Bibliography

1

S. Abarbanel and D. Gottlieb.
A mathematical analysis of the PML method.
J. Computational Physics, 134(2):357-63, 1 July 1997.

2

S. Abarbanel and D. Gottlieb.
On the construction and analysis of absorbing layers in CEM.
Applied Numerical Mathematics, 27(4):331-40, Aug. 1998.

3

R. Abraham.
Linear and Multilinear Algebra.
W. A. Benjamin, Inc., New York, 1966.

4

S. Akhtarzad and P. B. Johns.
Solution of Maxwell's equations in three space dimensions and time by the T.L.M. method of numerical analysis.
Proc. IEE, 122(12):1344-8, Dec. 1975.

5

K. Balemarthy and S. Bass.
General, linear boundary conditions in MD wave digital simulations.
In Proc. 1995 IEEE Int. Symp. on Circuits and Systems, volume 1, pages 73-76, Seattle, Washington, 28 Apr.-3 May 1995.

6

M. Banerjee.
On the vibration of skew plates of variable thickness.
J. Sound Vibration, 63(3):377-83, 8 Apr. 1979.

7

S. Bass.
Sampling grid properties in wave digital PDE simulations.
Technical Report CSE-TR-26-94, University of Notre Dame, 1994.

8

S. Basu and A. Fettweis.
On the factorization of scattering transfer matrices for multidimensional lossless two-ports.
IEEE Trans. Circuits and Systems, CAS-32(9):925-34, Sept. 1985.

9

S. Basu and A. Fettweis.
On synthesizable multidimensional lossless two-ports.
IEEE Trans. Circuits and Systems, 35(12):1478-86, Dec. 1988.

10

S. Basu and A. Zerzghi.
Multidimensional digital filter approach for numerical solution of a class of PDEs of the propagating wave type.
In Proc. 1998 IEEE Int. Symp. on Circuits and Systems, volume 5, pages 74-77, Monterey, California, 31 May-3 June 1998. IEEE Press.

11

V. Belevitch.
Summary of the history of circuit theory.
Proc. IRE, 50:848-55, May 1962.

12

V. Belevitch.
Classical Network Theory.
Holden Day, San Francisco, 1968.

13

J.-P. Berenger.
A perfectly matched layer for the absorption of electromagnetic waves.
J. Computational Physics, 114(2):185-200, Oct. 1994.

14

J.-P. Berenger.
Three-dimensional perfectly matched layer for the absorption of electromagnetic waves.
J. Computational Physics, 127(2):363-379, Sept. 1996.

15

D. P. Berners.
Acoustics and Signal Processing Techniques for Physical Modelling of Brass Instruments.
PhD thesis, Department of Electrical Engineering, Stanford University, 1999.

16

R. Bernhardt and D. Dahlhaus.
Numerical integration of the Euler equations by means of wave digital filters.
In Proc. IEEE Int. Conf. Acoust., Speech, and Sig. Proc., volume 6, pages 1-4, Adelaide, Australia, 19-22 Apr. 1994. IEEE Press.

17

D. Beskos, editor.
Boundary Element Analysis of Plates and Shells.
Springer-Verlag, New York, 1991.

18

S. Bilbao.
Digital waveguide networks as multidimensional wave digital filters.
In Proc. COST G-6 Conference on Digital Audio Effects, pages 49-54, Verona, Italy, 7-9 Dec. 2000.

19

S. Bilbao.
Digital waveguide networks in inhomogeneous media.
In Proc. COST G-6 Conference on Digital Audio Effects, pages 249-253, Verona, Italy, 7-9 Dec. 2000.

20

N. K. Bose.
Applied Multidimensional Systems Theory.
Van Nostrand Reinhold, New York, 1982.

21

A. Bossavit and L. Kettunen.
Yee-like schemes on a tetrahedral mesh, with diagonal lumping.
Int. J. of Numerical Modelling, 12:129-42, Jan.-Apr. 1999.

22

A. Bruckstein and T. Kailath.
An inverse scattering framework for several problems in signal processing.
IEEE ASSP Magazine, 4(1):6-20, Jan. 1987.

23

K. P. Bube and R. Burridge.
The one-dimensional inverse problem of reflection seismology.
SIAM Review, 25(4):497-559, 1983.

24

R. Cacoveanu, P. Saguet, and F. Ndagijimana.
TLM method: A new approach for the central node in polar meshes.
Electronics Letters, 31(4):297-8, 16 Feb. 1995.

25

A. Chaigne and A. Askenfelt.
Numerical simulations of struck strings. I. A physical model for a struck string using finite difference methods.
J. Acoust. Soc. Amer., 95(2):1112-8, Feb. 1994.

26

D. Chandrasekharaiah.
Thermoelasticity with second sound: A review.
Appl. Mech. Review, 39(3):355-376, Mar. 1986.

27

Z. Chen, M. M. Ney, and W. J. R. Hoefer.
A new finite difference time-domain formulation and its equivalence with the TLM symmetrical condensed node.
IEEE Trans. Microwave Theory Tech., MTT-39(12), Dec. 1991.

