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Related Concept Videos

Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

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.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
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...
Determination of Expected Frequency01:08

Determination of Expected Frequency

Suppose one wants to test independence between the two variables of a contingency table. The values in the table constitute the observed frequencies of the dataset. But how does one determine the expected frequency of the dataset? One of the important assumptions is that the two variables are independent, which means the variables do not influence each other. For independent variables, the statistical probability of any event involving both variables is calculated by multiplying the individual...
Doppler Effect - II01:05

Doppler Effect - II

The Doppler effect has several practical, real-world applications. For instance, meteorologists use Doppler radars to interpret weather events based on the Doppler effect. Typically, a transmitter emits radio waves at a specific frequency toward the sky from a weather station. The radio waves bounce off the clouds and precipitation and travel back to the weather station. The radio frequency of the waves reflected back to the station appears to decrease if the clouds or precipitation are moving...
Expected Frequencies in Goodness-of-Fit Tests01:19

Expected Frequencies in Goodness-of-Fit Tests

A goodness-of-fit test is conducted to determine whether the observed frequency values are statistically similar to the frequencies expected for the dataset. Suppose the expected frequencies for a dataset are equal such as when predicting the frequency of any number appearing when casting a die. In that case, the expected frequency is the ratio of the total number of observations (n) to the number of categories (k).
Doppler Effect - I00:56

Doppler Effect - I

The Doppler effect and Doppler shift were named after the Austrian physicist and mathematician Christian Johann Doppler in 1842, who conducted experiments with both moving sources and moving observers. Consider an observer standing on a street corner, observing an ambulance with a siren sound passing by at a constant speed. The observer experiences two characteristic changes in the sound of the siren. Initially, the sound increases in loudness as the ambulance approaches and decreases in...

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Related Experiment Video

Updated: Jun 22, 2026

Doppler Optical Coherence Tomography of Retinal Circulation
10:46

Doppler Optical Coherence Tomography of Retinal Circulation

Published on: September 18, 2012

Frequency estimation precision in Doppler optical coherence tomography using the Cramer-Rao lower bound.

Siavash Yazdanfar, Changhuei Yang, Marinko Sarunic

    Optics Express
    |June 3, 2009
    PubMed
    Summary
    This summary is machine-generated.

    Doppler optical coherence tomography (DOCT) reveals fundamental limits in blood flow imaging precision due to noise. Careful selection of noise models is crucial for accurate frequency estimation in DOCT systems.

    Related Experiment Videos

    Last Updated: Jun 22, 2026

    Doppler Optical Coherence Tomography of Retinal Circulation
    10:46

    Doppler Optical Coherence Tomography of Retinal Circulation

    Published on: September 18, 2012

    Area of Science:

    • Biomedical Optics
    • Medical Imaging
    • Optical Physics

    Background:

    • Doppler optical coherence tomography (DOCT) enables simultaneous imaging of tissue structure and blood flow.
    • Understanding noise limitations is critical for optimizing DOCT performance.

    Purpose of the Study:

    • To derive the fundamental uncertainty limits on frequency estimation precision in DOCT.
    • To experimentally verify theoretical limits using a mirror and a scattering phantom.
    • To investigate the influence of stochastic frequency noise on flow imaging precision.

    Main Methods:

    • Theoretical derivation of Cramer-Rao lower bound for frequency estimation precision.
    • Analysis of additive noise sources (thermal, shot noise).
    • Experimental validation using optical coherence tomography setups.

    Main Results:

    • The Cramer-Rao lower bound provides fundamental limits on frequency estimation precision in DOCT.
    • Experimental results align with theoretical predictions, confirming the derived limits.
    • Stochastic nature of frequency noise significantly impacts the precision of blood flow imaging.

    Conclusions:

    • The precision of DOCT flow imaging is influenced by the stochastic properties of frequency noise.
    • Judicious selection of noise models is essential for accurate frequency precision estimation in DOCT.
    • This study provides a framework for understanding and improving DOCT imaging precision.