메뉴 건너뛰기




Volumn 9780521886710, Issue , 2008, Pages 1-751

Quantization noise: Roundoff error in digital computation, signal processing, control, and communications

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATION THEORY; DIGITAL ARITHMETIC; DIGITAL SIGNAL PROCESSING; SIGNAL PROCESSING;

EID: 84925134546     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1017/CBO9780511754661     Document Type: Book
Times cited : (453)

References (128)
  • 5
    • 33751512263 scopus 로고
    • Spectra of quantized signals
    • Bennett, W. R. (1948). Spectra of quantized signals, Bell System Technical Journal 27(4): 446-472.
    • (1948) Bell System Technical Journal , vol.27 , Issue.4 , pp. 446-472
    • Bennett, W.R.1
  • 6
    • 0000128845 scopus 로고
    • The effect of quantization in sampled-feedback systems
    • Bertram, J. E. (1958). The effect of quantization in sampled-feedback systems, Transactions of the AIEE, Part 2, 77: 177-82.
    • (1958) Transactions of the AIEE, Part , vol.77 , pp. 177-182
    • Bertram, J.E.1
  • 7
    • 84925157930 scopus 로고
    • Recovering a bandlimited density function from histogram values. Manuscript
    • Blachman, N. M. (1995). Recovering a bandlimited density function from histogram values. Manuscript.
    • (1995)
    • Blachman, N.M.1
  • 12
    • 0001152466 scopus 로고
    • Sampling theorem for the fourier transform of a distribution with bounded support
    • Campbell, L. L. (1968). Sampling theorem for the Fourier transform of a distribution with bounded support, SIAM Journal of Applied Mathematics 16(3): 626-636.
    • (1968) SIAM Journal of Applied Mathematics , vol.16 , Issue.3 , pp. 626-636
    • Campbell, L.L.1
  • 13
    • 3042844111 scopus 로고
    • CCITT. Fascicle III.3. Recommendation G.711, Pulse Code Modulation (PCM) of Voice Frequencies
    • CCITT (1984). Red Book, Vol. III, CCITT. Fascicle III.3. Recommendation G.711, Pulse Code Modulation (PCM) of Voice Frequencies.
    • (1984) Red Book , vol.3
  • 16
    • 0000523068 scopus 로고
    • An algorithm for the machine computation of complex fourier series
    • Cooley, J. W. and Tukey, J. W. (1965). An algorithm for the machine computation of complex Fourier series, Mathematical Computation 19: 297-301.
    • (1965) Mathematical Computation , vol.19 , pp. 297-301
    • Cooley, J.W.1    Tukey, J.W.2
  • 18
    • 84925133942 scopus 로고
    • Generalizations of the osvd: Structure, properties and applications
    • R. J. Vaccaro (ed.), Algorithms, Analysis and Applications, Elsevier Science Publishers B.V., Amsterdam, pp
    • De Moor, B. (1991). Generalizations of the OSVD: Structure, properties and applications, in R. J. Vaccaro (ed.), SVD and Signal Processing, Vol. II, Algorithms, Analysis and Applications, Elsevier Science Publishers B.V., Amsterdam, pp. 83-98.
    • (1991) SVD and Signal Processing , vol.2 , pp. 83-98
    • De Moor, B.1
  • 20
    • 0038739420 scopus 로고    scopus 로고
    • Ulam's scheme revisited: Digital modeling of chaotic attractors via micro-perturbations
    • Domokos, G. and Szasz, D. (2003). Ulam's scheme revisited: digital modeling of chaotic attractors via micro-perturbations, Discrete and Continuous Dynamical Systems, Ser. A. 9(4): 859-876.
    • (2003) Discrete and Continuous Dynamical Systems, Ser. A , vol.9 , Issue.4 , pp. 859-876
    • Domokos, G.1    Szasz, D.2
  • 23
    • 84925157927 scopus 로고
    • Correzioni dei momenti quando la curva e simmetrica (Correction of moments for symmetrical curves)
    • Italian
    • Elderton, W. P. (1938). Correzioni dei momenti quando la curva e simmetrica (Correction of Moments for Symmetrical Curves), Giornale dell’Istituto Italiano degliAttuari 9: 145. In Italian.