28

D. Cheng.
Field and Wave Electromagnetics, page 438.
Addison-Wesley, second edition, 1990.

29

C. Christopoulos.
The Transmission-Line Modelling Method.
IEEE Press, New York, 1995.

30

P. R. Cook.
Identification of Control Parameters in an Articulatory Vocal Tract Model with Applications to the Synthesis of Singing.
PhD thesis, Department of Electrical Engineering, Stanford University, 1990.

31

R. Cooper and M. Naghdi.
Propagation of non-axially symmetric waves in elastic cylindrical shells.
J. Acoust. Soc. Amer., 29(12):1365-73, Dec. 1957.

32

G. Dahlquist.
A special stability problem for linear multistep methods.
BIT, 3:27-43, 1963.

33

D. de Cogan.
Transmission Line Matrix (TLM) Techniques for Diffusion Applications.
Gordon and Breach Science Publishers, Amsterdam, 1998.

34

C. de Vaal and R. Nouta.
Suppression of parasitic oscillations in floating point wave digital filters.
In Proc. 1978 IEEE Int. Symp. on Circuits and Systems, pages 1018-22, New York, New York, 17-19 May 1978.

35

W. Elmore and M. Heald.
Physics of Waves.
McGraw-Hill, New York, 1969.

36

M. Erbar and E.-H. Horneber.
Models for transmission lines with connecting transistors based on wave digital filters.
Int. J. of Circ. Theory and Applications, 23:395-412, July-Aug. 1995.

37

K. Erickson and A. N. Michel.
Stability analysis of fixed-point digital filters using computer generated Lyapunov functions--part ii: Wave digital filters and lattice digital filters.
IEEE Trans. Circuits and Systems, CAS-32(2):132-142, Feb. 1985.

38

C. Eswarappa and W. J. R. Hoefer.
Bridging the gap between TLM and FDTD.
IEEE Microwave and Guided Wave Letters, 43(8):4-6, Aug. 1995.

39

T. Felderhoff.
Simulation of nonlinear circuits with period-doubling and chaotic behavior by wave digital filter principles.
IEEE Trans. Circuits and Systems, 41(7):485-9, July 1994.

40

T. Felderhoff.
Jacobi's method for massive parallel wave digital filter algorithm.
In Proc. 1996 IEEE Int. Symp. on Circuits and Systems, volume 2, pages 1621-4, Atlanta, Georgia, 12-15 May 1996.

41

A. Fettweis.
Digital filters related to classical structures.
AEU: Archive für Elektronik und Übertragungstechnik, 25:79-89, Feb. 1971.
(See also U.S. Patent 3,967,099, 1976, now expired.).

42

A. Fettweis.
Pseudopassivity, sensitivity, and stability of wave digital filters.
IEEE Trans. Circuit Theory, 19(6):668-673, Nov. 1972.

43

A. Fettweis.
On sensitivity and roundoff noise in wave digital filters.
IEEE Trans. on Acoust., Speech, and Signal Proc., ASSP-22(5):383-4, Oct. 1974.

44

A. Fettweis.
Digital signal processing.
In J. K. Aggarwal, editor, Principles of Multidimensional Wave Digital Filtering, pages 261-82. Western Periodicals, North Hollywood, California, 1978.

45

A. Fettweis.
Multidimensional circuit and systems theory.
In Proc. 1984 IEEE Int. Symp. on Circuits and Systems, pages 951-957, Montreal, Canada, 7-10 May 1984. IEEE Press.

46

A. Fettweis.
Wave digital filters: Theory and practice.
Proc. IEEE, 74(2):270-327, Feb. 1986.

47

A. Fettweis.
The role of passivity and losslessness in multidimensional digital signal processing-new challenges.
In Proc. 1991 IEEE Int. Symp. on Circuits and Systems, volume 1, pages 112-115, Singapore, 11-14 June 1991. IEEE Press.

48

A. Fettweis.
Discrete passive modelling of physical systems described by PDEs.
In SIGNAL PROCESSING VI: Theory and Applications. Proceedings of EUSIPCO-92, Sixth European Signal Processing Conference, volume 1, pages 55-62, Brussels, Belgium, 24-27 Aug. 1992. Elsevier Science Publishers.

49

A. Fettweis.
Discrete passive modelling of viscous fluids.
In Proc. 1992 IEEE Int. Symp. on Circuits and Systems, pages 1640-1643, San Diego, California, 10-13 May 1992. IEEE Press.

50

A. Fettweis.
Multidimensional wave digital filters for discrete-time modelling of Maxwell's equations.
Int. J. of Numerical Modelling, 5:183-201, Aug. 1992.

51

A. Fettweis.
Multidimensional wave digital principles: From filtering to numerical integration.
In Proc. IEEE Int. Conf. Acoust., Speech, and Sig. Proc., volume 6, pages 173-181, Adelaide, Australia, 19-22 Apr. 1994. IEEE Press.

52

A. Fettweis and S. Basu.
On improved representation theorems for multidimensional lossless bounded matrices.
Int. J. of Circ. Theory and Applications, 19(5):453-57, Sept.-Oct. 1991.

