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Related Concept Videos

Convolution Properties II01:17

Convolution Properties II

176
The important convolution properties include width, area, differentiation, and integration properties.
The width property indicates that if the durations of input signals are T1 and T2, then the width of the output response equals the sum of both durations, irrespective of the shapes of the two functions. For instance, convolving two rectangular pulses with durations of 2 seconds and 1 second results in a function with a width of 3 seconds.
The area property asserts that the area under the...
176
Convolution: Math, Graphics, and Discrete Signals01:24

Convolution: Math, Graphics, and Discrete Signals

236
In any LTI (Linear Time-Invariant) system, the convolution of two signals is denoted using a convolution operator, assuming all initial conditions are zero. The convolution integral can be divided into two parts: the zero-input or natural response and the zero-state or forced response, with t0 indicating the initial time.
To simplify the convolution integral, it is assumed that both the input signal and impulse response are zero for negative time values. The graphical convolution process...
236

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Related Experiment Video

Updated: Jun 14, 2025

Quasi-light Storage for Optical Data Packets
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Tunable optical matrix convolution of 20-Gbit/s QPSK 2-D data with a kernel using optical wave mixing.

Amir Minoofar, Abdulrahman Alhaddad, Wing Ko

    Optics Letters
    |August 29, 2024
    PubMed
    Summary
    This summary is machine-generated.

    Optical matrix convolution enables high-speed, phase-encoded data processing without optical-to-electronic-to-optical conversions. This reconfigurable method achieves error-free 16-QAM and 64-QAM outputs using a periodically poled lithium niobate waveguide.

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    Area of Science:

    • Photonics
    • Optical Signal Processing
    • Nonlinear Optics

    Background:

    • Optical matrix convolution offers advantages over electronic methods, particularly for high-rate, phase-encoded data, by eliminating costly optical-to-electronic-to-optical (OEO) conversions.
    • Phase-encoded data formats like quadrature phase-shift keying (QPSK) are crucial for high-capacity optical communication systems.

    Purpose of the Study:

    • To experimentally demonstrate a reconfigurable optical matrix convolution system for processing QPSK-encoded data.
    • To showcase the system's ability to handle variable kernel sizes and high data rates.

    Main Methods:

    • Serialization of two-dimensional (2-D) input data and generation of time-shifted data replicas (TSDRs).
    • Convolution of 2-D data with a 1-D kernel using nonlinear wave mixing in a periodically poled lithium niobate (PPLN) waveguide.
    • Adjustment of kernel coefficients by tuning the relative phase and amplitude of kernel pumps.

    Main Results:

    • Successful demonstration of reconfigurable matrix convolution with error-free outputs for both 2x1 and 3x1 kernels.
    • Achieved 16-quadrature amplitude modulation (QAM) output with an error vector magnitude (EVM) of ~5.1-8.5% for a 2x1 kernel.
    • Achieved 64-QAM output with an EVM of ~4.9-5.5% for a 3x1 kernel, processing data at rates from 6-20 Gbit/s.

    Conclusions:

    • The proposed optical matrix convolution technique is a tunable and reconfigurable approach for high-speed signal processing.
    • This method effectively avoids OEO conversions and achieves high-order modulation formats with low EVM, paving the way for advanced optical communication systems.