메뉴 건너뛰기




Volumn , Issue 9780817683726, 2013, Pages 193-239

Gabor frames in finite dimensions

Author keywords

Applications to compressed sensing; Channel identification; Coherence; Erasure channel error correction; Gabor analysis on finite Abelian groups; Linear independence; Restricted isometry constants of Gabor frames

Indexed keywords


EID: 85008200329     PISSN: 22965009     EISSN: 22965017     Source Type: Book Series    
DOI: 10.1007/978-0-8176-8373-3_6     Document Type: Chapter
Times cited : (46)

References (99)
  • 1
    • 84939349092 scopus 로고
    • Complex sequences with low periodic correlations
    • Alltop, W.O.: Complex sequences with low periodic correlations. IEEE Trans. Inf. Theory 26(3), 350–354 (1980)
    • (1980) IEEE Trans. Inf. Theory , vol.26 , Issue.3 , pp. 350-354
    • Alltop, W.O.1
  • 2
    • 59649115633 scopus 로고    scopus 로고
    • Chirp sensing codes: Deterministic compressed sensing measurements for fast recovery
    • Applebaum, L., Howard, S.D., Searle, S., Calderbank, R.: Chirp sensing codes: deterministic compressed sensing measurements for fast recovery. Appl. Comput. Harmon. Anal. 26(2), 283–290 (2009)
    • (2009) Appl. Comput. Harmon. Anal. , vol.26 , Issue.2 , pp. 283-290
    • Applebaum, L.1    Howard, S.D.2    Searle, S.3    Calderbank, R.4
  • 3
    • 33646490258 scopus 로고    scopus 로고
    • Density, overcompleteness, and localization of frames. I: Theory
    • Balan, R., Casazza, P.G., Heil, C., Landau, Z.: Density, overcompleteness, and localization of frames. I: theory. J. Fourier Anal. Appl. 12(2), 105–143 (2006)
    • (2006) J. Fourier Anal. Appl. , vol.12 , Issue.2 , pp. 105-143
    • Balan, R.1    Casazza, P.G.2    Heil, C.3    Landau, Z.4
  • 4
    • 33646893694 scopus 로고    scopus 로고
    • Density, overcompleteness, and localization of frames. II: Gabor systems
    • Balan, R., Casazza, P.G., Heil, C., Landau, Z.: Density, overcompleteness, and localization of frames. II: Gabor systems. J. Fourier Anal. Appl. 12(3), 307–344 (2006)
    • (2006) J. Fourier Anal. Appl. , vol.12 , Issue.3 , pp. 307-344
    • Balan, R.1    Casazza, P.G.2    Heil, C.3    Landau, Z.4
  • 5
    • 0000421860 scopus 로고
    • Un principe d’incertitude fort en théorie du signal on en mécanique quantique
    • Balian, R.: Un principe d’incertitude fort en théorie du signal on en mécanique quantique. C. R. Acad. Sci. Paris 292, 1357–1362 (1981)
    • (1981) C. R. Acad. Sci. Paris , vol.292 , pp. 1357-1362
    • Balian, R.1
  • 6
    • 0030103713 scopus 로고    scopus 로고
    • On the discrete Gabor transform and the discrete Zak transform
    • Bastiaans, M.J., Geilen, M.: On the discrete Gabor transform and the discrete Zak transform. Signal Process. 49(3), 151–166 (1996)
    • (1996) Signal Process , vol.49 , Issue.3 , pp. 151-166
    • Bastiaans, M.J.1    Geilen, M.2
  • 8
    • 84861198098 scopus 로고    scopus 로고
    • Optimal ambiguity functions and Weil’s exponential sum bound
    • Benedetto, J.J., Benedetto, R.L., Woodworth, J.T.: Optimal ambiguity functions and Weil’s exponential sum bound. J. Fourier Anal. Appl. 18(3), 471–487 (2012)
    • (2012) J. Fourier Anal. Appl. , vol.18 , Issue.3 , pp. 471-487
    • Benedetto, J.J.1    Benedetto, R.L.2    Woodworth, J.T.3
  • 9
    • 34249289752 scopus 로고    scopus 로고
    • Ambiguity function and frame theoretic properties of periodic zero autocorrelation waveforms
