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Related Concept Videos

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 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.
Discrete Fourier Transform01:15

Discrete Fourier Transform

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...
Convergence of Fourier Series01:21

Convergence of Fourier Series

The Fourier series is a powerful mathematical tool for representing periodic signals as an infinite sum of complex exponentials. In practice, this infinite series is truncated to a finite number of terms, yielding a partial sum. This truncation makes the approximation of the signal feasible but introduces certain challenges, particularly near discontinuities, known as the Gibbs phenomenon.
The Gibbs phenomenon refers to the persistent oscillations and overshoots that occur near discontinuities...
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...
Trigonometric Fourier series01:17

Trigonometric Fourier series

Fourier series is a foundational mathematical technique that decomposes periodic functions into an infinite series of sinusoidal harmonics. This method enables the representation of complex periodic signals as sums of simple sine and cosine functions, facilitating their analysis and interpretation in various fields, including signal processing, acoustics, and electrical engineering.
The trigonometric Fourier series specifically expresses a periodic function with a defined period T using sine...

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Related Experiment Video

Updated: Jun 17, 2026

Recording Ultra-Realistic Full-Color Analog Holograms for Use in a Moving Hologram Display
09:04

Recording Ultra-Realistic Full-Color Analog Holograms for Use in a Moving Hologram Display

Published on: January 14, 2020

Sampled fourier transform hologram generated by computer.

W H Lee

    Applied Optics
    |January 16, 2010
    PubMed
    Summary
    This summary is machine-generated.

    A new technique quantifies hologram transmittance using sample positions to record phase information. This method, limited by 256-level quantization, enables real, nonnegative transmittance determination for synthesized holograms.

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    Area of Science:

    • Optics and Photonics
    • Digital Holography

    Background:

    • Holography enables wavefront reconstruction.
    • Determining transmittance of synthesized holograms is crucial for applications.
    • Existing methods may have limitations in accuracy or scope.

    Purpose of the Study:

    • To describe a novel technique for determining the real nonnegative transmittance function of synthesized holograms.
    • To utilize sample positions within the hologram for phase information recording.

    Main Methods:

    • A flying spot scanner displays synthesized holograms.
    • Holograms are recorded on film.
    • Phase information is captured using the spatial positions of hologram samples.
    • Transmittance is quantized to 256 levels due to hardware constraints.

    Main Results:

    • The described technique successfully determines a real nonnegative function for hologram transmittance.
    • The method leverages positional data to encode phase information.
    • The process is compatible with flying spot scanner display and film recording.

    Conclusions:

    • The developed technique provides a method for characterizing synthesized hologram transmittance.
    • Positional encoding of phase information is demonstrated.
    • Hardware limitations, such as 256-level quantization, influence the final transmittance representation.