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Book cover Fast Fourier Transform - Algorithms and Applications

Part of the book series: Signals and Communication Technology ((SCT))

Abstract

This chapter focuses on applications of FFT/IFFT in a number of diverse fields. In view of the extensive nature of their applications they are intentionally described in a conceptual form. The reader is directed to the references wherein the applications are described in detail along with the theoretical background, examples, limitations, etc. The overall objective is to expose the reader to the limitless applications of DFT in the general areas of signal/image processing.

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Notes

  1. 1.

    AAC is used in MPEG-2 Part 7 and MPEG-4 Part 3.

  2. 2.

    The conjugate symmetric sequence for N = 8 is defined as

    {X F(0), X F(1),…, X F(7)} = {X F(0), X F(1), X F(2), X F(3), X F(4), [X F(3)]*, [X F(2)]*, [X F(1)]*}

  3. 3.

    The conjugate antisymmetric sequence for N = 8 is defined as

    {X F(0), X F(1),…, X F(7)} = {X F(0), X F(1), X F(2), X F(3), X F(4), −[X F(3)]*, −[X F(2)]*, −[X F(1)]*}

References

  1. A.K. Jain, Fundamentals of Digital Image Processing (Prentice-Hall, Englewood Cliffs, NJ, 1989)

    MATH  Google Scholar 

  2. M.F. Cátedra et al., The CG-FFT Method: Application of Signal Processing Techniques to Electromagnetics. CG = Conjugate Gradient (Artech, Norwood, MA, 1994)

    Google Scholar 

  3. K.R. Rao, P.C. Yip (eds.), The Transform and Data Compression Handbook (CRC Press, Boca Raton, FL, 2001)

    MATH  Google Scholar 

  4. S.J. Leon, Linear Algebra with Applications, 6th edn. (Prentice-Hall, Upper Saddle River, NJ, 2006)

    Google Scholar 

  5. L.C. Ludeman, Random Processes: Filtering, Estimation and Detection (Wiley, Hoboken, NJ, 2003)

    Google Scholar 

  6. W.K. Pratt, Digital Image Processing, IVth edn. (Wiley, New York, 2007)

    Book  Google Scholar 

  7. S.D. Stearns, R.A. David, Signal Processing Algorithms (Englewood Cliffs, NJ, Prentice-Hall, 1988). Chapter 10 – Decimation and Interpolation Routines. Chapter 9 – Convolution and correlation using FFT

    MATH  Google Scholar 

  8. J.P. Princen, A.B. Bradley, Analysis/synthesis filter bank design based on time domain aliasing cancellation. IEEE Trans. ASSP 34, 1153–1161 (Oct. 1986)

    Article  Google Scholar 

  9. J.P. Princen, A.W. Johnson, A.B. Bradley, Subband/transform coding using filter bank designs based on time domain aliasing cancellation. IEEE ICASSP April, 2161–2164 (1987)

    Google Scholar 

  10. J.D. Johnston, Transform coding of audio signals using perceptual noise criteria. IEEE JSAC 6, 314–323 (Feb. 1988)

    Google Scholar 

  11. J.D. Johnston, Estimation of perceptual entropy using noise masking criteria, in IEEE ICASSP, vol. 5, New York, Apr. 1988, pp. 2524–2527

    Google Scholar 

  12. J.H. Chung, R.W. Schafer, A 4.8 kbps homomorphic vocoder using analysis-by-synthesis excitation analysis, in IEEE ICASSP, vol. 1, Glasgow, Scotland, May 1989, pp. 144–147

    Google Scholar 

  13. J.D. Johnston, Perceptual transform coding of wideband stereo signals, in IEEE ICASSP, vol. 3, Glasgow, Scotland, May 1989, pp. 1993–1996

    Google Scholar 

  14. Y.-F. Dehery, A digital audio broadcasting system for mobile reception, in ITU-COM 89, CCETT of France, Geneva, Switzerland, Oct. 1989, pp. 35–57

