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Related Concept Videos

Continuous -time Fourier Transform01:11

Continuous -time Fourier Transform

The Fourier series is instrumental in representing periodic functions, offering a powerful method to decompose such functions into a sum of sinusoids. This technique, however, necessitates modification when applied to nonperiodic functions. Consider a pulse-train waveform consisting of a series of rectangular pulses. When these pulses have a finite period, they can be accurately represented by a Fourier series. Yet, as the period approaches infinity, resulting in a single, isolated pulse, the...
Time and frequency -Domain Interpretation of Phase-lead Control01:24

Time and frequency -Domain Interpretation of Phase-lead Control

Phase-lead controllers are commonly used in various control systems to enhance response speed and stability. Adjusting the brightness on a television screen offers a practical example of phase-lead control. When contrast is enhanced, a phase-lead controller is employed. Mathematically, phase-lead control is identified when the first parameter is smaller than the second.
The design of phase-lead control involves the strategic placement of poles and zeros to balance steady-state error and system...
Time and frequency -Domain Interpretation of Phase-lag Control01:21

Time and frequency -Domain Interpretation of Phase-lag Control

Phase-lag controllers are widely used in control systems to improve stability and reduce steady-state errors. A dimmer switch controlling the brightness of a light bulb serves as a practical example of phase-lag control, gradually adjusting the bulb's brightness. Mathematically, phase-lag control or low-pass filtering is represented when the factor 'a' is less than 1.
Phase-lag controllers do not place a pole at zero, but instead influence the steady-state error by amplifying any finite,...
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...
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...
Discrete-time Fourier transform01:26

Discrete-time Fourier transform

The Discrete-Time Fourier Transform (DTFT) is an essential mathematical tool for analyzing discrete-time signals, converting them from the time domain to the frequency domain. This transformation allows for examining the frequency components of discrete signals, providing insights into their spectral characteristics. In the DTFT, the continuous integral used in the continuous-time Fourier transform is replaced by a summation to accommodate the discrete nature of the signal.
One of the notable...

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Related Experiment Video

Updated: Jun 19, 2026

Uncovering Hidden Dynamics of Natural Photonic Structures Using Holographic Imaging
05:45

Uncovering Hidden Dynamics of Natural Photonic Structures Using Holographic Imaging

Published on: March 31, 2022

Time domain visualization using acoustic holography implemented by temporal and spatial complex envelope.

Choon-Su Park, Yang-Hann Kim

    The Journal of the Acoustical Society of America
    |October 10, 2009
    PubMed
    Summary

    This study introduces a spatial envelope method for acoustic holography, enabling efficient source localization and radiation pattern analysis. This approach significantly reduces data processing time compared to conventional techniques.

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    Area of Science:

    • Acoustics
    • Signal Processing
    • Holography

    Background:

    • The spatial envelope concept, proposed by Park and Kim, visualizes acoustic source locations and radiation patterns.
    • This concept is valuable for time-domain acoustic holography, offering insights into source positions and energy propagation.
    • The temporal envelope can further reduce data requirements in acoustic analysis.

    Discussion:

    • A novel holographic process is presented to derive the spatial envelope.
    • The effectiveness of this process is experimentally verified.
    • The study compares the computational efficiency of the spatial envelope method against conventional holography.

    Key Insights:

    • The spatial envelope provides crucial information for understanding acoustic phenomena.
    • Implementing spatial and temporal envelopes streamlines acoustic holography.
    • Significant reductions in processing time are achievable with this envelope-based approach.

    Outlook:

    • This method holds potential for advancing real-time acoustic imaging and source identification.
    • Further research could explore applications in noise control and structural health monitoring.
    • Optimization of the holographic process may lead to even greater computational efficiencies.