    • Benedetto, J.J., Donatelli, J.J.: Ambiguity function and frame theoretic properties of periodic zero autocorrelation waveforms. In: IEEE J. Special Topics Signal Process, vol. 1, pp. 6–20 (2007)
    • (2007) IEEE J. Special Topics Signal Process , vol.1 , pp. 6-20
    • Benedetto, J.J.1    Donatelli, J.J.2
  • 12
    • 0042776133 scopus 로고
    • p whose Fourier transforms have constant modulus
    • I, II, Budapest, 1985. Colloq. Math. Soc. János Bolyai, North-Holland, Amsterdam
    • p whose Fourier transforms have constant modulus. In: A. Haar memorial conference, Vol. I, II, Budapest, 1985. Colloq. Math. Soc. János Bolyai, vol. 49, pp. 193–197. North-Holland, Amsterdam (1987)
    • (1987) A. Haar Memorial Conference , vol.49 , pp. 193-197
    • Björck, G.1
  • 14
    • 0003858079 scopus 로고
    • Brigham, E. (ed.), Prentice Hall, Englewood Cliffs
    • Brigham, E. (ed.): The Fast Fourier Transform. Prentice Hall, Englewood Cliffs (1974)
    • (1974) The Fast Fourier Transform
  • 15
    • 33745604236 scopus 로고    scopus 로고
    • Stable signal recovery from incomplete and inaccurate measurements
    • Candès, E., Romberg, J., Tao, T.: Stable signal recovery from incomplete and inaccurate measurements. Commun. Pure Appl. Math. 59(8), 1207–1223 (2006)
    • (2006) Commun. Pure Appl. Math. , vol.59 , Issue.8 , pp. 1207-1223
    • Candès, E.1    Romberg, J.2    Tao, T.3
  • 16
    • 33947416035 scopus 로고    scopus 로고
    • Near optimal signal recovery from random projections: Universal encoding strategies?
    • Candès, E., Tao, T.: Near optimal signal recovery from random projections: universal encoding strategies? IEEE Trans. Inf. Theory 52(12), 5406–5425 (2006)
    • (2006) IEEE Trans. Inf. Theory , vol.52 , Issue.12 , pp. 5406-5425
    • Candès, E.1    Tao, T.2
  • 17
    • 42649140570 scopus 로고    scopus 로고
    • The restricted isometry property and its implications for compressed sensing
    • Candès, E.J.: The restricted isometry property and its implications for compressed sensing. C. R. Math. Acad. Sci. Paris 346(9–10), 589–592 (2008)
    • (2008) C. R. Math. Acad. Sci. Paris , vol.346 , Issue.9-10 , pp. 589-592
    • Candès, E.J.1
  • 18
    • 0346494937 scopus 로고    scopus 로고
    • Equal-norm tight frames with erasures
    • Casazza, P., Kovačević, J.: Equal-norm tight frames with erasures. Adv. Comput. Math. 18(2–4), 387–430 (2003)
    • (2003) Adv. Comput. Math , vol.18 , Issue.2-4 , pp. 387-430
    • Casazza, P.1    Kovačević, J.2
  • 20
    • 84861408239 scopus 로고    scopus 로고
    • Matrix probing and its conditioning
    • Chiu, J., Demanet, L.: Matrix probing and its conditioning. SIAM J. Numer. Anal. 50(1), 171–193 (2012)
    • (2012) SIAM J. Numer. Anal. , vol.50 , Issue.1 , pp. 171-193
    • Chiu, J.1    Demanet, L.2
  • 21
    • 0030335735 scopus 로고    scopus 로고
    • Atomic decomposition via projective group representations
    • Christensen, O.: Atomic decomposition via projective group representations. Rocky Mt. J. Math. 26(4), 1289–1313 (1996)
    • (1996) Rocky Mt. J. Math. , vol.26 , Issue.4 , pp. 1289-1313
    • Christensen, O.1
  • 23
    • 84968470212 scopus 로고
    • An algorithm for the machine calculation of complex Fourier series
    • Cooley, J., Tukey, J.: An algorithm for the machine calculation of complex Fourier series. Math. Comput. 19, 297–301 (1965)
    • (1965) Math. Comput. , vol.19 , pp. 297-301
    • Cooley, J.1    Tukey, J.2
  • 24
