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Related Concept Videos

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 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.
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...
Sampling Distribution01:12

Sampling Distribution

Given simple random samples of size n from a given population with a measured characteristic such as mean, proportion, or standard deviation for each sample, the probability distribution of all the measured characteristics is called a sampling distribution. How much the statistic varies from one sample to another is known as the sampling variability of a statistic. You typically measure the sampling variability of a statistic by its standard error. The standard error of the mean is an example...
Imaging Biological Samples with Optical Microscopy01:18

Imaging Biological Samples with Optical Microscopy

Optical microscopy uses optic principles to provide detailed images of samples. Antonie van Leeuwenhoek designed the first compound optical microscope in the 17th century to visualize blood cells, bacteria, and yeast cells. In 1830, Joseph Jackson Lister created an essentially modern light microscope. The 20th century saw the development of microscopes with enhanced magnification and resolution.
In optical microscopy, the specimen to be viewed is placed on a glass slide and clipped on the stage...
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...

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Related Experiment Video

Updated: Jun 14, 2026

Integrated Photoacoustic Ophthalmoscopy and Spectral-domain Optical Coherence Tomography
11:21

Integrated Photoacoustic Ophthalmoscopy and Spectral-domain Optical Coherence Tomography

Published on: January 15, 2013

Impact of sampled data on an optical joint transform correlator.

D F Elliott, I L Ayala

    Applied Optics
    |March 25, 2010
    PubMed
    Summary

    Undersampling in optical joint transform correlators (OJTCs) retains essential correlation data and shape. However, this undersampling necessitates reducing input data by a factor of i, impacting performance.

    Area of Science:

    • Optics and Photonics
    • Signal Processing
    • Image Recognition

    Background:

    • Coherent optical systems excel at Fourier transforms, Fresnel transforms, and pattern recognition.
    • Optical correlators are fundamental to pattern recognition in these systems.
    • Joint transform correlators (JTCs) are a key type of optical correlator.

    Purpose of the Study:

    • To analyze the impact of undersampling on optical joint transform correlators (OJTCs).
    • To determine if essential correlation data is preserved despite undersampling.
    • To quantify the trade-offs associated with undersampling in OJTCs.

    Main Methods:

    • Investigated OJTCs with sampled-data input and specific detector resolutions in Fourier and correlation planes.
    • Analyzed the theoretical effects of undersampling on correlation plane data and surface shape.

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  • Employed digital simulations using discrete Fourier transform (DFT) to predict and verify optical correlator performance.

    • Main Results:

    • Undersampling in OJTCs does not alter the shape of correlation surfaces.
    • Essential correlation data remains present in the correlation plane post-undersampling.
    • A significant consequence of undersampling is the reduction of input data by a factor of i.

    Conclusions:

    • Undersampling in OJTCs is feasible, preserving crucial information.
    • The primary penalty for undersampling is a reduction in the usable input data.
    • Digital simulations accurately predict the performance of optical correlators, validating theoretical findings.