53

A. Fettweis and T. Leickel.
On floating-point implementations of modified wave digital filters.
In Proc. 1992 IEEE Int. Symp. on Circuits and Systems, volume 4, pages 1812-5, San Diego, California, 10-13 May 1992.

54

A. Fettweis, T. Leickel, M. Bolle, and U. Sauvagerd.
Realization of filter banks by means of wave digital filters.
In Proc. 1990 IEEE Int. Symp. on Circuits and Systems, volume 3, pages 2013-16, New Orleans, Louisiana, 1-3 May 1990.

55

A. Fettweis, H. Levin, and A. Sedlmeyer.
Wave digital lattice filters.
Int. J. of Circ. Theory and Applications, 2(2):203-11, June 1974.

56

A. Fettweis and K. Meerkötter.
Suppression of parasitic oscillations in wave digital filters.
IEEE Trans. Circuits and Systems, CAS-22(3):239-46, Mar. 1974.

57

A. Fettweis and K. Meerkötter.
On adaptors for wave digital filters.
IEEE Trans. on Acoust., Speech, and Signal Proc., ASSP-23(6):516-25, Dec. 1975.

58

A. Fettweis and K. Meerkötter.
On parasitic oscillations in digital filters under looped conditions.
IEEE Trans. Circuits and Systems, CAS-24(9):475-81, Sept. 1975.

59

A. Fettweis and G. Nitsche.
Numerical integration of partial differential equations by means of multidimensional wave digital filters.
In Proc. 1990 IEEE Int. Symp. on Circuits and Systems, volume 2, pages 954-7, New Orleans, Louisiana, 1-3 May 1990.

60

A. Fettweis and G. Nitsche.
Massively parallel algorithms for numerical integration of partial differential equations.
In Algorithms and Parallel VLSI Architectures. Lectures and Tutorials Presented at the International Workshop, volume B, pages 475-484. Elsevier, 1991.

61

A. Fettweis and G. Nitsche.
Numerical integration of partial differential equations using principles of multidimensional wave digital filters.
J. of VLSI Sig. Proc., 3(1-2):7-24, June 1991.

62

A. Fettweis and G. Nitsche.
Transformation approach to numerically integrating PDEs by means of WDF principles.
Multidimensional Systems Sig. Proc., 2(2):127-159, May 1991.

63

A. Fettweis and G. A. Seraji.
New results in numerically integrating PDEs by the wave digital approach.
In Proc. 1999 IEEE Int. Symp. on Circuits and Systems, volume 5, pages 17-20, Orlando, Florida, 30 May-2 June 1999.

64

A. Fiedler and H. Grotstollen.
Simulation of power electronic circuits with principles used in wave digital filters.
IEEE Trans. Industry Applications, 33(1):49-57, Jan./Feb. 1997.

65

H. D. Fischer.
Wave digital filters for numerical integration.
ntz-Archiv, 6:37-40, Feb. 1984.

66

N. Fletcher and T. Rossing.
The Physics of Musical Instruments.
Springer-Verlag, New York, 1991.

67

F. Fontana and D. Rocchesso.
Physical modelling of membranes for percussive instruments.
Acustica United with Acta Acustica, 84:529-542, May/June 1998.

68

K. Friedrichs and P. Lax.
Systems of conservation equations with a convex extension.
In Proceedings of the National Academy of Sciences of the U.S.A., pages 1686-1688. New York University, 1971.

69

M. Fries.
Multidimensional reactive elements on curvilinear coordinate systems and their MDWDF discretization.
In Proc. IEEE Int. Conf. Acoust., Speech, and Sig. Proc., volume 6, pages 9-12, Adelaide, Australia, 19-22 Apr. 1994. IEEE Press.

70

M. Fries.
Simulation of one-dimensional Euler flow by means of multidimensional wave digital filters.
In Proc. 1994 IEEE Int. Symp. on Circuits and Systems, volume 6, pages 9-12, London, UK, 30 May-2 June 1994. IEEE Press.

71

M. Fries and A. Schrick.
MDWDF-Verfahren und TLM-Methode zur Integration der 2D Maxwell-Gleichungen.
In Tagungsband ITG-Diskussionssitzung Neue Anwendungen theoretischer Konzepte in der Elektrotechnik, pages 137-144, Berlin, Germany, 1995.
In German.

72

M. Fusco.
FDTD algorithm in curvilinear coordinates.
IEEE Trans. Antennas and Propagation, 38(1):76-89, Jan. 1990.

73

M. Fusco, M. Smith, and L. Gordon.
A three-dimensional FDTD algorithm in curvilinear coordinates.
IEEE Trans. Antennas and Propagation, 39(10):1463-6, Oct. 1991.

74

P. Garabedian.
Partial Differential Equations.
Chelsea Publishing Company, New York, second edition, 1986.

75

Y. Genin.
An algebraic approach to A-stable linear multistep-multiderivative integration formulas.
BIT, 14(4):382-406, 1974.

76

C. Giguere and P. Woodland.
A computational model of the auditory periphery for speech and hearing.
J. Acoust. Soc. Amer., 95(1):331-49, Jan. 1994.