    • 0025482241 scopus 로고
    • The wavelet transform, time-frequency localization and signal analysis
    • Daubechies, I.: The wavelet transform, time-frequency localization and signal analysis. IEEE Trans. Inf. Theory 36(5), 961–1005 (1990)
    • (1990) IEEE Trans. Inf. Theory , vol.36 , Issue.5 , pp. 961-1005
    • Daubechies, I.1
  • 25
    • 85047384156 scopus 로고
    • CBMS-NSF Reg. Conf. Series in Applied Math. Society for Industrial and Applied Mathematics, Philadelphia
    • Daubechies, I.: Ten Lectures on Wavelets. CBMS-NSF Reg. Conf. Series in Applied Math. Society for Industrial and Applied Mathematics, Philadelphia (1992)
    • (1992) Ten Lectures on Wavelets
    • Daubechies, I.1
  • 28
    • 33144483155 scopus 로고    scopus 로고
    • Stable recovery of sparse overcomplete representations in the presence of noise
    • Donoho, D.L., Elad, M., Temlyakov, V.N.: Stable recovery of sparse overcomplete representations in the presence of noise. IEEE Trans. Inf. Theory 52(1), 6–18 (2006)
    • (2006) IEEE Trans. Inf. Theory , vol.52 , Issue.1 , pp. 6-18
    • Donoho, D.L.1    Elad, M.2    Temlyakov, V.N.3
  • 29
    • 0001616908 scopus 로고
    • Uncertainty principles and signal recovery
    • Donoho, D.L., Stark, P.B.: Uncertainty principles and signal recovery. SIAM J. Appl. Math. 49(3), 906–931 (1989)
    • (1989) SIAM J. Appl. Math. , vol.49 , Issue.3 , pp. 906-931
    • Donoho, D.L.1    Stark, P.B.2
  • 30
    • 84968468760 scopus 로고
    • A class of nonharmonic Fourier series
    • Duffin, R.J., Schaeffer, A.C.: A class of nonharmonic Fourier series. Trans. Am. Math. Soc. 72(2), 341–366 (1952)
    • (1952) Trans. Am. Math. Soc. , vol.72 , Issue.2 , pp. 341-366
    • Duffin, R.J.1    Schaeffer, A.C.2
  • 31
    • 84968469827 scopus 로고
    • Generalized Vandermonde determinants and roots of unity of prime order
    • Evans, R.J., Isaacs, I.M.: Generalized Vandermonde determinants and roots of unity of prime order. Proc. Am. Math. Soc. 58, 51–54 (1976)
    • (1976) Proc. Am. Math. Soc. , vol.58 , pp. 51-54
    • Evans, R.J.1    Isaacs, I.M.2
  • 32
    • 0000548718 scopus 로고
    • Theory and practice of irregular sampling
    • Benedetto, J.J., Frazier, M.W. (eds.), CRC Press, Boca Raton
    • Feichtinger, H.G., Gröchenig, K.: Theory and practice of irregular sampling. In: Benedetto, J.J., Frazier, M.W. (eds.) Wavelets: Mathematics and Applications. CRC Press, Boca Raton (1994)
    • (1994) Wavelets: Mathematics and Applications
    • Feichtinger, H.G.1    Gröchenig, K.2
  • 33
    • 0031161747 scopus 로고    scopus 로고
    • Gabor frames and time-frequency analysis of distributions
    • Feichtinger, H.G., Gröchenig, K.: Gabor frames and time-frequency analysis of distributions. J. Funct. Anal. 146(2), 464–495 (1996)
    • (1996) J. Funct. Anal , vol.146 , Issue.2 , pp. 464-495
    • Feichtinger, H.G.1    Gröchenig, K.2
  • 34
    • 0002947656 scopus 로고    scopus 로고
    • Quantization of TF-lattice invariant operators on elementary LCA groups
    • Feichtinger, H.G., Strohmer, T. (eds.), Birkhäuser, Boston
    • Feichtinger, H.G., Kozek, W.: Quantization of TF-lattice invariant operators on elementary LCA groups. In: Feichtinger, H.G., Strohmer, T. (eds.) Gabor Analysis and Algorithms: Theory and Applications, pp. 233–266. Birkhäuser, Boston (1998)
    • (1998) Gabor Analysis and Algorithms: Theory and Applications , pp. 233-266
    • Feichtinger, H.G.1    Kozek, W.2
