence properties.
  • Techniques like Fast Fourier Transform (FFT) can estimate optimal sampling rates but may necessitate analytical models or frequency content analysis.

Purpose of the Study:

  • To propose a novel, practical, and experimental method for estimating the optimal sampling rate for optical turbulence measurements.
  • To develop an approach that is independent of any imposed statistical model of the turbulence.
  • To ensure that the chosen sampling rate prevents information loss while avoiding unnecessary oversampling.

Main Methods:

  • Utilizing the discrete wavelet transform (DWT) as the core methodology.
  • Applying the DWT to experimental data series related to light propagation through turbulence.
  • Analyzing the wavelet decomposition to identify appropriate frequency content and determine the sampling rate.

Main Results:

  • The proposed discrete wavelet transform method provides a practical approach to determine sampling rates.
  • This method effectively prevents the loss of critical information during measurement.
  • The approach successfully avoids oversampling, leading to more efficient data acquisition.
  • The method's independence from prior knowledge of turbulence statistics is demonstrated.

Conclusions:

  • The discrete wavelet transform offers a robust and versatile tool for setting sampling rates in optical turbulence experiments.
  • This technique enhances the reliability and efficiency of optical turbulence measurements.
  • The method provides a valuable alternative to existing approaches, particularly when turbulence characteristics are unknown.