메뉴 건너뛰기




Volumn 32, Issue 1, 2010, Pages 73-102

Alternative dual frames for digital-to-analog conversion in sigma-delta quantization

Author keywords

Alternative dual frames; Finite frames; Sigma delta quantization

Indexed keywords


EID: 72549114454     PISSN: 10197168     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10444-008-9088-1     Document Type: Article
Times cited : (31)

References (32)
  • 1
    • 72549095645 scopus 로고
    • Portraits of frames
    • Aldroubi, A.: Portraits of frames. Proceedings of AMS 123, 357-385 (1995).
    • (1995) Proceedings of AMS , vol.123 , pp. 357-385
    • Aldroubi, A.1
  • 2
    • 0037212207 scopus 로고    scopus 로고
    • Finite normalized tight frames
    • Benedetto, J. J., Fickus, M.: Finite normalized tight frames. Adv. Comput. Math. 18(2-4), 357-385 (2003).
    • (2003) Adv. Comput. Math. , vol.18 , Issue.2-4 , pp. 357-385
    • Benedetto, J.J.1    Fickus, M.2
  • 3
    • 4544312441 scopus 로고    scopus 로고
    • In: Proceedings of the International Conference on Acoustics, Speech and Signal Processing, Montreal, QC, Canada, May
    • Benedetto, J. J., Powell, A. M., Yi{dotless}lmaz, Ö.: Sigma-delta quantization and finite frames. In: Proceedings of the International Conference on Acoustics, Speech and Signal Processing, vol. 3, pp. 937-940. Montreal, QC, Canada (May 2004).
    • (2004) Sigma-delta Quantization and Finite Frames , vol.3 , pp. 937-940
    • Benedetto, J.J.1    Powell, A.M.2    Yilmaz, Ö.3
  • 4
    • 33646028180 scopus 로고    scopus 로고
    • Sigma-delta (ΣΔ) quantization and finite frames
    • Benedetto, J. J., Powell, A. M., Yi{dotless}lmaz, Ö.: Sigma-delta (ΣΔ) quantization and finite frames. IEEE Trans. Inform. Theory 52(5), 1990-2005 (2006).
    • (2006) IEEE Trans. Inform. Theory , vol.52 , Issue.5 , pp. 1990-2005
    • Benedetto, J.J.1    Powell, A.M.2    Yilmaz, Ö.3
  • 5
    • 32044458439 scopus 로고    scopus 로고
    • Second order sigma-delta (ΣΔ) quantization of finite frame expansions
    • Benedetto, J. J., Powell, A. M., Yi{dotless}lmaz, Ö.: Second order sigma-delta (ΣΔ) quantization of finite frame expansions. Appl. Comput. Harmon. Anal. 20(1), 126-148 (2006).
    • (2006) Appl. Comput. Harmon. Anal. , vol.20 , Issue.1 , pp. 126-148
    • Benedetto, J.J.1    Powell, A.M.2    Yilmaz, Ö.3
  • 6
    • 33751512263 scopus 로고
    • Spectra of quantized signals
    • Bennett, W.: Spectra of quantized signals. Bell Syst. Tech. J. 27, 446-472 (1949).
    • (1949) Bell Syst. Tech. J. , vol.27 , pp. 446-472
    • Bennett, W.1
  • 8
    • 33846643042 scopus 로고    scopus 로고
    • Frame paths and error bounds for sigma-delta quantization
    • Bodmann, B. G., Paulsen, V. I.: Frame paths and error bounds for sigma-delta quantization. Appl. Comput. Harmon. Anal. 22(2), 176-197 (2007).
    • (2007) Appl. Comput. Harmon. Anal. , vol.22 , Issue.2 , pp. 176-197
    • Bodmann, B.G.1    Paulsen, V.I.2
  • 9
    • 34548542753 scopus 로고    scopus 로고
    • Smooth frame path termination for higher order sigma-delta quantization
    • Bodmann, B. G., Paulsen, V. I., Abdulbaki, S.: Smooth frame path termination for higher order sigma-delta quantization. J. Fourier Anal. Appl. 13, 285-307 (2007).
    • (2007) J. Fourier Anal. Appl. , vol.13 , pp. 285-307
    • Bodmann, B.G.1    Paulsen, V.I.2    Abdulbaki, S.3
  • 10
    • 0035094967 scopus 로고    scopus 로고
    • Noise reduction in oversampled filter banks using predictive quantization
