Generalized discrete fourier transform: Theory and design methods

Ali N. Akansu, Handan Agirman-Tosun

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Scopus citations


Constant amplitude transforms like discrete Fourier transform (DFT), Walsh transform, nonlinear phase Walsh-like transforms and Gold codes have been successfully used in many wire-line and wireless communications technologies including code division multiple access (CDMA), discrete multi-tone (DMT), and orthogonal frequency division multiplexing (OFDM) types. In this paper, we present a generalized framework for DFT called Generalized DFT (GDFT) with nonlinear phase by exploiting the phase space. It is shown that GDFT offers sizable performance improvements over Walsh, Gold and DFT codes in multi-carrier communications scenarios considered. We also highlight that known constant modulus code families are special solutions of the proposed GDFT framework. Moreover, we introduce practical design methods offering computationally efficient implementations for GDFT. We expect performance improvements in future communications systems employing GDFT intelligently.

Original languageEnglish (US)
Title of host publication2009 IEEE Sarnoff Symposium, SARNOFF 2009 - Conference Proceedings
StatePublished - 2009
Event2009 IEEE Sarnoff Symposium, SARNOFF 2009 - Princeton, NJ, United States
Duration: Mar 30 2009Apr 1 2009

Publication series

Name2009 IEEE Sarnoff Symposium, SARNOFF 2009 - Conference Proceedings


Other2009 IEEE Sarnoff Symposium, SARNOFF 2009
Country/TerritoryUnited States
CityPrinceton, NJ

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Electrical and Electronic Engineering
  • Communication


  • DMT
  • Discrete fourier transform
  • Generalized discrete fourier transform
  • Gold codes
  • OFDM
  • Walsh codes


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