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.
TUTORIALS, INVITED TALKS

A.N. Akansu,
"Generalized DFT Waveforms for MIMO Radar Systems,"
9th Military Antennas, Washington DC, Sept. 2427, 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: NonLinear Phase DFT for Improved Multicarrier Communications,"
EUSIPCO, Glasgow, Aug. 2009.
PAPERS
 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. AgirmanTosun,
"Generalized Discrete Fourier Transform with Nonlinear Phase,"
IEEE Transactions on Signal Processing, vol. 58, no. 9, pp. 45474556, Sept. 2010.
 A.N. Akansu, H. AgirmanTosun, and M.U. Torun,
"Optimal Design of Phase Function in Generalized DFT,"
Physical Communication, Elsevier, vol. 3, issue 4, pp. 255264, Dec. 2010.
 A.N. Akansu and H. AgirmanTosun,
"Generalized Discrete Fourier Transform with Optimum Correlations,"
Proc. IEEE ICASSP, pp. 40544047, March 2010.
 A.N. Akansu and H. AgirmanTosun,
"Improved Correlation of Generalized Discrete Fourier Transform
with Nonlinear Phase for OFDM and CDMA Communications,"
Proc. EUSIPCO, pp. 13691373, Aug. 2009.
 A.N. Akansu and H. AgirmanTosun,
"Generalized
Discrete Fourier Transform: Theory and Design Methods,"
Proc. IEEE Sarnoff Symposium, pp. 17, 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. 14, April 2011.
 S.G. Johnson,
"Modified CooleyTukey Algorithms Based on a Generalized DFT Framework,"
Oct. 2008.
 A.N. Akansu and R. Poluri, "Walshlike
Nonlinear Phase Orthogonal Codes for Direct Sequence CDMA Communications,"
IEEE Trans. on Signal Processing, vol. 55, pp. 38003806, July 2007.
 C. Tseng,
"Eigenvalues and Eigenvectors of Generalized DFT, Generalized DHT, DCTIV and DSTIV Matrices,"
IEEE Trans. on Signal Processing, vol. 50, pp. 866877, 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. 135150, Dec. 1999.
 J.L. Massey and S. Serconek,
Linear Complexity of Periodic Sequences: A General Theory,
Advances on CryptologyCRYPTO'96, Springer Berlin/Heidelberg, vol. 1109,
pp. 358371, 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 FourierRiccatiBessel Transform,
Computer Physics Communications, vol. 85, pp. 336370, 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. 20822090, Nov. 1994.
 P. Corsini and G. Frosini,
"Properties of the Multidimensional Generalized Discrete Fourier Transform,"
IEEE Trans. Computers C28, pp. 819830, Nov. 1979.
 G. Bongiovanni, P. Corsini and G. Frosini,
"Onedimensional and Twodimensional Generalized Discrete Fourier Transform,"
IEEE Trans. Acoust. Speech Signal Process. Vol. ASSP24, pp. 9799, Feb. 1976.