    • (1938) Giornale dell’Istituto Italiano Degliattuari , vol.9 , Issue.145
    • Elderton, W.P.1
  • 32
    • 0026122066 scopus 로고
    • What every computer scientist should know about floatingpoint arithmetic
    • Goldberg, D. (1991). What every computer scientist should know about floatingpoint arithmetic, ACM Computing Surveys 23(1): 5-48. URL: http://docs-pdf.sun.com/800-7895/800-7895.pdf.
    • (1991) ACM Computing Surveys , vol.23 , Issue.1 , pp. 5-48
    • Goldberg, D.1
  • 33
    • 0004236492 scopus 로고
    • The Johns Hopkins University Press, Baltimore and London
    • Golub, G. G. and van Loan, C. F. (1989). Matrix Computations, The Johns Hopkins University Press, Baltimore and London.
    • (1989) Matrix Computations
    • Golub, G.G.1    Van Loan, C.F.2
  • 37
    • 0001028172 scopus 로고
    • Digital-correlation techniques in radio science
    • Hagen, J. B. and Farley, D. T. (1973). Digital-correlation techniques in radio science, Radio Science 8-9(8): 775-84.
    • (1973) Radio Science , vol.8-9 , Issue.8 , pp. 775-784
    • Hagen, J.B.1    Farley, D.T.2
  • 39
    • 84925157925 scopus 로고
    • Kvantalasi hibak FFT alapu spektrumbecsleseknel (Quantization errors in FFT based spectrum estimations), Cand. Sci. Thesis, Hungarian Academy of Sciences. In Hungarian
    • Horvath, G. 1987. Kvantalasi hibak FFT alapu spektrumbecsleseknel (Quantization errors in FFT based spectrum estimations), Cand. Sci. Thesis, Hungarian Academy of Sciences. In Hungarian.
    • (1987)
    • Horvath, G.1
  • 40
    • 0035271235 scopus 로고    scopus 로고
    • Asymptotic analysis of optimal fixed-rate uniform scalar quantization
    • Hui, D. and Neuhoff, D. L. (2001). Asymptotic analysis of optimal fixed-rate uniform scalar quantization, IEEE Transactions on Information Theory 47(3): 957-977.
    • (2001) IEEE Transactions on Information Theory , vol.47 , Issue.3 , pp. 957-977
    • Hui, D.1    Neuhoff, D.L.2
  • 42
    • 84925157924 scopus 로고
    • IEEE standard for binary floating-point arithmetic. ANSI/IEEE Standard, New York, NJ
    • IEEE (1985). IEEE standard for binary floating-point arithmetic. ANSI/IEEE Standard 754-1985, New York, NJ.
    • (1985) , pp. 754-1985
  • 43
    • 84925157923 scopus 로고
    • IEEE standard for radix-independent floating-point arithmetic. ANSI/IEEE Standard, New York, NJ
    • IEEE (1987). IEEE standard for radix-independent floating-point arithmetic. ANSI/IEEE Standard 854-1987, New York, NJ.
    • (1987) , pp. 854-1987
  • 46
    • 0001593561 scopus 로고
    • Classical chaos
    • Jensen, R. V. (1987). Classical chaos, American Scientist 75(2): 168-81.
    • (1987) American Scientist , vol.75 , Issue.2 , pp. 168-181
    • Jensen, R.V.1
  • 47
    • 0017558676 scopus 로고
    • The shannon sampling theorem - its various extensions and applications: A tutorial review
    • Jerri, A. J. (1977). The Shannon sampling theorem - its various extensions and applications: A tutorial review, Proceedings of the IEEE 65(11): 1565-96.