    Google Scholar 

  15. ISO/IEC JTC1/SC2/WG8 MPEG Document 89/129 proposal package description, 1989

    Google Scholar 

  16. “ASPEC”, AT&T Bell Labs, Deutsche Thomson Brandt and Fraunhofer Gesellschaft – FhG AIS, ISO/IEC JTC1/SC2/WG8 MPEG 89/205

    Google Scholar 

  17. K. Brandenburg et al., Transform coding of high quality digital audio at low bit rates-algorithms and implementation, in IEEE ICC 90, vol. 3, Atlanta, GA, Apr. 1990, pp. 932–936

    Google Scholar 

  18. G. Stoll, Y.-F. Dehery, High quality audio bit-rate reduction system family for different applications, in IEEE ICC, vol. 3, Atlanta, GA, Apr. 1990, pp. 937–941

    Google Scholar 

  19. J.H. Chung, R.W. Schafer, Excitation modeling in a homomorphic vocoder, in IEEE ICASSP, vol. 1, Albuquerque, NM, Apr. 1990, pp. 25–28

    Google Scholar 

  20. G.A. Davidson, L.D. Fielder, M. Artill, Low-complexity transform coder for satellite link applications, in AES 89th Convention, Los Angeles, CA, 21–25 Sept. 1990, http://www.aes.org/

  21. T.D. Lookabaugh, M.G. Perkins, Application of the Princen-Bradley filter bank to speech and image compression. IEEE Trans. ASSP 38, 1914–1926 (Nov. 1990)

    Article  Google Scholar 

  22. H.G. Musmann, The ISO audio coding standard, in IEEE GLOBECOM, vol. 1, San Diego, CA, Dec. 1990, pp. 511–517

    Google Scholar 

  23. Y. Mahieux, J.P. Petit, Transform coding of audio signals at 64 kbit/s, in IEEE GLOBECOM, vol. 1, San Diego, CA, Dec. 1990, pp. 518–522

    Google Scholar 

  24. K. Brandenburg et al., ASPEC: Adaptive spectral perceptual entropy coding of high quality music signals, in 90th AES Convention, Preprint 3011 (A-4), Paris, France, 19–22 Feb. 1991

    Google Scholar 

  25. P. Duhamel, Y. Mahieux, J.P. Petit, A fast algorithm for the implementation of filter banks based on ‘time domain aliasing cancellation’. IEEE ICASSP 3, 2209–2212 (Apr. 1991)

    Google Scholar 

  26. L.D. Fielder, G.A. Davidson, AC-2: A family of low complexity transform based music coders, in AES 10th Int’l Conference, London, England, 7–9 Sept. 1991, pp. 57–69

    Google Scholar 

  27. M. Iwadare et al., A 128 kb/s Hi-Fi audio CODEC based on adaptive transform coding with adaptive block size MDCT. IEEE JSAC 10, 138–144 (Jan. 1992)

    Google Scholar 

  28. G.A. Davidson, W. Anderson, A. Lovrich, A low-cost adaptive transform decoder implementation for high-quality audio. IEEE ICASSP 2, 193–196 (Mar. 1992)

    Google Scholar 

  29. K. Brandenburg et al., The ISO/MPEG audio codec: A generic standard for coding of high quality digital audio, in 92th AES Convention, Preprint 3336, Vienna, Austria, Mar. 1992, http://www.aes.org/

  30. L.D. Fielder, G.A. Davidson, Low bit rate transform coder, decoder and encoder/decoder for high quality audio, U.S. Patent 5,142,656, 25 Aug. 1992

    Google Scholar 

  31. A.G. Elder, S.G. Turner, A real-time PC based implementation of AC-2 digital audio compression, in AES 95th Convention, Preprint 3773, New York, 7–10 Oct 1993

    Google Scholar 

  32. D. Pan, An overview of the MPEG/Audio compression algorithm, in IS&T/SPIE Symposium on Electronic Imaging: Science and Technology, vol. 2187, San Jose, CA, Feb. 1994, pp. 260–273