  • 36
    • 67650094314 scopus 로고    scopus 로고
    • Wiener amalgam spaces for the Fundamental Identity of Gabor Analysis
    • (Extra Volume)
    • Feichtinger, H.G., Luef, F.: Wiener amalgam spaces for the Fundamental Identity of Gabor Analysis. Collect. Math. 57, 233–253 (2006) (Extra Volume)
    • (2006) Collect. Math. , vol.57 , pp. 233-253
    • Feichtinger, H.G.1    Luef, F.2
  • 37
    • 0029313722 scopus 로고
    • A group-theoretical approach to Gabor analysis
    • Feichtinger, H.G., Strohmer, T., Christensen, O.: A group-theoretical approach to Gabor analysis. Opt. Eng. 34(6), 1697–1704 (1995)
    • (1995) Opt. Eng , vol.34 , Issue.6 , pp. 1697-1704
    • Feichtinger, H.G.1    Strohmer, T.2    Christensen, O.3
  • 38
    • 0039768601 scopus 로고    scopus 로고
    • The uncertainty principle: A mathematical survey
    • Folland, G., Sitaram, A.: The uncertainty principle: a mathematical survey. J. Fourier Anal. Appl. 3(3), 207–238 (1997)
    • (1997) J. Fourier Anal. Appl. , vol.3 , Issue.3 , pp. 207-238
    • Folland, G.1    Sitaram, A.2
  • 41
    • 0000293183 scopus 로고
    • Theory of communication
    • Gabor, D.: Theory of communication. J. IEE, London 93(3), 429–457 (1946)
    • (1946) J. IEE, London , vol.93 , Issue.3 , pp. 429-457
    • Gabor, D.1
  • 42
    • 79955794653 scopus 로고    scopus 로고
    • On uncertainty principles in the finite dimensional setting
    • Ghobber, S., Jaming, P.: On uncertainty principles in the finite dimensional setting. Linear Algebra Appl. 435(4), 751–768 (2011)
    • (2011) Linear Algebra Appl , vol.435 , Issue.4 , pp. 751-768
    • Ghobber, S.1    Jaming, P.2
  • 44
    • 32944458952 scopus 로고    scopus 로고
    • On the exponential convergence of matching pursuits in quasi-incoherent dictionaries
    • Gribonval, R., Vandergheynst, P.: On the exponential convergence of matching pursuits in quasi-incoherent dictionaries. IEEE Trans. Inf. Theory 52(1), 255–261 (2006)
    • (2006) IEEE Trans. Inf. Theory , vol.52 , Issue.1 , pp. 255-261
    • Gribonval, R.1    Vandergheynst, P.2
  • 45
    • 0037813506 scopus 로고    scopus 로고
    • Aspects of Gabor analysis on locally compact abelian groups
    • Feichtinger, H., Strohmer, T. (eds.), Birkhäuser, Boston
    • Gröchenig, K.: Aspects of Gabor analysis on locally compact abelian groups. In: Feichtinger, H., Strohmer, T. (eds.) Gabor Analysis and Algorithms: Theory and Applications, pp. 211– 231. Birkhäuser, Boston (1998)
    • (1998) Gabor Analysis and Algorithms: Theory and Applications , pp. 211-231
    • Gröchenig, K.1
  • 47
    • 29144479677 scopus 로고    scopus 로고
    • Uncertainty principles for time-frequency representations
    • Feichtinger, H., Strohmer, T. (eds.), Birkhäuser, Boston
    • Gröchenig, K.: Uncertainty principles for time-frequency representations. In: Feichtinger, H., Strohmer, T. (eds.) Advances in Gabor Analysis, pp. 11–30. Birkhäuser, Boston (2003)
    • (2003) Advances in Gabor Analysis , pp. 11-30
    • Gröchenig, K.1
  • 48
    • 2442697562 scopus 로고    scopus 로고
    • Localization of frames, Banach frames, and the invertibility of the frame operator
    • Gröchenig, K.: Localization of frames, Banach frames, and the invertibility of the frame operator. J. Fourier Anal. Appl. 10(2), 105–132 (2004)
    • (2004) J. Fourier Anal. Appl. , vol.10 , Issue.2 , pp. 105-132
    • Gröchenig, K.1
  • 49
    • 34147200195 scopus 로고    scopus 로고
