Related Experiment Video

Updated: Jun 19, 2026

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
08:39

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

Published on: January 28, 2019

Optical interpretation of a complex-order Fourier transform

C C Shih

    Optics Letters
    |October 28, 2009
    PubMed

    More Related Videos

    A Guide to Structured Illumination TIRF Microscopy at High Speed with Multiple Colors11:15

    A Guide to Structured Illumination TIRF Microscopy at High Speed with Multiple Colors

    Published on: May 30, 2016

    Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping09:43

    Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping

    Published on: March 20, 2017

    Related Concept Videos

    Parseval's Theorem for Fourier transform01:15

    Parseval's Theorem for Fourier transform

    Parseval's theorem is a fundamental principle in signal processing that enables the calculation of a signal's energy in either the time domain or the frequency domain. This theorem is pivotal in demonstrating energy conservation between these two domains, ensuring that the computed energy value remains consistent regardless of the domain of analysis.
    To understand Parseval's theorem, it is essential to first comprehend how signal energy is typically calculated. When considering a signal's...
    Properties of Fourier Transform II01:24

    Properties of Fourier Transform II

    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...
    Properties of Fourier Transform I01:21

    Properties of Fourier Transform I

    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...
    Basic signals of Fourier Transform01:07

    Basic signals of Fourier Transform

    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 zero. It...
    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...
    Exponential Fourier series01:24

    Exponential Fourier series

    In audio signal processing, the exponential Fourier series plays a crucial role in sound synthesis, allowing complex sounds to be broken down into simpler sinusoidal components. This decomposition process is fundamental in analyzing and reconstructing musical notes and other audio signals. The exponential Fourier series expresses periodic signals as the sum of complex exponentials at both positive and negative harmonic frequencies, providing a powerful tool for signal analysis.
    Euler's identity...