    Google Scholar 

  33. A.S. Spanias, Speech coding: A tutorial review. Proc. IEEE 82, 1541–1582 (Oct. 1994)

    Article  Google Scholar 

  34. M. Bosi, S.E. Forshay, High quality audio coding for HDTV: An overview of AC-3, in 7th Int’l Workshop on HDTV, Torino, Italy, Oct. 1994

    Google Scholar 

  35. D. Sevic, M. Popovic, A new efficient implementation of the oddly stacked Princen-Bradley filter bank. IEEE SP Lett. 1, 166–168 (Nov 1994)

    Article  Google Scholar 

  36. P. Noll, Digital audio coding for visual communications. Proc. IEEE 83, 925–943 (June 1995)

    Article  Google Scholar 

  37. M. Bosi et al., ISO/IEC MPEG-2 advanced audio coding, in AES 101st Convention, Los Angeles, CA, 8–11 Nov. 1996. Also appeared in J. Audio Engineering Soc., vol. 45, pp. 789–814, Oct. 1997

    Google Scholar 

  38. K.R. Rao, J.J. Hwang, Techniques and Standards for Image, Video and Audio Coding (Prentice-Hall, Upper Saddle River, NJ, 1996)

    Google Scholar 

  39. K. Brandenburg, M. Bosi, Overview of MPEG audio: Current and future standards for low bit-rate audio coding. J Audio Eng Soc 45, 4–21 (Jan./Feb. 1997)

    Google Scholar 

  40. MPEG-2 Advanced Audio Coding (AAC), ISO/IEC JTC1/SC29/WG 11, Doc. N1650, Apr. 1997, MPEG-2 IS 13818-7. Pyschoacoustic model for NBC (Nonbackward Compatible) – AAC (Advanced Audio Coder) audio coder, IS for MPEG-2. Also adopted by MPEG-4 in T/F coder, http://www.mpeg.org/

  41. S. Shlien, The modulated lapped transform, its time-varying forms, and its applications to audio coding standards. IEEE Trans. Speech Audio Process. 5, 359–366 (July 1997)

    Article  Google Scholar 

  42. MPEG-4 WD ISO/IEC 14496-3, V4.0/10/22/1997 (FFT in ‘CELP’ coder)

    Google Scholar 

  43. C.-M. Liu, W.-C. Lee, A unified fast algorithm for cosine modulated filter banks in current audio coding standards. J. Audio Eng. Soc. 47, 1061–1075 (Dec. 1999)

    Google Scholar 

  44. Method for objective measurements of perceived audio quality. Recommendation ITU-R BS.1387-1, 1998–2001

    Google Scholar 

  45. R. Geiger et al., Audio coding based on integer transforms, in AES 111th Convention, New York, 21–24 Sept. 2001, pp. 1–9

    Google Scholar 

  46. S.-W. Lee, Improved algorithm for efficient computation of the forward and backward MDCT in MPEG audio coder. IEEE Trans. Circ. Syst. II Analog Digital Signal Process. 48, 990–994 (Oct. 2001)

    Article  Google Scholar 

  47. V. Britanak, K.R. Rao, A new fast algorithm for the unified forward and inverse MDCT/MDST computation. Signal Process. 82, 433–459 (Mar. 2002)

    Article  MATH  Google Scholar 

  48. M. Bosi, R.E. Goldberg, Introduction to Digital Audio Coding and Standards (Kluwer, Norwell, MA, 2003)

    Book  Google Scholar 

  49. G.A. Davidson et al., ATSC video and audio coding. Proc. IEEE 94, 60–76 (Jan. 2006)

    Article  Google Scholar 

  50. J.M. Boyce, The U.S. digital television broadcasting transition. IEEE SP Mag. 26, 102–110 (May 2009)

    Article  Google Scholar 

  51. I.Y. Choi et al., Objective measurement of perceived auditory quality in multichannel audio compression coding systems. J. Audio Eng. Soc. 56, 3–17 (Jan. 2008)

