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Related Concept Videos

Fast Fourier Transform01:10

Fast Fourier Transform

978
The Fast Fourier Transform (FFT) is a computational algorithm designed to compute the Discrete Fourier Transform (DFT) efficiently. By breaking down the calculations into smaller, manageable sections, the FFT significantly reduces the computational complexity involved. Direct computation of an N-point DFT requires N2 complex multiplications, whereas the FFT algorithm needs only (N/2)log⁡2N multiplications, offering a much faster performance.
The computational efficiency of the FFT becomes...
978
Properties of Fourier Transform I01:21

Properties of Fourier Transform I

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The application of Fourier Transform properties in radio broadcasting is multifaceted, enabling significant advancements in the way signals are transmitted and received. Key areas where these properties are utilized include simultaneous multi-channel transmission, audio clip speed adjustments, live broadcast delays for different time zones, audio frequency adjustments, and signal demodulation.
In radio broadcasting, multiple audio signals often need to be transmitted simultaneously. The Fourier...
700
Properties of Fourier Transform II01:24

Properties of Fourier Transform II

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The Fourier Transform (FT) is an essential mathematical tool in signal processing, transforming a time-domain signal into its frequency-domain representation. This transformation elucidates the relationship between time and frequency domains through several properties, each revealing unique aspects of signal behavior.
The Frequency Shifting property of Fourier Transforms highlights that a shift in the frequency domain corresponds to a phase shift in the time domain. Mathematically, if x(t) has...
807
Discrete Fourier Transform01:15

Discrete Fourier Transform

938
The Discrete Fourier Transform (DFT) is a fundamental tool in signal processing, extending the discrete-time Fourier transform by evaluating discrete signals at uniformly spaced frequency intervals. This transformation converts a finite sequence of time-domain samples into frequency components, each representing complex sinusoids ordered by frequency. The DFT translates these sequences into the frequency domain, effectively indicating the magnitude and phase of each frequency component present...
938
Basic signals of Fourier Transform01:07

Basic signals of Fourier Transform

993
The Fourier Transform is a pivotal mathematical tool in signal processing, enabling the transformation of time-domain signals into their frequency-domain representations. Among the numerous elements within this domain, certain functions like the sinc function, delta function, and exponential signals hold significant importance due to their unique properties and implications.
The sinc function, defined as sinc(x) = sin(πx)/(πx), is particularly notable for its symmetry and behavior at...
993
Continuous -time Fourier Transform01:11

Continuous -time Fourier Transform

941
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...
941

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A Multimodal Wide-Field Fourier-Transform Raman Microscope
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Dynamic microscopic 3D shape measurement based on marker-embedded Fourier transform profilometry.

Yan Hu, Qian Chen, Yuzhen Zhang

    Applied Optics
    |February 6, 2018
    PubMed
    Summary
    This summary is machine-generated.

    Marker-embedded Fourier transform profilometry (MEFTP) reconstructs absolute phase with only two patterns, ideal for dynamic 3D shape measurement. This technique enhances accuracy for fast-moving objects compared to traditional methods.

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    Area of Science:

    • Optics and Photonics
    • Metrology and Measurement Science
    • Computer Vision and Image Processing

    Background:

    • Fringe projection profilometry (FPP) is promising for dynamic 3D microscopic surface measurement.
    • Dynamic measurements require minimizing motion sensitivity by reducing projected patterns.
    • Traditional phase-shifting methods need multiple patterns (≥6), demanding high-speed hardware.

    Purpose of the Study:

    • To develop a novel method for dynamic 3D measurement with fewer projected patterns.
    • To improve robustness and accuracy in measuring fast-moving or surface-changing objects.
    • To enable absolute phase reconstruction using only two fringe patterns.

    Main Methods:

    • Introduced marker-embedded Fourier transform profilometry (MEFTP), extending modified Fourier transform profilometry.
    • Embedded two markers to aid the phase-unwrapping process.
    • Combined embedded markers with temporal phase difference for absolute phase reconstruction.

    Main Results:

    • Achieved reliable absolute phase reconstruction using only two projected patterns.
    • Demonstrated MEFTP's suitability for dynamic scenes, outperforming phase-shifting methods.
    • Verified accurate and robust measurement of a vibrating diaphragm at 200 fps.

    Conclusions:

    • MEFTP offers a robust solution for dynamic 3D surface measurement with reduced pattern projection.
    • The method is highly suitable for high-speed applications and objects with changing surfaces.
    • MEFTP provides accurate and reliable absolute phase maps with significantly less data acquisition.