77

K. Graff.
Wave Motion in Elastic Solids.
Dover, New York, 1975.

78

A. H. Gray, Jr.
Passive cascaded lattice digital filters.
IEEE Trans. Circuits and Systems, CAS-27(5):337-44, May 1980.

79

A. H. Gray, Jr. and J. D. Markel.
Digital lattice and ladder filter synthesis.
IEEE Trans. Audio and Electroacoustics, AU-21:491-500, Dec. 1973.

80

A. H. Gray, Jr. and J. D. Markel.
A normalized digital filter structure.
IEEE Trans. on Acoust., Speech, and Signal Proc., ASSP-23:268-77, June 1975.

81

J. Greenspon.
Vibrations of a thick-walled cylindrical shell--comparison of the exact theory with approximate theories.
J. Acoust. Soc. Amer., 32(5):571-8, May 1960.

82

B. Gustaffson, H.-O. Kreiss, and J. Oliger.
Time Dependent Problems and Difference Methods.
John Wiley and Sons, New York, 1995.

83

C. Harris and C. Crede, editors.
Shock and Vibration Handbook.
McGraw-Hill, 1976.

84

A. Harten.
On the symmetric form of systems of conservation laws.
J. Computational Physics, 49:151-164, Jan. 1983.

85

G. Hemetsberger.
Stability verification of multidimensional Kirchoff circuits by suitable energy functions.
In Proc. IEEE Int. Conf. Acoust., Speech, and Sig. Proc., volume 6, pages 13-16, Adelaide, Australia, 19-22 Apr. 1994. IEEE Press.

86

G. Hemetsberger and R. Hellfajer.
Approach to simulating acoustics in supersonic flow by means of multidimensional vector-WDFs.
In Proc. 1994 IEEE Int. Symp. on Circuits and Systems, pages 73-76, London, UK, 30 May-2 June 1994. IEEE Press.

87

J. L. Herring and C. Christolopoulos.
Solving electromagnetic field problems using a multiple grid transmission-line modelling method.
IEEE Trans. Antennas and Propagation, 42(12):1654-1658, Dec. 1994.

88

J. L. Herring and C. Christopoulos.
Multigrid transmission-line modelling method for solving electromagnetic field problems.
Electronics Letters, 27(20):1794-5, 26 Sept. 1991.

89

C. Hirsch.
Numerical Computation of Internal and External Flows.
Wiley, Chichester, England, 1988.

90

W. J. R. Hoefer.
The Electromagnetic Wave Simulator.
Chichester, New York, 1991.

91

R. Holland.
Finite-difference solution of Maxwell's equations in generalized non-orthogonal coordinates.
IEEE Trans. Nuclear Science, NS-30(6):4589-91, Dec. 1983.

92

R. Horn and C. Johnson.
Matrix Analysis.
Cambridge University Press, Cambridge, England, 1985.

93

F. Hu.
On absorbing boundary conditions for linearized Euler equations by a perfectly matched layer.
J. Computational Physics, 129(1):201-19, Nov. 1996.

94

H. Huang.
Static and Dynamic Analyses of Plates and Shells.
Springer-Verlag, London, U.K., 1989.

95

T. Hughes, L. Franca, F. Chalot, and Z. Johan.
Stabilized finite element methods in fluid mechanics.
Course reader for Mechanical Engineering 234, Stanford University, 1996-7.

96

D. Jaffe and J. O. Smith.
Extensions of the Karplus-Strong plucked string algorithm.
Computer Music J., 7(2):56-68, Summer 1983.

97

P. B. Johns.
The solution of inhomogeneous waveguide problems using a transmission-line matrix.
IEEE Trans. Microwave Theory Tech., MTT-22:209-215, Mar. 1974.

98

P. B. Johns.
On the relationship between TLM and finite-difference methods for Maxwell's equations.
IEEE Trans. Microwave Theory Tech., MTT-35(1), Jan. 1987.

99

P. B. Johns.
A symmetrical condensed node for the TLM method.
IEEE Trans. Microwave Theory Tech., MTT-35(4):370-7, Apr. 1987.

100

P. B. Johns and R. L. Beurle.
Numerical solution of 2-dimensional scattering problems using a transmission-line matrix.
Proc. IEE, 118:1203-1208, Sept. 1971.

101

S. Kaliski and L. Solarz.
Vibrations and Waves.
Elsevier, New York, 1992.

102

M. Karjalainen and J. O. Smith.
Body modelling techniques for string instrument synthesis.
In Proc. Int. Computer Music Conf., Hong Kong, 18-21 Aug. 1996.

103

K. Karplus and A. Strong.
Digital synthesis of plucked-string and drum timbres.
Computer Music J., 7(2):43-55, Summer 1983.

104

J. L. Kelly and C. C. Lochbaum.
Speech synthesis.
In Proc. Fourth Int. Congress on Acoustics, pages 1-4, Copenhagen, Denmark, 1962.
Paper G42.

105

T. Koga.
Synthesis of finite passive $n$-ports with prescribed two-variable reacance matrices.
IEEE Trans. Circuit Theory, CT-13:31-52, Mar. 1966.