    Google Scholar 

  52. E. De Castro, C. Morandi, Registration of translated and rotated images using finite Fourier transforms. IEEE Trans. PAMI 9, 700–703 (Sept. 1987)

    Article  Google Scholar 

  53. W.M. Lawton, Multidimensional chirp algorithms for computing Fourier transforms. IEEE Trans. IP 1, 429–431 (July 1992)

    Google Scholar 

  54. W. Philips, On computing the FFT of digital images in quadtree format. IEEE Trans. SP 47, 2059–2060 (July 1999)

    Article  Google Scholar 

  55. R.W. Cox, R. Tong, Two- and three-dimensional image rotation using the FFT. IEEE Trans. IP 8, 1297–1299 (Sept. 1999)

    MathSciNet  MATH  Google Scholar 

  56. K. Ito et al., Fingerprint matching algorithm using phase-only correlation. IEICE Trans. Fundam. E87–A, 682–691 (Mar. 2004)

    Google Scholar 

  57. O. Urhan, M.K. Güllü, S. Ertürk, Modified phase-correlation based robust hard-cut detection with application to archive film. IEEE Trans. CSVT 16, 753–770 (June 2006)

    Google Scholar 

  58. Ibid., 3rd edn. (Prentice-Hall, Upper Saddle River, NJ, 2007)

    Google Scholar 

  59. P.C. Cosman, Homework 4 and its solution on registration for digital image processing lecture, 2008, available: http://code.ucsd.edu/∼pcosman/

  60. JPEG Software, The Independent JPEG Group, Mar. 1998, available: http://www.ijg.org/

  61. M. Ghanbari, Standard Codecs: Image Compression to Advanced Video Coding (IEE, Hertfordshire, UK, 2003)

    Google Scholar 

  62. S. Kumar et al., Error resiliency schemes in H.264/AVC standard, J. Visual Commun. Image Represent. (JVCIR) (special issue on H.264/AVC), 17, 425–450 (Apr. 2006)

    Google Scholar 

  63. K. Sayood, Introduction to Data Compression, 3rd edn. (Morgan Kaufmann, San Francisco, CA, 2006)

    Google Scholar 

  64. M. Ramkumar, G.V. Anand, An FFT-based technique for fast fractal image compression. Signal Process. 63, 263–268 (Dec. 1997)

    Article  MATH  Google Scholar 

  65. H. Hartenstein, D. Saupe, Lossless acceleration of fractal image encoding via the fast Fourier transform. Signal Process. Image Commun. 16, 383–394 (Nov. 2000)

    Article  Google Scholar 

  66. W. Bender et al., Techniques for data hiding. IBM Syst. J. 35(3/4), 313–335 (1996)

    Article  Google Scholar 

  67. J.J.K.Ơ. Ruanaidh, W.J. Dowling, F.M. Boland, Phase watermarking of digital images, in Proceedings of the ICIP’96, vol. 3, Lausanne, Switzerland, Sept. 1996, pp. 239–242

    Google Scholar 

  68. J.J.K.Ơ. Ruanaidh, T. Pun, Rotation, scale and translation invariant spread spectrum digital image watermarking. Signal Process (Elsevier) 66, 303–317 (May 1998)

    MATH  Google Scholar 

  69. V. Solachidis, I. Pitas, Self-similar ring shaped watermark embedding in 2D- DFT domain, in EUSIPCO 2000, Tampere, Finland, Sept. 2000, available: http://www.eurasip.org

  70. M.D. Swanson et al., Robust audio watermarking using perceptual masking. Signal Process. 66, 337–355 (May 1998) (Special Issue on Watermarking)

    Article  MATH  Google Scholar 

  71. B. Ji, F. Yan, D. Zhang, A robust audio watermarking scheme using wavelet modulation. IEICE Trans. Fundam. 86, 3303–3305 (Dec. 2003)

    Google Scholar 

  72. M. Boucheret et al., Fast convolution filter banks for satellite payloads with on-board processing. IEEE J. Sel. Areas Commun. 17, 238–248 (Feb. 1999)

