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Linear Approximation in Frequency Domain

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Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
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Properties of Fourier Transform I

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Properties of Fourier Transform II

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Updated: May 31, 2026

Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping

Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping

Published on: March 20, 2017

Adaptive frequency-domain equalization in digital coherent optical receivers.

Md Saifuddin Faruk¹, Kazuro Kikuchi

¹Department of Electrical Engineering and Information Systems, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan. faruk@ginjo.t.u-tokyo.ac.jp

|July 1, 2011

Summary

A new frequency-domain adaptive equalizer for digital coherent optical receivers significantly reduces computational complexity. This novel equalizer adjusts sampling phase and demultiplexes polarization tributaries, improving performance in high-speed optical transmissions.

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Generation and Coherent Control of Pulsed Quantum Frequency Combs

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Published on: June 8, 2018

Area of Science:

Optical Communications
Digital Signal Processing
Signal Equalization

Background:

Digital coherent optical receivers commonly use time-domain adaptive equalizers with finite-impulse-response (FIR) filters.
These conventional equalizers can be computationally intensive.
Accurate sampling phase recovery is crucial for optimal performance in optical systems.

Purpose of the Study:

To introduce a novel frequency-domain adaptive equalizer for digital coherent optical receivers.
To reduce the computational complexity compared to traditional time-domain FIR filters.
To enable flexible operation with free-running analog-to-digital converters (ADCs) and demultiplex polarization tributaries.

Main Methods:

Developed a frequency-domain adaptive equalization algorithm.
Enabled operation with ADCs sampling at two samples per symbol, allowing arbitrary initial phase adjustment.
Configured the equalizer in a butterfly structure for polarization demultiplexing and linear impairment equalization.

Main Results:

Demonstrated reduced computational complexity compared to time-domain FIR equalizers.
Successfully adjusted arbitrary initial sampling phases from free-running ADCs to achieve symbol-spaced sequences.
Verified the equalizer's ability to demultiplex polarization tributaries alongside equalization.

Conclusions:

The proposed frequency-domain adaptive equalizer offers a computationally efficient solution for digital coherent optical receivers.
The scheme effectively handles arbitrary sampling phases and enables integrated polarization demultiplexing.
Validated through 40-Gbits/s dual-polarization QPSK transmission experiments, showing practical applicability.