106

H. Krauss.
Wave digital simulation of transmission lines with arbitrary initial potential and current distributions.
In 1996 IEEE Digital Signal Processing Workshop Proceedings, pages 195-198, Loen, Norway, 1-4 Sept. 1996. IEEE Press.

107

H. Krauss and R. Rabenstein.
Application of multidimensional wave digital filters to boundary value problems.
IEEE Signal Processing Letters, 2(7):183-201, July 1995.

108

H. Krauss, R. Rabenstein, and M. Gerken.
Simulation of wave propagation by multidimensional wave digital filters.
Simulation Practice and Theory, 4:361-382, Nov. 1996.

109

G. Kron.
Equivalent circuit of the field equations of Maxwell.
Proc. IRE, 32(5):284-299, May 1944.

110

M. Krumpholz, C. Huber, and P. Russer.
A field-theoretical comparison of FDTD and TLM.
IEEE Trans. Microwave Theory Tech., 43(8):1935-1950, Aug. 1995.

111

W. Ku and S. Ming.
Floating-point coefficient sensitivity and roundoff noise of recursive digital filters realized in ladder structures.
IEEE Trans. Circuits and Systems, CAS-22(12):927-36, Dec. 1975.

112

P. Kundu.
Fluid Mechanics.
Academic Press, San Diego, California, 1990.

113

J. Kuttler and V. Sigillito.
Vibrational frequencies of clamped plates of variable thickness.
J. Sound Vibration, 86(2):181-9, 22 Jan. 1983.

114

T. Laakso, V. Välimäki, M. Karjalainen, and U. Laine.
Splitting the unit delay--tools for fractional delay filter design.
IEEE Signal Processing Magazine, 13(1):30-60, Jan. 1996.

115

S. Lawson, 2000.
private communication.

116

P. Lax.
Shock Waves and Entropy, in Contributions to Nonlinear Functional Analysis, E. Zarantonello, Ed.
Academic Press, New York, 1971.

117

T. Leickel and A. Fettweis.
Efficient digital-signal-processor realization of multirate filter banks using wave digital filters.
In Proc. 1992 IEEE Int. Symp. on Circuits and Systems, volume 4, pages 1812-15, San Diego, California, 10-13 May 1992.

118

P. Lennarz and W. Drews.
Design of circularly symmetric 2-D wave digital filters.
In Proc. 2nd Eur. Signal Processing Conf., pages 199-202, Erlangen, Germany, Sept. 1983.

119

P. Lennarz and L. Hofmann.
Computer realization of two-dimensional wave digital filters.
In Proc. 1978 Eur. Conf. on Circuit Theory and Design, pages 360-4, Lausanne, Switzerland, Sept. 1978.

120

K. Liew, C. Wang, Y. Xiang, and S. Kitipornchai.
Vibration of Mindlin plates: Programming the p-version Ritz Method.
Elsevier, Amsterdam, The Netherlands, first edition, 1998.

121

X. Liu and L. Bruton.
A new three-port adaptor suitable for floating-point arithmetic and/or DSP implementations.
In Proc. IEEE Int. Conf. Acoust., Speech, and Sig. Proc., volume 6, pages 17-20, Adelaide, Australia, 19-22 Apr. 1994.

122

X. Liu and A. Fettweis.
Multidimensional digital filtering by using parallel algorithms based on diagonal processing.
Multidimensional Systems Sig. Proc., 1(1):51-66, Mar. 1990.

123

R. H. MacNeal.
An asymmetrical finite difference network.
Quarterly of App. Math., 9(3):295-310, Oct. 1953.

124

J. D. Markel and A. H. Gray, Jr.
Linear Prediction of Speech Signals.
Springer-Verlag, New York, 1976.

125

K. Meerkötter.
Incremental pseudopassivity of wave digital filters.
In Signal Processing: Theories and Applications. Proceedings EUSIPCO-80, First European Signal Processing Conference, pages 27-31, Lausanne, Switzerland, 1980.

126

K. Meerkötter and T. Felderhoff.
Simulation of nonlinear transmission lines by wave digital filter principles.
In Proc. 1992 IEEE Int. Symp. on Circuits and Systems, volume 2, pages 875-8, San Diego, 10-13 May 1992.

127

B. G. Mertzios and F. N. Koumboulis.
Analysis and numerical integration of nonlinear systems using MD-passive circuits.
In Proc. 1999 IEEE Int. Symp. on Circuits and Systems, volume 5, pages 25-28, Orlando, Florida, 30 May-2 June 1999.

128

M. Naghdi and R. Cooper.
Propagation of elastic waves in cylindrical shells, including the effects of transverse shear and rotatory inertia.
J. Acoust. Soc. Amer., 28(1):56-63, Jan. 1956.

129

Y. Naka, H. Ikuno, M. Nishimoto, and A. Yata.
FD-TD method with PMLs ABC based on the principles of multidimensional wave digital filters for discrete-time modelling of Maxwell's equations.
Trans. of the Inst. of Electronics, Information and Communication Engineers: Electronics, 81(2):305-314, Feb. 1998.