    Article  Google Scholar 

  73. E.J. Candès, D.L. Donoho, L. Ying, Fast discrete curvelet transform, SIAM J. Multiscale Model. Simul. 5, 861–899 (Sept. 2006). (The software CurveLab is available at http://www.curvelet.org )

  74. Y. Rakvongthai, Hidden Markov tree modeling of the uniform discrete curvelet transform for image denoising. EE5359 Project (UT–Arlington, TX, Summer 2008), http://www-ee.uta.edu/dip/ click on courses

  75. Y. Rakvongthai, S. Oraintara, Statistics and dependency analysis of the uniform discrete curvelet coefficients and hidden Markov tree modeling, in IEEE ISCAS, Taipei, Taiwan, May 2009, pp. 525–528

    Google Scholar 

  76. E. Viscito, J.P. Allebach, The analysis and design of multidimensional FIR perfect reconstruction filter banks for arbitrary sampling lattices. IEEE Trans. CAS 38, 29–41 (Jan. 1991)

    Article  Google Scholar 

  77. R.H. Bamberger, M.J.T. Smith, A filter bank for the directional decomposition of images: Theory and design. IEEE Trans. SP 40, 882–893 (Apr. 1992)

    Article  Google Scholar 

  78. G. Strang, T. Nguyen, Wavelets and Filter Banks, 2nd edn. (Wellesley-Cambridge Press, Wellesley, MA, 1997)

    Google Scholar 

  79. S.-I. Park, M.J.T. Smith, R.M. Mersereau, Improved structures of maximally decimated directional filter banks for spatial image analysis. IEEE Trans. IP 13, 1424–1431 (Nov. 2004)

    Google Scholar 

  80. Y. Tanaka, M. Ikehara, T.Q. Nguyen, Multiresolution image representation using combined 2-D and 1-D directional filter banks. IEEE Trans. IP 18, 269–280 (Feb. 2009)

    MathSciNet  Google Scholar 

  81. J. Wisinger, R. Mahapatra, FPGA based image processing with the curvelet transform. Technical Report # TR-CS-2003-01-0, Department of Computer Science, Texas A&M University, College Station, TX

    Google Scholar 

  82. M.N. Do, M. Vetterli, Orthonormal finite ridgelet transform for image compression. IEEE ICIP, vol. 2, Vancouver, Canada, Sept. 2000, pp. 367–370

    Google Scholar 

  83. J.L. Starck, E.J. Candès, D.L. Donoho, The curvelet transform for image denoising. IEEE Trans. IP 11, 670–684 (June 2002)

    Google Scholar 

  84. M.N. Do, M. Vetterli, The finite ridgelet transform for image representation. IEEE Trans. IP 12, 16–28 (Jan. 2003)

    MathSciNet  Google Scholar 

  85. B. Eriksson, The very fast curvelet transform, ECE734 Project, University of Wisconsin (UW), Madison, WI, 2006

    Google Scholar 

  86. T.T. Nguyen, H. Chauris, The uniform discrete curvelet transform, IEEE Trans. SP, Oct. 2009 (see demo code). (Under review)

    Google Scholar 

  87. O. Edfors et al., Analysis of DFT-based channel estimators for OFDM, in Wireless Personal Communications, vol. 12 (Netherlands: Springer, Jan. 2000), pp. 55−70

    Google Scholar 

  88. M.-L. Ku, C.-C. Huang, A derivation on the equivalence between Newton’s method and DF DFT-based method for channel estimation in OFDM systems. IEEE Trans. Wireless Commun. 7, 3982–3987 (Oct. 2008)

    Article  Google Scholar 

  89. S.B. Weinstein, P.M. Ebert, Data transmission by frequency-division multiplexing using the discrete Fourier transform. IEEE Trans. Commun. Technol. 19, 628–634 (OCt. 1971)