    • Bölcskei, H., Hlawatsch, F.: Noise reduction in oversampled filter banks using predictive quantization. IEEE Trans. Inform. Theory 47(1), 155-172 (2001).
    • (2001) IEEE Trans. Inform. Theory , vol.47 , Issue.1 , pp. 155-172
    • Bölcskei, H.1    Hlawatsch, F.2
  • 11
    • 0001736880 scopus 로고    scopus 로고
    • The art of frame theory
    • Casazza, P.: The art of frame theory. Taiwanese J. Math. 4(2), 129-210 (2000).
    • (2000) Taiwanese J. Math. , vol.4 , Issue.2 , pp. 129-210
    • Casazza, P.1
  • 12
    • 33746912013 scopus 로고    scopus 로고
    • Characterization of oblique dual frame pairs
    • Frames and overcomplete representations in signal processing, communications, and information theory, Art. ID 92674
    • Christensen, O., Eldar, Y.: Characterization of oblique dual frame pairs. EURASIP J. Appl. Signal Proc. Frames and overcomplete representations in signal processing, communications, and information theory, pp. 11. Art. ID 92674 (2006).
    • (2006) EURASIP J. Appl. Signal Proc. , pp. 11
    • Christensen, O.1    Eldar, Y.2
  • 13
    • 0037355947 scopus 로고    scopus 로고
    • Resilience properties of redundant expansions under additive noise quantization
    • Cvetković, Z.: Resilience properties of redundant expansions under additive noise quantization. IEEE Trans. Inform. Theory 49(3), 644-656 (2003).
    • (2003) IEEE Trans. Inform. Theory , vol.49 , Issue.3 , pp. 644-656
    • Cvetković, Z.1
  • 14
    • 0347544077 scopus 로고    scopus 로고
    • Approximating a bandlimited function from very coarsely quantized data: A family of stable sigma-delta modulators of arbitrary order
    • Daubechies, I., DeVore, R.: Approximating a bandlimited function from very coarsely quantized data: a family of stable sigma-delta modulators of arbitrary order. Ann. of Math. (2) 158(2), 679-710 (2003).
    • (2003) Ann. Of Math. (2) , vol.158 , Issue.2 , pp. 679-710
    • Daubechies, I.1    Devore, R.2
  • 17
    • 0346398557 scopus 로고    scopus 로고
    • Approximating a bandlimited function using very coarsely quantized data: Improved error estimates in sigma-delta modulation
    • Güntürk, C. S.: Approximating a bandlimited function using very coarsely quantized data: improved error estimates in sigma-delta modulation. J. Amer. Math. Soc. 17(1), 229-242 (2004).
    • (2004) J. Amer. Math. Soc. , vol.17 , Issue.1 , pp. 229-242
    • Güntürk, C.S.1
  • 18
    • 0346513750 scopus 로고    scopus 로고
    • One-bit sigma-delta quantization with exponential accuracy
    • Güntürk, C. S.: One-bit sigma-delta quantization with exponential accuracy. Comm. Pure Appl. Math. 56(11), 1608-1630 (2003).
    • (2003) Comm. Pure Appl. Math. , vol.56 , Issue.11 , pp. 1608-1630
    • Güntürk, C.S.1
  • 19
    • 0025519836 scopus 로고
    • Quantization noise spectra
    • Gray, R.: Quantization noise spectra. IEEE Trans. Inform. Theory 36(6), 1220-1244 (1990).
    • (1990) IEEE Trans. Inform. Theory , vol.36 , Issue.6 , pp. 1220-1244
    • Gray, R.1
  • 20
    • 0026867753 scopus 로고
    • Multi-loop sigma-delta quantization
    • He, N., Kuhlmann, F., Buzo, A.: Multi-loop sigma-delta quantization. IEEE Trans. Inform. Theory 38(3), 1015-1028 (1992).
    • (1992) IEEE Trans. Inform. Theory , vol.38 , Issue.3 , pp. 1015-1028
    • He, N.1    Kuhlmann, F.2    Buzo, A.3
  • 21
    • 36248996522 scopus 로고    scopus 로고
    • White noise hypothesis for uniform quantization errors
    • Jimenez, D., Wang, L., Wang, Y.: White noise hypothesis for uniform quantization errors. SIAM J. Math. Anal. 38(6), 2042-2056 (2007).
    • (2007) SIAM J. Math. Anal. , vol.38 , Issue.6 , pp. 2042-2056