    • History and evolution of the density theorem for Gabor frames
    • Heil, C.: History and evolution of the density theorem for Gabor frames. J. Fourier Anal. Appl. 12, 113–166 (2007)
    • (2007) J. Fourier Anal. Appl. , vol.12 , pp. 113-166
    • Heil, C.1
  • 50
    • 21444434839 scopus 로고    scopus 로고
    • Linear independence of time–frequency translates
    • Heil, C., Ramanathan, J., Topiwala, P.: Linear independence of time–frequency translates. Proc. Amer. Math. Soc. 124(9), 2787–2795 (1996)
    • (1996) Proc. Amer. Math. Soc , vol.124 , Issue.9 , pp. 2787-2795
    • Heil, C.1    Ramanathan, J.2    Topiwala, P.3
  • 53
    • 0000393325 scopus 로고
    • Gabor representation of generalized functions
    • Janssen, A.J.E.M.: Gabor representation of generalized functions. J. Math. Anal. Appl. 83, 377–394 (1981)
    • (1981) J. Math. Anal. Appl. , vol.83 , pp. 377-394
    • Janssen, A.J.E.M.1
  • 54
    • 84951608719 scopus 로고
    • Duality and biorthogonality for Weyl-Heisenberg frames
    • Janssen, A.J.E.M.: Duality and biorthogonality for Weyl-Heisenberg frames. J. Fourier Anal. Appl. 1(4), 403–436 (1995)
    • (1995) J. Fourier Anal. Appl , vol.1 , Issue.4 , pp. 403-436
    • Janssen, A.J.E.M.1
  • 55
    • 1842780849 scopus 로고    scopus 로고
    • From continuous to discrete Weyl-Heisenberg frames through sampling
    • Janssen, A.J.E.M.: From continuous to discrete Weyl-Heisenberg frames through sampling. J. Fourier Anal. Appl. 3(5), 583–596 (1997)
    • (1997) J. Fourier Anal. Appl. , vol.3 , Issue.5 , pp. 583-596
    • Janssen, A.J.E.M.1
  • 56
    • 13844281131 scopus 로고    scopus 로고
    • Approximation of the Fourier transform and the dual Gabor window
    • Kaiblinger, N.: Approximation of the Fourier transform and the dual Gabor window. J. Fourier Anal. Appl. 11(1), 25–42 (2005)
    • (2005) J. Fourier Anal. Appl. , vol.11 , Issue.1 , pp. 25-42
    • Kaiblinger, N.1
  • 58
    • 70349128524 scopus 로고    scopus 로고
    • Using NFFT 3—a software library for various nonequispaced fast Fourier transforms
    • Keiner, J., Kunis, S., Potts, D.: Using NFFT 3—a software library for various nonequispaced fast Fourier transforms. ACM Trans. Math. Softw. 36(4), 30 (2009), Art. 19
    • (2009) ACM Trans. Math. Softw. , vol.36 , Issue.4 , pp. 30
    • Keiner, J.1    Kunis, S.2    Potts, D.3
  • 59
    • 48349105627 scopus 로고    scopus 로고
    • Uncertainty in time-frequency representations on finite abelian groups and applications
    • Krahmer, F., Pfander, G.E., Rashkov, P.: Uncertainty in time-frequency representations on finite abelian groups and applications. Appl. Comput. Harmon. Anal. 25(2), 209–225 (2008)
    • (2008) Appl. Comput. Harmon. Anal. , vol.25 , Issue.2 , pp. 209-225
    • Krahmer, F.1    Pfander, G.E.2    Rashkov, P.3
  • 61
    • 0002884848 scopus 로고
    • Necessary density conditions for sampling an interpolation of certain entire functions
    • Landau, H.: Necessary density conditions for sampling an interpolation of certain entire functions. Acta Math. 117, 37–52 (1967)
    • (1967) Acta Math , vol.117 , pp. 37-52
    • Landau, H.1
  • 62
    • 0027635335 scopus 로고
    • On the density of phase-space expansions
    • Landau, H.: On the density of phase-space expansions. IEEE Trans. Inf. Theory 39(4), 1152– 1156 (1993)
    • (1993) IEEE Trans. Inf. Theory , vol.39 , Issue.4 , pp. 1152-1156
    • Landau, H.1
  • 63
    • 84857887285 scopus 로고