    Article  Google Scholar 

  90. W.Y. Zou, W. Yiyan, COFDM: An overview. IEEE Trans. Broadcast. 41, 1–8 (Mar. 1995)

    Article  Google Scholar 

  91. P. Combelles et al., A receiver architecture conforming to the OFDM based digital video broadcasting standard for terrestrial transmission (DVB-T), IEEE ICC, vol. 2, Atlanta, GA, June 1998, pp. 780–785

    Google Scholar 

  92. P.M. Shankar, Introduction to Wireless Systems (Wiley, New York, 2002)

    Google Scholar 

  93. M. Farshchian, S. Cho, W.A. Pearlman, Robust image transmission using a new joint source channel coding algorithm and dual adaptive OFDM, in SPIE and IS&T, VCIP, vol. 5308, San Jose, CA, Jan. 2004, pp. 636–646

    Google Scholar 

  94. R.M. Jiang, An area-efficient FFT architecture for OFDM digital video broadcasting. IEEE Trans. CE 53, 1322–1326 (Nov. 2007)

    Google Scholar 

  95. M. Borgerding, Turning overlap-save into a multiband mixing, downsampling filter bank. IEEE SP Mag. 23, 158–161 (Mar. 2006)

    Article  Google Scholar 

  96. N. Ahmed, K.R. Rao, Orthogonal Transforms for Digital Signal Processing (Springer, New York, 1975)

    Book  MATH  Google Scholar 

  97. O.K. Ersoy, A comparative review of real and complex Fourier-related transforms. Proc. IEEE 82, 429–447 (Mar. 1994)

    Article  Google Scholar 

  98. H.C. Andrews, K.L. Caspari, A generalized technique for spectral analysis. IEEE Trans. Comput. 19, 16–25 (Jan. 1970)

    Article  MATH  Google Scholar 

  99. H.C. Andrews, Computer Techniques in Image Processing (Academic Press, New York, 1970)

    Google Scholar 

  100. H.C. Andrews, J. Kane, Kronecker matrices, computer implementation and generalized spectra. J. Assoc. Comput. Machinary (JACM) 17, 260–268 (Apr. 1970)

    Article  MathSciNet  MATH  Google Scholar 

  101. H.C. Andrews, Multidimensional rotations in feature selection. IEEE Trans. Comput. 20, 1045–1051 (Sept. 1971)

    Article  MATH  Google Scholar 

  102. R.T. Lynch, J.J. Reis, Haar transform image coding, in Proc. Nat’l Telecommun. Conf., Dallas, TX, 1976, pp. 44.3-1−44.3-5

    Google Scholar 

  103. S. Wendling, G. Gagneux, G.A. Stamon, Use of the Haar transform and some of its properties in character recognition, in IEEE Proceedings of the 3rd Int’l Conf. on Pattern Recognition (ICPR), Coronado, CA, Nov. 1976, pp. 844−848

    Google Scholar 

  104. S. Wendling, G. Gagneux, G.A. Stamon, Set of invariants within the power spectrum of unitary transformations. IEEE Trans. Comput. 27, 1213–1216 (Dec. 1978)

    Article  MathSciNet  MATH  Google Scholar 

  105. V.V. Dixit, Edge extraction through Haar transform, in IEEE Proceedings of the 14th Asilomar Conference on Circuits Systems and Computations, Pacific Grove, CA, 1980, pp. 141−143

    Google Scholar 

  106. J.E. Shore, On the application of Haar functions. IEEE Trans. Commun. 21, 209–216 (Mar. 1973)

    Article  Google Scholar 

  107. D.F. Elliott, K.R. Rao, Fast Transforms: Algorithms, Analyses, Applications (Academic Press, Orlando, FL, 1982)

    MATH  Google Scholar 

  108. S. Venkataraman et al., Discrete transforms via the Walsh-Hadamard transform. Signal Process. 14, 371–382 (June 1988)

    Article  MathSciNet  Google Scholar 

  109. B.G. Jo, H. Sunwoo, New continuous-flow mixed-radix (CFMR) FFT processor using novel in-place strategy. IEEE Trans. Circ. Syst. I Reg. Papers 52, 911–919 (May 2005)

