Generalized Discrete Fourier Transform (GDFT) with Nonlinear Phase

Generalized Discrete Fourier Transform (GDFT) with Nonlinear Phase has been forwarded in the literature offering improved correlations and flexible designs over traditional Linear Phase DFT for OFDM communications and many other applications. We maintain this page to provide the interested researchers and technology developers our up to date contributions on GDFT along with other relevant literature.

Although the term "Generalized Discrete Fourier Transform (GDFT)" was used earlier in the literature, the GDFT framework described here is a marked departure from the prior studies due to its use of nonlinear phase basis functions. Moreover, "nonlinear phase orthogonal set" framework is extended to other varieties of Fourier analysis and Laplace transform.

The next generation wireless communications systems employing OFDM based technologies and other DFT applications might benefit from the GDFT framework exploiting the entire phase space.

PH.D THESES

• Y. Wang, Generalized DFT: Extensions in Communications. New Jersey Institute of Technology, Newark, NJ. 2016.
• H. Agirman-Tosun, Generalized Discrete Fourier Transform with Nonlinear Phase: Theory and Design. New Jersey Institute of Technology, Newark, NJ. 2009.

TUTORIALS, INVITED TALKS

• A.N. Akansu, "Generalized DFT Waveforms for MIMO Radar Systems," 9th Military Antennas, Washington DC, Sept. 24-27, 2012.
• A.N. Akansu, "Generalized DFT for OFDM Communications," IEEE COMSOC Digital Library, Globecom 2009 Tutorials (Streaming), Jan. 2010.
• A.N. Akansu, "Generalized DFT for OFDM Communications," IEEE GLOBECOM, Honolulu, Dec. 2009.
• A.N. Akansu, "Generalized Discrete Fourier Transform: Non-Linear Phase DFT for Improved Multicarrier Communications," EUSIPCO, Glasgow, Aug. 2009.

PAPERS

• Y. Wang and A.N. Akansu, "PAPR Reduction for OFDM System Using Symbol Alphabet Modifier Matrix," IEEE 50th Annual Conference on Information Sciences and Systems (CISS), March 2016.
• Y. Wang and A.N. Akansu, "A Low-Complexity Peak-to-Average Power Ratio Reduction Method for OFDM Communications," IET Communications, vol. 9, issue 17, pp. 2153-2159, Nov. 2015.
• Y. Wang, A.N. Akansu and A. Haimovich, "Generalized DFT Waveforms for MIMO Radar," The Seventh IEEE Sensor Array and Multichannel Signal Porcessing Workshop, June 2012.
• Y. Wang and A.N. Akansu, "Generalized DFT Based Partial Matched Filter Bank for Doppler Estimation," IEEE 46th Annual Conference on Information Sciences and Systems (CISS), March 2012.
• W.P. Weydig, M.U. Torun and A.N. Akansu, "Implementation of Generalized DFT on Field Programmable Gate Array," IEEE ICASSP, March 2012.
• A.N. Akansu and H. Agirman-Tosun, "Generalized Discrete Fourier Transform with Nonlinear Phase," IEEE Transactions on Signal Processing, vol. 58, no. 9, pp. 4547-4556, Sept. 2010.
• A.N. Akansu, H. Agirman-Tosun, and M.U. Torun, "Optimal Design of Phase Function in Generalized DFT," Physical Communication, Elsevier, vol. 3, issue 4, pp. 255-264, Dec. 2010.
• A.N. Akansu and H. Agirman-Tosun, "Generalized Discrete Fourier Transform with Optimum Correlations," Proc. IEEE ICASSP, pp. 4054-4047, March 2010.
• A.N. Akansu and H. Agirman-Tosun, "Improved Correlation of Generalized Discrete Fourier Transform with Nonlinear Phase for OFDM and CDMA Communications," Proc. EUSIPCO, pp. 1369-1373, Aug. 2009.
• A.N. Akansu and H. Agirman-Tosun, "Generalized Discrete Fourier Transform: Theory and Design Methods," Proc. IEEE Sarnoff Symposium, pp. 1-7, March 2009.

RELEVANT PAPERS

• J.S. Pereira and H.J.A. da Silva, "Perfect DFT Sequences Transformed into Orthogonal Sequences," Proc. IEEE EUROCON - International Conference on Computer as a Tool, pp. 1-4, April 2011.
• S.G. Johnson, "Modified Cooley-Tukey Algorithms Based on a Generalized DFT Framework," Oct. 2008.
• A.N. Akansu and R. Poluri, "Walsh-like Nonlinear Phase Orthogonal Codes for Direct Sequence CDMA Communications," IEEE Trans. on Signal Processing, vol. 55, pp. 3800-3806, July 2007.
• C. Tseng, "Eigenvalues and Eigenvectors of Generalized DFT, Generalized DHT, DCT-IV and DST-IV Matrices," IEEE Trans. on Signal Processing, vol. 50, pp. 866-877, April 2002.
• V. Britanak and K.R. Rao, "The Fast Generalized Discrete Fourier Transforms: A Unified Approach to The Discrete Sinusoidal Transforms Computation," Signal Processing, vol. 79, pp. 135-150, Dec. 1999.
• J.L. Massey and S. Serconek, Linear Complexity of Periodic Sequences: A General Theory, Advances on Cryptology-CRYPTO'96, Springer Berlin/Heidelberg, vol. 1109, pp. 358-371, Nov. 1996.
• L. Rinaldi and P.E. Ricci, "Complex Symmetric Functions and Generalized Discrete Fourier Transform," Rendiconti del Circolo Matematico di Palermo, vol. 45, no. 1, Jan. 1996.
• E. Stade and E.G. Layton, Generalized Discrete Fourier Transforms: The Discrete Fourier-Riccati-Bessel Transform, Computer Physics Communications, vol. 85, pp. 336-370, March 1995.
• B.S. Rajan and M.U. Siddiqi, "A Generalized DFT for Abelian Codes over Zm," IEEE Trans. on Information Theory, vol. 40, pp. 2082-2090, Nov. 1994.
• P. Corsini and G. Frosini, "Properties of the Multidimensional Generalized Discrete Fourier Transform," IEEE Trans. Computers C-28, pp. 819-830, Nov. 1979.
• G. Bongiovanni, P. Corsini and G. Frosini, "One-dimensional and Twodimensional Generalized Discrete Fourier Transform," IEEE Trans. Acoust. Speech Signal Process. Vol. ASSP-24, pp. 97-99, Feb. 1976.

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