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Related Concept Videos

Rectangular and Triangular Pulse Function01:19

Rectangular and Triangular Pulse Function

The unit rectangular pulse function is mathematically represented by a rectangular function centered at the origin with a height of one unit. This function is defined by two parameters: T, which specifies the center location of the pulse along the time axis, and τ, which determines the pulse duration.
For example, consider a rectangular pulse with a 5V amplitude, a 3-second duration, and centered at t=2 seconds. This pulse can be expressed using the rectangular function, written as,
NMR Spectrometers: Radiofrequency Pulses and Pulse Sequences01:17

NMR Spectrometers: Radiofrequency Pulses and Pulse Sequences

A pulse is a short burst of radio waves distributed over a range of frequencies that simultaneously excites all the nuclei in the sample. Upon passing a radio frequency pulse along the x-axis, the nuclei absorb energy corresponding to their Larmor frequencies and achieve resonance. This shifts the net magnetization vector from the z-axis toward the transverse plane. This angle of rotation of the magnetization vector, or the flip angle, is proportional to the duration and intensity of the pulse.
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...
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.
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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...
Fast Fourier Transform01:10

Fast Fourier Transform

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...

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A programmable Fresnel transform pulse shaper.

G Mínguez-Vega, J McKinney, A Weiner

    Optics Express
    |June 6, 2009
    PubMed
    Summary
    This summary is machine-generated.

    We developed a novel reprogrammable pulse shaper using a liquid crystal spatial light modulator for precise control over optical waveforms. This apparatus enables user-defined spectral scaling for advanced spectroscopy applications.

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    Area of Science:

    • Optics and Photonics
    • Spectroscopy
    • Femtosecond Lasers

    Background:

    • Traditional pulse shapers often lack reprogrammability and precise spectral control.
    • Direct space-to-time (DST) pulse shaping offers temporal control but can be complex to reconfigure.

    Purpose of the Study:

    • To demonstrate the first reprogrammable Fresnel transform pulse shaper.
    • To enable user-defined spectral scaling in a pulse shaping apparatus.

    Main Methods:

    • Utilized a modified direct space-to-time (DST) apparatus.
    • Implemented pulse shaping via a dual-layer liquid crystal spatial light modulator (LC-SLM).
    • Employed a free-space Fresnel transform for quadratic dispersion of the temporal waveform.

    Main Results:

    • Achieved a reprogrammable Fresnel transform pulse shaper.
    • Demonstrated user-defined spectral scaling of the passband function.
    • Verified operation through time- and frequency-domain experiments.

    Conclusions:

    • The developed LC-SLM based pulse shaper offers unprecedented flexibility and control.
    • This technology advances tunable spectral filtering and optical waveform generation.