    Article  MathSciNet  Google Scholar 

  110. I.J. Good, The interaction algorithm and practical Fourier analysis. J. Royal Stat. Soc. B 20, 361–372 (1958)

    MathSciNet  MATH  Google Scholar 

  111. D.J. Mulvaney, D.E. Newland, K.F. Gill, A comparison of orthogonal transforms in their application to surface texture analysis. Proc. Inst. Mech. Engineers 200, no. C6, 407–414 (1986)

    Article  Google Scholar 

  112. T.K. Sarkar, E. Arvas, S.M. Rao, Application of FFT and the conjugate gradient method for the solution of electromagnetic radiation from electrically large and small conducting bodies. IEEE Trans. Antennas Propagat. 34, 635–640 (May 1986)

    Article  Google Scholar 

  113. T.J. Peters, J.L. Volakis, Application of a conjugate gradient FFT method to scattering from thin planar material plates. IEEE Trans. Antennas Propagat. 36, 518–526 (Apr. 1988)

    Article  Google Scholar 

  114. H. Zhai et al., Analysis of large-scale periodic array antennas by CG-FFT combined with equivalent sub-array preconditioner. IEICE Trans. Commun. 89, 922–928 (Mar. 2006)

    Article  Google Scholar 

  115. H. Zhai et al., Preconditioners for CG-FMM-FFT implementation in EM analysis of large-scale periodic array antennas, IEICE Trans. Commun., vol. 90, pp. 707–710, 2007

    Google Scholar 

  116. Y. Wu, B. Caron, Digital television terrestrial broadcasting. IEEE Commun. Magazine 32, 46–52 (May 1994)

    Google Scholar 

  117. H. Dutagaci, B. Sankur, Y. Yemez, 3D face recognition by projection-based methods, in Proc. SPIE-IS&T, vol. 6072, San Jose, CA, Jan. 2006, pp. 60720I-1 thru 11

    Google Scholar 

  118. 3D Database, http://www.sic.rma.ac.be/∼beumier/DB/3d_rma.html

  119. J. Wu, W. Zhao, New precise measurement method of power harmonics based on FFT, in IEEE ISPACS, Hong Kong, China, Dec. 2005, pp. 365–368

    Google Scholar 

  120. A.M. Raičević, B.M. Popović, An effective and robust fingerprint enhancement by adaptive filtering in frequency domain, Series: Electronics and Energetics (Facta Universitatis, University of Niš, Serbia, Apr. 2009), pp. 91–104, available: http://factaee.elfak.ni.ac.rs/

  121. B.G. Sherlock, D.M. Monro, K. Millard, Fingerprint enhancement by directional Fourier filtering. IEE Proc. Image Signal Process. 141, 87–94 (Apr. 1994)

    Article  Google Scholar 

  122. J. Ma, G. Plonka, The curvelet transform [A review of recent applications]. IEEE SP Mag. 27(2), 118–133 (Mar. 2010)

    Article  Google Scholar 

  123. J.H. Mathews, CSUF, Numerical analysis: http://mathews.ecs.fullerton.edu/n2003/ Newton’s method http://mathews.ecs.fullerton.edu/n2003/NewtonSearchMod.html

  124. J.P. Hornak, The Basics of MRI (1996–2010), http://www.cis.rit.edu/htbooks/mri/

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Authors and Affiliations

  1. Electr. Engineering, Univ. of Texas at Arlington, Neddermann Hall Yates St. 416, 76013, Arlington, Texas, USA

    Dr. K. R. Rao

  2. School of Electron. & Inform. Engineering, Kunsan National Univ., 68 Miryong-dong, 573-701, Kunsan, Korea, Republic of (South Korea)

    Dr. J. J. Hwang

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Rao, K.R., Kim, D.N., Hwang, J.J. (2010). Applications. In: Fast Fourier Transform - Algorithms and Applications. Signals and Communication Technology. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-6629-0_8

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