    • (1977) Proceedings of the IEEE , vol.65 , Issue.11 , pp. 1565-1596
    • Jerri, A.J.1
  • 48
    • 84925157922 scopus 로고    scopus 로고
    • Matlab's loss is nobody's gain, World-wide web:, revised July 31, 2004
    • Kahan, W. (1998). Matlab's loss is nobody's gain, World-wide web: http://www.cs.berkeley.edurwkahan/MxMulEps.pdf. revised July 31, 2004.
    • (1998)
    • Kahan, W.1
  • 51
    • 33747917269 scopus 로고
    • On errors introduced by combined sampling and quantization
    • Katzenelson, J. (1962). On errors introduced by combined sampling and quantization, IRE Transactions on Automatic Control AC-7(3): 58-68.
    • (1962) IRE Transactions on Automatic Control , vol.7 , Issue.3 , pp. 58-68
    • Katzenelson, J.1
  • 53
  • 55
    • 85032410606 scopus 로고
    • Technoinform, Budapest
    • OMIKK Technoinform, Budapest, 1987, pp. 125-129.
    • (1987) , pp. 125-129
  • 58
    • 84911342382 scopus 로고
    • Tools and methods of signal analysis
    • L. Schnell (ed.), John Wiley and Sons, Chichester
    • Kollar, I. (1993). Tools and methods of signal analysis, in L. Schnell (ed.), Technology of Electrical Measurement John Wiley and Sons, Chichester, pp. 249380.
    • (1993) Technology of Electrical Measurement
    • Kollar, I.1
  • 59
    • 0028524183 scopus 로고
    • Bias of mean value and mean square value measurements based on quantized data
    • Kollar, I. (1994). Bias of mean value and mean square value measurements based on quantized data, IEEE Transactions on Instrumentation and Measurement43(5): 733-9.
    • (1994) IEEE Transactions on Instrumentation and Measurement , vol.43 , Issue.5 , pp. 733-739
    • Kollar, I.1
  • 60
    • 84925157840 scopus 로고    scopus 로고
    • Quantization noise, Doct. Sci. Thesis, Hungarian Academy of Sciences, Budapest
    • Kollar, I. (1997). Quantization noise, Doct. Sci. Thesis, Hungarian Academy of Sciences, Budapest.
    • (1997)
    • Kollar, I.1
  • 62
    • 27644534850 scopus 로고    scopus 로고
    • Improved determination of the best fitting sine wave in adc testing
    • Kollar, I. and Blair, J. J. (2005). Improved determination of the best fitting sine wave in ADC testing, IEEE Transactions on Instrumentation and Measurement54(5): 1978-83.
    • (2005) IEEE Transactions on Instrumentation and Measurement , vol.54 , Issue.5 , pp. 1978-1983
    • Kollar, I.1    Blair, J.J.2
  • 64
    • 84965889418 scopus 로고
    • Statistical measurements with quantized data
    • Korn, G. A. (1965). Statistical measurements with quantized data, Simulation 7(4): 229-239.
    • (1965) Simulation , vol.7 , Issue.4 , pp. 229-239
    • Korn, G.A.1
  • 66
    • 46649091837 scopus 로고
    • On the transmission capacity of ‘ether’ and wire in electrocommunications
    • Izd. Red. Upr. Svyazi RKKA, Moscow, In Russian
    • Kotel’nikov, V. A. (1933). On the transmission capacity of ‘ether’ and wire in electrocommunications, First All-Union Conference on Questions of Communications, 1933, Izd. Red. Upr. Svyazi RKKA, Moscow, pp. 1-19. In Russian.
    • (1933) First All-Union Conference on Questions of Communications, 1933 , pp. 1-19
    • Kotel’nikov, V.A.1
  • 69
    • 84925157839 scopus 로고
    • Analysis and design of sampled data control systems, DSc. Thesis. MIT Project Whirlwind Report R-170
    • Linvill, W. K. (1949). Analysis and design of sampled data control systems, DSc. Thesis. MIT Project Whirlwind Report R-170.
    • (1949)
    • Linvill, W.K.1
  • 70
    • 33747898845 scopus 로고
    • Sampled-data control systems studied through comparison of sampling with amplitude modulation
    • Linvill, W. K. (1951). Sampled-data control systems studied through comparison of sampling with amplitude modulation, AIEE Transactions 70: 1779-1788.