    • Prolate spheroidal wave functions, Fourier analysis and uncertainty. II
    • Landau, H., Pollak, H.: Prolate spheroidal wave functions, Fourier analysis and uncertainty. II. Bell Syst. Tech. J. 40, 65–84 (1961)
    • (1961) Bell Syst. Tech. J. , vol.40 , pp. 65-84
    • Landau, H.1    Pollak, H.2
  • 64
    • 29644443325 scopus 로고    scopus 로고
    • Linear independence of Gabor systems in finite dimensional vector spaces
    • Lawrence, J., Pfander, G.E., Walnut, D.F.: Linear independence of Gabor systems in finite dimensional vector spaces. J. Fourier Anal. Appl. 11(6), 715–726 (2005)
    • (2005) J. Fourier Anal. Appl. , vol.11 , Issue.6 , pp. 715-726
    • Lawrence, J.1    Pfander, G.E.2    Walnut, D.F.3
  • 65
    • 0033185001 scopus 로고    scopus 로고
    • Discrete multi-Gabor expansions
    • Li, S.: Discrete multi-Gabor expansions. IEEE Trans. Inf. Theory 45(6), 1954–1967 (1999)
    • (1999) IEEE Trans. Inf. Theory , vol.45 , Issue.6 , pp. 1954-1967
    • Li, S.1
  • 66
    • 0002544660 scopus 로고
    • Complete sets of wave packets
    • DeTar, C. (ed.), World Scientific, Singapore
    • Low, F.: Complete sets of wave packets. In: DeTar, C. (ed.) A Passion for Physics—Essay in Honor of Geoffrey Chew, pp. 17–22. World Scientific, Singapore (1985)
    • (1985) A Passion for Physics—Essay in Honor of Geoffrey Chew , pp. 17-22
    • Low, F.1
  • 67
    • 0037838467 scopus 로고
    • Frames in the Bargmann space of entire functions
    • Lyubarskii, Y.I.: Frames in the Bargmann space of entire functions. Adv. Sov. Math. 429, 107–113 (1992)
    • (1992) Adv. Sov. Math , vol.429 , pp. 107-113
    • Lyubarskii, Y.I.1
  • 69
    • 14644429637 scopus 로고    scopus 로고
    • The Donoho-Stark uncertainty principle for a finite abelian group. Acta
    • Matusiak, E., Özaydın, M., Przebinda, T.: The Donoho-Stark uncertainty principle for a finite abelian group. Acta Math. Univ. Comen. (N.S.) 73(2), 155–160 (2004)
    • (2004) Math. Univ. Comen. (N.S.) , vol.73 , Issue.2 , pp. 155-160
    • Matusiak, E.1    Özaydın, M.2    Przebinda, T.3
  • 71
    • 0027679088 scopus 로고
    • Derivation of the finite discrete Gabor transform by periodization and sampling
    • Orr, R.: Derivation of the finite discrete Gabor transform by periodization and sampling. Signal Process. 34(1), 85–97 (1993)
    • (1993) Signal Process , vol.34 , Issue.1 , pp. 85-97
    • Orr, R.1
  • 72
    • 0031269523 scopus 로고    scopus 로고
    • An introduction to discrete finite frames
    • Pei, S.C., Yeh, M.H.: An introduction to discrete finite frames. IEEE Signal Process. Mag. 14(6), 84–96 (1997)
    • (1997) IEEE Signal Process. Mag. , vol.14 , Issue.6 , pp. 84-96
    • Pei, S.C.1    Yeh, M.H.2
  • 73
    • 84923132097 scopus 로고
    • The Khintchine inequalities and martingale expanding sphere of their action
    • Pevskir, G., Shiryaev, A.N.: The Khintchine inequalities and martingale expanding sphere of their action. Russ. Math. Surv. 50(5), 849–904 (1995)
    • (1995) Russ. Math. Surv. , vol.50 , Issue.5 , pp. 849-904
    • Pevskir, G.1    Shiryaev, A.N.2
  • 74
    • 84946068287 scopus 로고    scopus 로고
    • Note on sparsity in signal recovery and in matrix identification
    • Pfander, G.E.: Note on sparsity in signal recovery and in matrix identification. Open Appl. Math. J. 1, 21–22 (2007)
    • (2007) Open Appl. Math. J , vol.1 , pp. 21-22
    • Pfander, G.E.1
  • 75
    • 77952098309 scopus 로고    scopus 로고
