Generalized Discrete Fourier Transform with Nonlinear Phase

IEEE Transactions on Signal Processing, Vol. 58, No. 9, pp. 1-10, 2010

10 Pages Posted: 17 Jan 2012

See all articles by Ali Akansu

Ali Akansu

New Jersey Institute of Technology

Handan Agirman-Tosun

affiliation not provided to SSRN

Date Written: September 1, 2010

Abstract

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.

Keywords: Discrete Fourier Transform, Generalized Discrete Fourier Transform, Walsh Codes, Gold Codes, OFDM, DMT, CDMA, auto-correlation function, cross-correlation function

Suggested Citation

Akansu, Ali and Agirman-Tosun, Handan, Generalized Discrete Fourier Transform with Nonlinear Phase (September 1, 2010). IEEE Transactions on Signal Processing, Vol. 58, No. 9, pp. 1-10, 2010, Available at SSRN: https://ssrn.com/abstract=1986816

Ali Akansu (Contact Author)

New Jersey Institute of Technology ( email )

University Heights
Newark, NJ 07102
United States

Handan Agirman-Tosun

affiliation not provided to SSRN

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