    • (1951) AIEE Transactions , vol.70 , pp. 1779-1788
    • Linvill, W.K.1
  • 71
    • 0014643208 scopus 로고
    • Error analysis of digital filters realized with floatingpoint arithmetic
    • Liu, B. and Kaneko, T. (1969). Error analysis of digital filters realized with floatingpoint arithmetic, Proceedings of the IEEE 57(10): 1735-1747.
    • (1969) Proceedings of the IEEE , vol.57 , Issue.10 , pp. 1735-1747
    • Liu, B.1    Kaneko, T.2
  • 72
    • 0003981320 scopus 로고
    • fourth edn, Springer-Verlag, New York. Original edition: Probability theory: foundations, random sequences, New York, Van Nostrand
    • Loeve, M. (1977). Probability Theory, fourth edn, Springer-Verlag, New York. Original edition: Probability theory: foundations, random sequences, New York, Van Nostrand, 1955.
    • (1977) Probability Theory , pp. 1955
    • Loeve, M.1
  • 76
    • 0018517207 scopus 로고
    • The digital coding of high-quality musical sound
    • Moorer, J. A. (1979). The digital coding of high-quality musical sound, Journal of the Audio Engineering Society 27(9): 657-66.
    • (1979) Journal of the Audio Engineering Society , vol.27 , Issue.9 , pp. 657-666
    • Moorer, J.A.1
  • 77
    • 84925157838 scopus 로고    scopus 로고
    • On the definition of ulp(x), Research Report No. 2005-09, Ecole Normale Superieure de Lyon, France
    • Muller, J.-M. (2005). On the definition of ulp(x), Research Report No. 2005-09, http://www.ens-lyon.fr/LIP/Pub/Rapports/RR/RR2005/RR2005-09.pdf. Ecole Normale Superieure de Lyon, France.
    • (2005)
    • Muller, J.-M.1
  • 79
    • 79957590676 scopus 로고
    • Certain topics in telegraph transmission theory
    • Nyquist, H. (1928). Certain topics in telegraph transmission theory, AIEE Transactions 47:617-644.
    • (1928) AIEE Transactions , vol.47 , pp. 617-644
    • Nyquist, H.1
  • 82
    • 33846236688 scopus 로고
    • Effects of finite register length in digital filtering and the fast fourier transform
    • Oppenheim, A. V. and Weinstein, C. J. (1972). Effects of finite register length in digital filtering and the fast Fourier transform, Proceedings of the IEEE 60(8): 957-76.
    • (1972) Proceedings of the IEEE , vol.60 , Issue.8 , pp. 957-976
    • Oppenheim, A.V.1    Weinstein, C.J.2
  • 85
    • 4644309577 scopus 로고    scopus 로고
    • Fast measurement of quantization distortions in dsp algorithms
    • Paduart, J., Schoukens, J. and Rolain, Y. (2004). Fast measurement of quantization distortions in DSP algorithms, Proceedings of the 21st IEEE Instrumentation and Measurement Technology Conference, Como, Italy, 18-20 May 2004, Vol. 1, pp. 140-145.
    • (2004) Proceedings of the 21St , vol.1 , pp. 140-145
    • Paduart, J.1    Schoukens, J.2    Rolain, Y.3
  • 89
    • 84904508900 scopus 로고
    • A high resolution, low frequency spectrum analyzer
    • Pendergrass, N. A. and Farnbach, J. S. (1978). A high resolution, low frequency spectrum analyzer, Hewlett-Packard Journal 29(13): 2-13.
    • (1978) Hewlett-Packard Journal , vol.29 , Issue.13 , pp. 2-13
    • Pendergrass, N.A.1    Farnbach, J.S.2
  • 93
    • 0041078636 scopus 로고
    • The analysis of sampled-data systems
    • Ragazzini, J. R. and Zadeh, L. A. (1952). The analysis of sampled-data systems, AIEE Transactions 71: 225-234.