    • Sparsity in time-frequency representations
    • Pfander, G.E., Rauhut, H.: Sparsity in time-frequency representations. J. Fourier Anal. Appl. 16(2), 233–260 (2010)
    • (2010) J. Fourier Anal. Appl. , vol.16 , Issue.2 , pp. 233-260
    • Pfander, G.E.1    Rauhut, H.2
  • 76
    • 54949110579 scopus 로고    scopus 로고
    • Identification of matrices having a sparse representation
    • Pfander, G.E., Rauhut, H., Tanner, J.: Identification of matrices having a sparse representation. IEEE Trans. Signal Process. 56(11), 5376–5388 (2008)
    • (2008) IEEE Trans. Signal Process. , vol.56 , Issue.11 , pp. 5376-5388
    • Pfander, G.E.1    Rauhut, H.2    Tanner, J.3
  • 77
    • 84908543122 scopus 로고    scopus 로고
    • The restricted isometry property for time-frequency structured random matrices
    • (to appear)
    • Pfander, G.E., Rauhut, H., Tropp, J.A.: The restricted isometry property for time-frequency structured random matrices. Probab. Theory Relat. Fields (to appear)
    • Probab. Theory Relat. Fields
    • Pfander, G.E.1    Rauhut, H.2    Tropp, J.A.3
  • 78
    • 33750576200 scopus 로고    scopus 로고
    • Measurement of time-variant channels
    • Pfander, G.E., Walnut, D.: Measurement of time-variant channels. IEEE Trans. Inf. Theory 52(11), 4808–4820 (2006)
    • (2006) IEEE Trans. Inf. Theory , vol.52 , Issue.11 , pp. 4808-4820
    • Pfander, G.E.1    Walnut, D.2
  • 79
    • 1842816594 scopus 로고    scopus 로고
    • Discrete Gabor transforms: The Gabor-Gram matrix approach
    • Qiu, S.: Discrete Gabor transforms: the Gabor-Gram matrix approach. J. Fourier Anal. Appl. 4(1), 1–17 (1998)
    • (1998) J. Fourier Anal. Appl. , vol.4 , Issue.1 , pp. 1-17
    • Qiu, S.1
  • 80
    • 0029393448 scopus 로고
    • Discrete Gabor structure and optimal representation
    • Qiu, S., Feichtinger, H.: Discrete Gabor structure and optimal representation. IEEE Trans. Signal Process. 43(10), 2258–2268 (1995)
    • (1995) IEEE Trans. Signal Process , vol.43 , Issue.10 , pp. 2258-2268
    • Qiu, S.1    Feichtinger, H.2
  • 83
    • 0010989208 scopus 로고
    • Tech. Rep. 95-03, University of Wisconsin, Madison (WI)
    • d). Tech. Rep. 95-03, University of Wisconsin, Madison (WI) (1995)
    • (1995) d)
    • Ron, A.1    Shen, Z.2
  • 84
    • 0003342710 scopus 로고
    • Fourier Analysis on Groups
    • Interscience Publishers (a division of John Wiley & Sons), New York–London
    • Rudin, W.: Fourier Analysis on Groups. Interscience Tracts in Pure and Applied Mathematics, vol. 12. Interscience Publishers (a division of John Wiley & Sons), New York–London (1962)
    • (1962) Interscience Tracts in Pure and Applied Mathematics , vol.12
    • Rudin, W.1
  • 85
    • 0001994272 scopus 로고
    • Density theorems for sampling and interpolation in the Bargmann-Fock space
    • Seip, K., Wallstén, R.: Density theorems for sampling and interpolation in the Bargmann-Fock space. I. J. Reine Angew. Math. 429, 91–106 (1992)
    • (1992) I. J. Reine Angew. Math , vol.429 , pp. 91-106
    • Seip, K.1    Wallstén, R.2
  • 86
    • 84941389507 scopus 로고
    • Density theorems for sampling and interpolation in the Bargmann-Fock space
    • Seip, K., Wallstén, R.: Density theorems for sampling and interpolation in the Bargmann-Fock space. II. J. Reine Angew. Math. 429, 107–113 (1992)
    • (1992) II. J. Reine Angew. Math , vol.429 , pp. 107-113
    • Seip, K.1    Wallstén, R.2
  • 90
