Generalized discrete Fourier transform with nonlinear phase

Ali N. Akansu, Handan Agirman-Tosun

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


Constant modulus transforms like discrete Fourier transform (DFT), Walsh transform, and Gold codes have been successfully used over several decades in several engineering applications, including discrete multi-tone (DMT), orthogonal frequency division multiplexing (OFDM) and code division multiple access (CDMA) communications systems. In this paper, we present a generalized framework for DFT called Generalized DFT (GDFT) with nonlinear phase by exploiting the phase space. We show that GDFT offers sizable correlation improvements over DFT, Walsh, Oppermann and Gold codes, leading to better performance in all multi-carrier communications scenarios investigated. We also highlight how known constant modulus orthogonal transforms are special solutions of the proposed GDFT framework. Moreover, we introduce practical design methods offering computationally efficient implementations of GDFT as enhancements to DFT. We conclude the paper with examples of communications applications where GDFT is shown to outperform DFT and other known constant modulus bases.

Original languageEnglish (US)
Article number5467212
Pages (from-to)4547-4556
Number of pages10
JournalIEEE Transactions on Signal Processing
Issue number9
StatePublished - Sep 2010

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Electrical and Electronic Engineering


  • Auto-correlation function
  • CDMA
  • DMT
  • Gold codes
  • OFDM
  • Walsh codes
  • cross-correlation function
  • discrete Fourier transform
  • generalized discrete Fourier transform


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