    • (1952) AIEE Transactions , vol.71 , pp. 225-234
    • Ragazzini, J.R.1    Zadeh, L.A.2
  • 95
    • 0014563520 scopus 로고
    • Computer study of quantizer output spectra
    • Robertson, G. H. (1969). Computer study of quantizer output spectra, Bell System Technical Journal 48(5): 2391-2403.
    • (1969) Bell System Technical Journal , vol.48 , Issue.5 , pp. 2391-2403
    • Robertson, G.H.1
  • 97
    • 78650273796 scopus 로고
    • Dither signals and their effect on quantization noise
    • Schuchman, L. (1964). Dither signals and their effect on quantization noise, IEEE Transactions on Communication Theory 12: 162-65.
    • (1964) IEEE Transactions on Communication Theory , vol.12 , pp. 162-165
    • Schuchman, L.1
  • 98
    • 84911837213 scopus 로고
    • Communication in the presence of noise
    • Shannon, C. E. (1949). Communication in the presence of noise, Proceedings of the IRE 47(1): 10-21.
    • (1949) Proceedings of the IRE , vol.47 , Issue.1 , pp. 10-21
    • Shannon, C.E.1
  • 99
    • 84960586939 scopus 로고
    • On the calculation of the most probable values of frequency-constants, for data arranged according to equidistant divisions of scale
    • Sheppard, W. F. (1898). On the calculation of the most probable values of frequency-constants, for data arranged according to equidistant divisions of scale, Proceedings of the London Mathematical Society 29: 353-380.
    • (1898) Proceedings of the London Mathematical Society , vol.29 , pp. 353-380
    • Sheppard, W.F.1
  • 101
  • 102
    • 0003441938 scopus 로고
    • 114th edn, US Department of Commerce, Economics and Statistics Administration, Bureau of the Census
    • Statistical Abstract (1994). Statistical Abstract of the United States: The National Data Book, 114th edn, US Department of Commerce, Economics and Statistics Administration, Bureau of the Census.
    • (1994) Statistical Abstract of The United States: The National Data Book
    • Abstract, S.1
  • 103
    • 0003477556 scopus 로고
    • sixth edn, Edward Arnold, London and John Wiley & Sons, New York
    • Stuart, A. and Ord, J. K. (1994). Kendall's Advanced Theory of Statistics, Vol. I. Distribution Theory, sixth edn, Edward Arnold, London and John Wiley & Sons, New York.
    • (1994) Kendall's Advanced Theory of Statistics , vol.1
    • Stuart, A.1    Ord, J.K.2
  • 105
    • 0017269604 scopus 로고
    • Fixed-point fast fourier transform error analysis
    • ASSP
    • Thong, T. and Liu, B. (1976). Fixed-point fast fourier transform error analysis, IEEE Trans. ASSP ASSP-24: 563-573.
    • (1976) IEEE Trans. ASSP , vol.24 , pp. 563-573
    • Thong, T.1    Liu, B.2
  • 106
    • 85032423703 scopus 로고
    • Stochastic-ergodic measurement techniques and their contribution towards the solution of metrological problems in science and technology
    • Tumfart, S. (1976). Stochastic-ergodic measurement techniques and their contribution towards the solution of metrological problems in science and technology, Acta IMEKO 1976, Proc. IMEKO VII. World Congress, London, 10-14 May, 1976, Vol 1, pp. 263-76.
    • (1976) Acta IMEKO 1976, Proc. IMEKO VII. World Congress, London, 10-14 May, 1976 , vol.1 , pp. 263-276
    • Tumfart, S.1
  • 110
    • 84925157835 scopus 로고
    • Subtractive and non-subtractive dithering: A comparative analysis
    • Preprint
    • Wannamaker, R. A. (1994). Subtractive and non-subtractive dithering: A comparative analysis, 97th Convention of the Audio Engineering Society. Preprint 3920 (N-3).