    • 34147212327 scopus 로고    scopus 로고
    • Gabor frames by sampling and periodization
    • Søndergaard, P.L.: Gabor frames by sampling and periodization. Adv. Comput. Math. 27(4), 355–373 (2007)
    • (2007) Adv. Comput. Math. , vol.27 , Issue.4 , pp. 355-373
    • Søndergaard, P.L.1
  • 91
    • 0041064594 scopus 로고    scopus 로고
    • Numerical algorithms for discrete Gabor expansions
    • Feichtinger, H., Strohmer, T. (eds.), Birkhäuser, Boston
    • Strohmer, T.: Numerical algorithms for discrete Gabor expansions. In: Feichtinger, H., Strohmer, T. (eds.) Gabor Analysis and Algorithms: Theory and Applications, pp. 267–294. Birkhäuser, Boston (1998)
    • (1998) Gabor Analysis and Algorithms: Theory and Applications , pp. 267-294
    • Strohmer, T.1
  • 92
    • 0242323185 scopus 로고    scopus 로고
    • Grassmannian frames with applications to coding and communication
    • Strohmer, T., Heath, R.W. Jr.: Grassmannian frames with applications to coding and communication. Appl. Comput. Harmon. Anal. 14(3), 257–275 (2003)
    • (2003) Appl. Comput. Harmon. Anal. , vol.14 , Issue.3 , pp. 257-275
    • Strohmer, T.1    Heath, R.W.2
  • 93
    • 17044386613 scopus 로고    scopus 로고
    • An uncertainty principle for groups of prime order
    • Tao, T.: An uncertainty principle for groups of prime order. Math. Res. Lett. 12, 121–127 (2005)
    • (2005) Math. Res. Lett. , vol.12 , pp. 121-127
    • Tao, T.1
  • 94
    • 0038679036 scopus 로고    scopus 로고
    • Fourier Analysis on Finite Groups and Applications
    • Cambridge University Press, Cambridge
    • Terras, A.: Fourier Analysis on Finite Groups and Applications. London Mathematical Society Student Texts, vol. 43. Cambridge University Press, Cambridge (1999)
    • (1999) London Mathematical Society Student Texts , vol.43
    • Terras, A.1
  • 95
    • 5444237123 scopus 로고    scopus 로고
    • Greed is good: Algorithmic results for sparse approximation
    • Tropp, J.A.: Greed is good: algorithmic results for sparse approximation. IEEE Trans. Inf. Theory 50(10), 2231–2242 (2004)
    • (2004) IEEE Trans. Inf. Theory , vol.50 , Issue.10 , pp. 2231-2242
    • Tropp, J.A.1
  • 96
    • 33645712308 scopus 로고    scopus 로고
    • Just relax: Convex programming methods for identifying sparse signals
    • Tropp, J.A.: Just relax: convex programming methods for identifying sparse signals. IEEE Trans. Inf. Theory 51(3), 1030–1051 (2006)
    • (2006) IEEE Trans. Inf. Theory , vol.51 , Issue.3 , pp. 1030-1051
    • Tropp, J.A.1
  • 97
    • 44249104733 scopus 로고    scopus 로고
    • On the conditioning of random subdictionaries
    • Tropp, J.A.: On the conditioning of random subdictionaries. Appl. Comput. Harmon. Anal. 25(1), 1–24 (2008)
    • (2008) Appl. Comput. Harmon. Anal , vol.25 , Issue.1 , pp. 1-24
    • Tropp, J.A.1
  • 98
    • 0025519408 scopus 로고
    • Discrete Gabor expansions
    • Wexler, J., Raz, S.: Discrete Gabor expansions. Signal Process. 21(3), 207–221 (1990)
    • (1990) Signal Process , vol.21 , Issue.3 , pp. 207-221
    • Wexler, J.1    Raz, S.2
  • 99
    • 0035338890 scopus 로고    scopus 로고
    • On the rank of the discrete Gabor transform matrix
    • Xia, X.G., Qian, S.: On the rank of the discrete Gabor transform matrix. Signal Process. 52(3), 1083–1087 (1999)
    • (1999) Signal Process , vol.52 , Issue.3 , pp. 1083-1087
    • Xia, X.G.1    Qian, S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.