130

G. Nitsche.
private communication.

131

G. Nitsche.
Numerische Lösung partieller Differentialgleichungen mit Hilfe von Wellendigitalfiltern.
PhD thesis, Ruhr-Universität Bochum, 1993.
In German.

132

R. Nouta.
The Jaumann structure in wave-digital filters.
Int. J. of Circ. Theory and Applications, 2(2):163-74, June 1974.

133

A. V. Oppenheim and R. Schafer.
Digital Signal Processing.
Prentice-Hall, Englewood Cliffs, New Jersey, 1975.

134

A. V. Oppenheim and R. Schafer.
Discrete-time Signal Processing.
Prentice-Hall, Englewood Cliffs, New Jersey, 1989.

135

H. Ozaki and T. Kasami.
Positive real functions of several variables and their application to variable networks.
IRE. Trans. Circuit Theory, CT-7:251-60, Sept. 1960.

136

P. Penfield.
Tellegen's Theorem and Electrical Networks.
MIT Press, Cambridge, Massachusetts, 1970.

137

J. Peng and C. Balanis.
A generalized reflection-free domain-truncation method: Transparent absorbing boundary.
IEEE Trans. Antennas and Propagation, 46(7), July 1998.

138

P. Petropoulos, L. Zhao, and A. Cangellaris.
A reflectionless sponge layer absorbing boundary condition for the solution of Maxwell's equations with high-order staggered finite difference schemes.
J. Computational Physics, 139(1):184-208, 1 Jan. 1998.

139

J. Proakis.
Digital Signal Processing.
Prentice-Hall, Englewood Cliffs, New Jersey, third edition, 1996.

140

T. Pulliam.
Course Notes, Aeronautics and Astronautics 214A, Autumn 1998-99, Stanford University.

141

R. Rabenstein.
A signal processing approach to the digital simulation of multidimensional continuous systems.
In Signal Processing III: Theories and Applications. Proceedings EUSIPCO-86, Third European Signal Processing Conference, volume 2, pages 665-668, The Hague, The Netherlands, 2-5 Sept. 1986.

142

R. Rabenstein, 2000.
private communication.

143

R. Rabenstein and L. Trautmann.
Solution of vector partial differential equations by transfer function models.
In Proc. 1999 IEEE Int. Symp. on Circuits and Systems, volume 5, pages 21-24, Orlando, Florida, 30 May-2 June 1999.

144

R. Rabenstein and L. Trautmann.
Solution of vector partial differential equations by transfer function models.
In Proc. 2000 IEEE Int. Symp. on Circuits and Systems, volume 1, pages 407-10, Geneva, Switzerland, 28-31 May 2000.

145

L. Rabiner and R. Schafer.
Digital Processing of Speech Signals.
Prentice-Hall, Englewood Cliffs, New Jersey, 1978.

146

S. S. Rao.
Mechanical Vibrations, 2nd Ed.
Addison-Wesley, 1990.

147

P. Regalia.
The digital all-pass filter: A versatile signal-processing building block.
Proc. IEEE, CAS-34(1):19-37, Jan. 1987.

148

D. J. Riley and C. D. Turner.
Interfacing unstructured tetrahedron grids to structured-grid FDTD.
IEEE Microwave and Guided Wave Letters, 5(9):284-6, Sept. 1995.

149

D. Rocchesso.
Maximally diffusive yet efficent feedback delay networks for artificial reverberation.
IEEE Signal Processing Letters, 4(9):252-255, Sept. 1997.

150

D. Rocchesso and J. O. Smith.
Circulant and elliptic feedback delay networks for artificial reverberation.
IEEE Trans. Speech and Audio Proc., 5(1):51-63, Jan. 1997.

151

M. Roitman and P. S. R. Diniz.
Simulation of non-linear and switching elements for transient analysis based on wave digital filters.
IEEE Trans. Power Delivery, 11(4):2042-8, Oct. 1996.

152

M. Roseau.
Vibrations in Mechanical Systems.
Springer-Verlag, Berlin, West Germany, 1984.

153

Z. Sacks, D. Kingsland, R. Lee, and J. Lee.
A perfectly matched absorber for use as an absorbing boundary condition.
IEEE Trans. Antennas and Propagation, 43(12), Dec. 1995.

154

A. Sarti and G. DePoli.
Generalized adaptors with memory for nonlinear wave digital structures.
In Proceedings EUSIPCO-96, VII European Signal Processing Conference, volume 3, pages 191-4, Trieste, Italy, 1996.

155

L. Savioja.
Improving the three-dimensional digital waveguide mesh by interpolation.
In Proc. Nordic Acoustical Meeting (NAM'98), pages 265-268, Stockholm, Sweden, 7-9 Sept. 1998.

156

L. Savioja, T. Rinne, and T. Takala.
Simulation of room acoustics with a 3-D finite-difference mesh.
In Proc. Int. Computer Music Conf., pages 463-466, Århus, Denmark, Sept. 1994.