    • Jimenez, D.1    Wang, L.2    Wang, Y.3
  • 23
    • 0037540019 scopus 로고
    • On general frame decompositions
    • Li, S.: On general frame decompositions. Numer. Funct. Anal. Optim. 16(9-10), 1181-1191 (1995).
    • (1995) Numer. Funct. Anal. Optim. , vol.16 , Issue.9-10 , pp. 1181-1191
    • Li, S.1
  • 24
    • 4544369762 scopus 로고    scopus 로고
    • Pseudoframes for subspaces with applications
    • Li, S., Ogawa, H.: Pseudoframes for subspaces with applications. J. Fourier Anal. Appl. 10(4), 409-431 (2004).
    • (2004) J. Fourier Anal. Appl. , vol.10 , Issue.4 , pp. 409-431
    • Li, S.1    Ogawa, H.2
  • 26
    • 18544373710 scopus 로고    scopus 로고
    • The validity of the additive noise model for uniform scalar quantizers
    • Marco, D., Neuhoff, D.: The validity of the additive noise model for uniform scalar quantizers. IEEE Trans. Inform. Theory 51(5), 1739-1755 (2005).
    • (2005) IEEE Trans. Inform. Theory , vol.51 , Issue.5 , pp. 1739-1755
    • Marco, D.1    Neuhoff, D.2
  • 27
    • 0027649358 scopus 로고
    • On the behavior of the double-loop sigma-delta modulator
    • Pinault, S. C., Lopresti, P. V.: On the behavior of the double-loop sigma-delta modulator. IEEE Trans. Circuits and Syst. II 40(8), 467-479 (1993).
    • (1993) IEEE Trans. Circuits and Syst. II , vol.40 , Issue.8 , pp. 467-479
    • Pinault, S.C.1    Lopresti, P.V.2
  • 28
    • 0017542211 scopus 로고
    • A necessary and sufficient condition for quantization errors to be uniform and white
    • Sripad, A., Snyder, D.: A necessary and sufficient condition for quantization errors to be uniform and white. IEEE Trans. Acoust. Speech Signal Proc. 25(5), 442-448 (1977).
    • (1977) IEEE Trans. Acoust. Speech Signal Proc. , vol.25 , Issue.5 , pp. 442-448
    • Sripad, A.1    Snyder, D.2
  • 29
    • 0028386320 scopus 로고
    • Deterministic analysis of oversampled A/D conversion and decoding improvement based on consistent estimates
    • Thao, N., Vetterli, M.: Deterministic analysis of oversampled A/D conversion and decoding improvement based on consistent estimates. IEEE Trans. Inform. Theory 42(3), 519-531 (1994).
    • (1994) IEEE Trans. Inform. Theory , vol.42 , Issue.3 , pp. 519-531
    • Thao, N.1    Vetterli, M.2
  • 30
    • 0035397701 scopus 로고    scopus 로고
    • On the whiteness of high-resolution quantization errors
    • Viswanathan, H., Zamir, R.: On the whiteness of high-resolution quantization errors. IEEE Trans. Inform. Theory, 47(5), 2029-2038 (2001).
    • (2001) IEEE Trans. Inform. Theory , vol.47 , Issue.5 , pp. 2029-2038
    • Viswanathan, H.1    Zamir, R.2
  • 31
    • 0035982979 scopus 로고    scopus 로고
    • Stability analysis for several second-order sigma-delta methods of coarse quantization of bandlimited functions
    • Yilmaz, O.: Stability analysis for several second-order sigma-delta methods of coarse quantization of bandlimited functions. Constr. Approx. 18(4), 599-623 (2002).
    • (2002) Constr. Approx. , vol.18 , Issue.4 , pp. 599-623
    • Yilmaz, Ö.1
  • 32
    • 2942754909 scopus 로고    scopus 로고
    • Normalized tight frames in finite dimensions
    • In: Jetter, K., Haussmann, W., Reimer, M. (eds.), Birkhäuser
    • Zimmermann, G.: Normalized tight frames in finite dimensions. In: Jetter, K., Haussmann, W., Reimer, M. (eds.) Recent Progress in Multivariate Approximation, Birkhäuser (2001).
    • (2001) Recent Progress in Multivariate Approximation
    • Zimmermann, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.