Generalized wavelet transforms over finite fields

References

• Mullen GL, Panario D. Handbook of finite fields. Boca Raton (FL): CRC Press; 2013. (Discrete mathematics and its applications).
   Google Scholar
• Vourdas A. Harmonic analysis on a Galois field and its subfields. J Fourier Anal Appl. 2008;14(1):102–123. doi: 10.1007/s00041-007-9000-2
   Web of Science ®Google Scholar
• Fekri F, McLaughlin SW, Mersereau RM, et al. Block error correcting codes using finite-field wavelet transforms. IEEE Trans Signal Process. 2006;54(3):991–1004. doi: 10.1109/TSP.2005.863011
   Web of Science ®Google Scholar
• Fekri F, Mersereau RM, Schafer RW. Theory of wavelet transform over finite fields. Proceedings of International Conference on Acoustics, Speech, and Signal Processing, 3; Phoenix, AZ, USA; 1999. p. 1213–1216.
   Google Scholar
• Lima JB, Campello de Souza RM. Fractional cosine and sine transforms over finite fields. Linear Algebra Appl. 2013;438(8):3217–3230. doi: 10.1016/j.laa.2012.12.021
   Web of Science ®Google Scholar
• McEliece RJ. Finite fields for computer scientists and engineers. Boston: Kluwer Academic Publishers; 1987. (The Springer international series in engineering and computer science).
   Google Scholar
• Pretzel O. Error-correcting codes and finite fields. New York: Oxford University Press; 1996. (Oxford applied mathematics and computing science series).
   Google Scholar
• Vanstone SA, Van Oorschot PC. An introduction to error correcting codes with applications. New York: Springer; 1989. (The Springer international series in engineering and computer science).
   Google Scholar
• Ghaani Farashahi A. Wave packet transforms over finite cyclic groups. Linear Algebra Appl. 2016;489:75–92. doi: 10.1016/j.laa.2015.10.001
   Web of Science ®Google Scholar
• Pfander G. Gabor frames in finite dimensions. In: Pfander G, Casazza PG, Kutyniok G, editors. Finite frames theory and applications. Boston: Birkhauser; 2013. p. 193–239. (Finite frames, applied and numerical harmonic analysis).
   Google Scholar
• Arefijamaal A, Zekaee E. Image processing by alternate dual Gabor frames. Bull Iranian Math Soc. 2016;42(6):1305–1314.
   Web of Science ®Google Scholar
• Arefijamaal A, Zekaee E. Signal processing by alternate dual Gabor frames. Appl Comput Harmon Anal. 2013;35(3):535–540. doi: 10.1016/j.acha.2013.06.001
   Web of Science ®Google Scholar
• Arefijamaal A, Kamyabi-Gol RA. On the square integrability of quasi regular representation on semidirect product groups. J Geom Anal. 2009;19(3):541–552. doi: 10.1007/s12220-009-9069-8
   Web of Science ®Google Scholar
• Führ H. Abstract harmonic analysis of continuous wavelet transforms. Berlin: Springer-Verlag; 2005.
   Google Scholar
• Ghaani Farashahi A. Structure of finite wavelet frames over prime fields. Bull Iranian Math Soc. 2017;43(1):109–120.
   Web of Science ®Google Scholar
• Ghaani Farashahi A. Classical wavelet systems over finite fields. Wavelets Linear Algebra. 2016;3(2):1–18.
   Google Scholar
• Ghaani Farashahi A. Classical wavelet transforms over finite fields. J Linear Topol Algebra. 2015;4(4):241–257.
   Google Scholar
• Ghaani Farashahi A. Cyclic wavelet systems in prime dimensional linear vector spaces. Wavelets Linear Algebra. 2015;2(1):11–24.
   Google Scholar
• Ghaani Farashahi A. Theoretical frame properties of wave-packet matrices over prime fields. Linear Multilinear Algebra. 2017;65(12):2508–2529. doi: 10.1080/03081087.2016.1278196
   Web of Science ®Google Scholar
• Ghaani Farashahi A. Wave packet transform over finite fields. Electron J Linear Algebra. 2015;30:507–529. doi: 10.13001/1081-3810.2903
   Web of Science ®Google Scholar
• Ghaani Farashahi A. Cyclic wave packet transform on finite Abelian groups of prime order. Int J Wavelets Multiresolut Inf Process. 2014;12(6):1450041, (14 pages). doi: 10.1142/S0219691314500416
   Web of Science ®Google Scholar
• Feichtinger HG, Kozek W, Luef F. Gabor analysis over finite Abelian groups. Appl Comput Harmon Anal. 2009;26(2):230–248. doi: 10.1016/j.acha.2008.04.006
   Web of Science ®Google Scholar
• Caire G, Grossman RL, Vincent Poor H. Wavelet transforms associated with finite cyclic groups. IEEE Trans Inform Theory. 1993;39(4):113–119. doi: 10.1109/18.243435
   Web of Science ®Google Scholar
• Sarkar S, Vincent Poor H. Cyclic wavelet transforms for arbitrary finite data lengths. Signal Process. 2000;80:2541–2552. doi: 10.1016/S0165-1684(00)00135-3
   Web of Science ®Google Scholar
• Flornes K, Grossmann A, Holschneider M, et al. Wavelets on discrete fields. Appl Comput Harmon Anal. 1994;1:137–146. doi: 10.1006/acha.1994.1001
   Google Scholar
• Johnston CP. On the pseudodilation representations of flornes, grossmann, holschneider, and torrésani. J Fourier Anal Appl. 1997;3(4):377–385. doi: 10.1007/BF02649102
   Web of Science ®Google Scholar
• Folland GB. A course in abstract harmonic analysis. Boca Raton (FL): CRC press; 1995.
   Google Scholar
• Reiter R, Stegeman JD. Classical harmonic analysis. 2nd ed. New York: Oxford University Press; 2000.
   Google Scholar
• Hardy GH, Wright EM. An introduction to the theory of numbers. Oxford: Oxford University Press; 1979.
   Google Scholar
• Ramakrishnan D, Valenza RJ. Fourier analysis on number fields. New York: Springer-Verlag; 1999.
   Google Scholar
• Riesel H. Prime numbers and computer methods for factorization. 2nd ed. Boston: Birkhauser; 1994.
   Google Scholar