    • (1994) 97Th Convention of the Audio Engineering Society , vol.3920
    • Wannamaker, R.A.1
  • 113
    • 0014566877 scopus 로고
    • Roundoff noise in floating point fast fourier transform computation
    • Weinstein, C. J. (1969). Roundoff noise in floating point fast Fourier transform computation, IEEE Transactions on Audio and Electroacoustics 17(3): 209-15.
    • (1969) IEEE Transactions on Audio and Electroacoustics , vol.17 , Issue.3 , pp. 209-215
    • Weinstein, C.J.1
  • 114
    • 0014628411 scopus 로고
    • A comparison of roundoff noise in floating point and fixed point digital filter realizations
    • Weinstein, C. and Oppenheim, A. V. (1969). A comparison of roundoff noise in floating point and fixed point digital filter realizations, Proceedings of the IEEE57(6): 1181-83.
    • (1969) Proceedings of the IEEE , vol.57 , Issue.6 , pp. 1181-1183
    • Weinstein, C.1    Oppenheim, A.V.2
  • 115
    • 0014522322 scopus 로고
    • A fixed-point fast fourier transform error analysis
    • Welch, P. D. (1969). A fixed-point fast Fourier transform error analysis, IEEE Transactions on Audio and Electroacoustics 17(2): 151-57.
    • (1969) IEEE Transactions on Audio and Electroacoustics , vol.17 , Issue.2 , pp. 151-157
    • Welch, P.D.1
  • 116
    • 0001693842 scopus 로고
    • On the functions which are represented by the expansion of interpolating theory
    • Whittaker, E. T. (1915). On the functions which are represented by the expansion of interpolating theory, Proceedings of the Royal Society of Edinburgh 35: 181-194.
    • (1915) Proceedings of the Royal Society of Edinburgh , vol.35 , pp. 181-194
    • Whittaker, E.T.1
  • 118
    • 84925157834 scopus 로고
    • A study of rough amplitude quantization by means of Nyquist sampling theory, Sc. D. Thesis. MIT, Department of Electrical Engineering
    • Widrow, B. (1956a). A study of rough amplitude quantization by means of Nyquist sampling theory, Sc. D. Thesis. MIT, Department of Electrical Engineering.
    • (1956)
    • Widrow, B.1
  • 119
    • 0000476523 scopus 로고
    • A study of rough amplitude quantization by means of nyquist sampling theory
    • Widrow, B. (1956b). A study of rough amplitude quantization by means of Nyquist sampling theory, IRE Transactions on Circuit Theory 3(4): 266-276.
    • (1956) IRE Transactions on Circuit Theory , vol.3 , Issue.4 , pp. 266-276
    • Widrow, B.1
  • 123
    • 0003494064 scopus 로고
    • Dover Publications, New York. Original edition: Prentice Hall
    • Wilkinson, J. H. (1994). Rounding Errors in Algebraic Processes, Dover Publications, New York. Original edition: Prentice Hall, 1963.
    • (1994) Rounding Errors in Algebraic Processes , pp. 1963
    • Wilkinson, J.H.1
  • 124
    • 0039664841 scopus 로고
    • Sheppard's correction formulae in several variables
    • Wold, H. (1934a). Sheppard's correction formulae in several variables, Skandinavisk Aktuartidskript 17: 248.
    • (1934) Skandinavisk Aktuartidskript , vol.17 , pp. 248
    • Wold, H.1
  • 125
    • 84925157833 scopus 로고
    • Sulla correzione di sheppard (On sheppard's corrections
    • Italian
    • Wold, H. (1934b). Sulla correzione di Sheppard (On Sheppard's corrections), Giornale dell’Istituto Italiano degli Attuari 5: 104. In Italian.
    • (1934) Giornale dell’Istituto Italiano Degli Attuari , vol.5 , Issue.104
    • Wold, H.1
  • 127
    • 0005721148 scopus 로고
    • Band-limited functions and the sampling theorem
    • Zakai, M. (1965). Band-limited functions and the sampling theorem, Information and Control 8(2): 143-158.
    • (1965) Information and Control , vol.8 , Issue.2 , pp. 143-158
    • Zakai, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.