157

L. Savioja and V. Välimäki.
Reducing the dispersion error in the digital waveguide mesh using interpolation and frequency-warping techniques.
IEEE Trans. Speech and Audio Proc., 8(2):184-194, Mar. 2000.

158

L. Savioja and V. Välimäki.
Interpolated 3-D digital waveguide mesh with frequency warping.
In Proc. IEEE Int. Conf. Acoust., Speech, and Sig. Proc., 7-11 May 2001.
To appear.

159

R. Scaramuzza and A. J. Lowery.
Hybrid symmetrical condensed node for the TLM method.
Electronics Letters, 26(23):1947-9, 1990.

160

G. P. Scavone.
An Acoustic Analysis of Single-Reed Woodwind Instruments with an Emphasis on Design and Performance Issues and Digital Waveguide Techniques.
PhD thesis, Stanford University, 1997.

161

J. O. Smith.
A physical derivation of wave digital filters.
In Lecture Notes for Music 421, Stanford University, Spring 1999-2000.

162

J. O. Smith.
Techniques for Digital Filter Design and System Identification with Application to the Violin.
PhD thesis, Stanford University, 1983.

163

J. O. Smith.
A new approach to digital reverberation using closed waveguide networks.
In Proc. Int. Computer Music Conf., Vancouver, Canada, 1985.
Appears in Technical Report STAN-M-39, pp. 1-7, Center for Computer Research in Music and Acoustics (CCRMA), Department of Music, Stanford University.

164

J. O. Smith.
Efficient simulation of the reed-bore and bow-string mechanisms.
In Music Applications of Digital Waveguides, pages 29-34. 1987.
Technical Report STAN-M-39, Center for Computer Research in Music and Acoustics (CCRMA), Department of Music, Stanford University.

165

J. O. Smith.
Elimination of limit cycles and overflow oscillations in time-varying lattice and ladder digital filters.
In Music Applications of Digital Waveguides, pages 47-78. 1987.
Technical Report STAN-M-39, Center for Computer Research in Music and Acoustics (CCRMA), Department of Music, Stanford University.

166

J. O. Smith.
Music applications of digital waveguides.
Technical Report STAN-M-39, Center for Computer Research in Music and Acoustics (CCRMA), Department of Music, Stanford University, 1987.

167

J. O. Smith.
Waveguide digital filters.
In Music Applications of Digital Waveguides, pages 108-181. 1987.
Technical Report STAN-M-39, Center for Computer Research in Music and Acoustics (CCRMA), Department of Music, Stanford University.

168

J. O. Smith, Spring 1999-2000.
Course notes for Music 421, Stanford University.

169

J. O. Smith and D. Rocchesso.
Aspects of digital waveguide modelling for acoustic modelling applications.
Submitted for publication.

170

P. P. M. So, C. Eswarappa, and W. J. R. Hoefer.
Parallel and distributed TLM computation with signal processing for electromagnetic field modeling.
Int. J. of Numerical Modelling, 8(3-4):169-185, May-Aug. 1995.

171

G. Sod.
A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws.
J. Computational Physics, 27(1):1-31, Apr. 1978.

172

I. Sokolnikoff.
Tensor Analysis Theory and Applications to Geometry and Mechanics of Continua.
Wiley, New York, second edition, 1964.

173

C. Steele, 2000.
Department of Mechanical Engineering, Stanford University. Private communication.

174

J. Stewart.
Calculus: Early Transcendentals.
Brooks/Cole, Pacific Grove, California, second edition, 1991.

175

S. Stoffels.
Full mesh warping techniques.
In Proc. COST G-6 Conference on Digital Audio Effects, Verona, Italy, Dec. 7-9 2000.

176

J. Strikwerda.
Finite Difference Schemes and Partial Differential Equations.
Wadsworth and Brooks/Cole Advanced Books and Software, Pacific Grove, Calif., 1989.

177

H. Strube.
Time-varying wave digital filters and vocal-tract models.
In Proc. IEEE Int. Conf. Acoust., Speech, and Sig. Proc., volume 2, pages 923-6, Paris, France, 3-5 May 1982.

178

H. Strube.
Time-varying wave digital filters for modelling analog systems.
IEEE Trans. on Acoust., Speech, and Signal Proc., ASSP-30(6):864-8, Dec. 1982.

179

S. Summerfeld, T. Wicks, and S. Lawson.
Wave digital filters using short signed digit coefficients.
Proc. IEE, 143(5):259-66, Oct. 1996.

180

L. Franca T. J. R. Hughes and M. Mallet.
A new finite element formulation for computational fluid dynamics: I. Symmetric forms of the Euler and Navier-Stokes equations and the second law of thermodynamics.
Computer Methods in Applied Mechanics and Engineering, 54:223-234, 1986.

181

E. Tadmor.
Skew-selfadjoint form for systems of conservation laws.
J. of Mathematical Analysis and Applications, 103:428-442, 1984.

182

E. Tadmor.
A minimum entropy principle in the gas dynamics equations.
Applied Numerical Mathematics, 2:151-164, Oct. 1986.

183

E. Tadmor.
Entropy functions for symmetric systems of conservation laws.
J. of Mathematical Analysis and Applications, 122:355-359, Mar. 1987.

184

A. Taflove.
Computational Electrodynamics.
Artech House, Boston, Massachusetts, 1995.

185

A. Taflove.
Advances in Computational Electrodynamics.
Artech House, Boston, Massachusetts, 1998.

186

L. Taxen.
Polyphase filter banks using wave digital filters.
IEEE Trans. on Acoust., Speech, and Signal Proc., 29(3):423-8, June 1981.

187

W. Thomson.
Theory of Vibrations with Applications.
Prentice-Hall, Upper Saddle River, New Jersey, fourth edition, 1993.

188

B. Tongue.
Principles of Vibration.
Oxford University Press, New York, 1996.

189

E. Turkel and A. Yefet.
Absorbing PML boundary layers for wave-like equations.
Applied Numerical Mathematics, 27(4):533-57, Aug. 1998.

190

L. Tyler.
Course notes for EE241, Stanford University, fall 1994-95.

191

T. Utsunomiya and A. Fettweis.
Discrete modelling of plasma equations with ion motion using technique of wave digital filters.
In Proc. IEEE Int. Conf. Acoust., Speech, and Sig. Proc., volume 6, pages 21-24, Adelaide, Australia, 19-22 Apr. 1994.

192

P. P. Vaidyanathan.
A unified approach to orthogonal digital filters and wave digital filters, based on LBR two-pair extraction.
IEEE Trans. Circuits and Systems, CAS-32(7), July 1985.

193

P. P. Vaidyanathan.
Multirate Systems and Filter Banks, page 288.
Prentice-Hall, Englewood Cliffs, New Jersey, 1993.

194

V. Välimäki.
Discrete-Time Modeling of Acoustic Tubes Using Fractional Delay Filters.
PhD thesis, Helsinki University of Technology, Faculty of Electrical Engineering, Laboratory of Acoustics and Audio Signal Processing, Espoo, Finland, 1995.

195

V. Välimäki and M. Karjalainen.
Implementation of fractional delay waveguide models using allpass filters.
In Proc. IEEE Int. Conf. Acoust., Speech, and Sig. Proc., pages 8-12, Detroit, Michigan, May 1995.

196

V. Välimäki, M. Karjalainen, and T. Laakso.
Modeling of woodwind bores with finger holes.
In Proc. Int. Computer Music Conf., pages 32-9, Tokyo, Japan, 1993.

197

S. A. VanDuyne, J. R. Pierce, and J. O. Smith.
Travelling wave implementation of a lossless mode-coupling filter and the wave digital hammer.
In Proc. Int. Computer Music Conf., pages 411-418, Århus, Denmark, Sept. 1994.

198

S. A. VanDuyne and J. O. Smith.
Physical modelling with the 2D digital waveguide mesh.
In Proc. Int. Computer Music Conf., pages 40-47, Tokyo, Japan, 1993.

199

S. A. VanDuyne and J. O. Smith.
A simplified approach to modelling dispersion caused by stiffness in strings and plates.
In Proc. Int. Computer Music Conf., Århus, Denmark, Sept. 1994.

200

S. A. VanDuyne and J. O. Smith.
The 3D tetrahedral digital waveguide mesh with musical applications.
In Proc. Int. Computer Music Conf., pages 9-16, Hong Kong, 18-21 Aug. 1996.

201

G. Verkroost and H. Butterweck.
Suppression of parasitic oscillations in wave digital filters and related structures by means of controlled rounding.
In Proc. 1976 IEEE Int. Symp. on Circuits and Systems, pages 628-9, Munich, West Germany, 27-29 Apr. 1976.

202

X. Wang and S. Bass.
The wave digital method and its use in a PIM chip array.
Technical Report TR-97-11, University of Notre Dame, 1997.

203

R. Warming, R. Beam, and B. Hyett.
Diagonalization and simultaneous symmetrization of the gas-dynamic matrices.
Mathematics of Computation, 29(132):1037-1045, Oct. 1975.

204

W. Wegener.
Design of wave digital filters with very short coefficient word lengths.
In Proc. 1976 IEEE Int. Symp. on Circuits and Systems, pages 473-6, Munich, West Germany, 27-29 Apr. 1976.

205

J. Wegner and J. Haddow.
Linear thermoelasticity, second sound and the entropy inequality.
Wave Motion, 18(1):67-77, Oct. 1993.

206

L. Weinberg.
Network Analysis and Synthesis.
McGraw-Hill, New York, 1962.

207

J. Wlodarczyk.
New multigrid interface for the TLM method.
Electronics Letters, 32(12):1111-1112, June 1996.

208

M. R. Wohlers.
Lumped and Distributed Passive Networks; A Generalized and Advanced Viewpoint.
Academic Press, New York, 1969.

209

F. Xiao and H. Yabe.
Numerical dispersion relation for FDTD method in general curvilinear coordinates.
IEEE Microwave and Guided Wave Letters, 7(2):48-50, Feb. 1997.

210

C. Q. Xu.
Accommodating lumped linear boundary conditions in the wave digital simulations of PDE systems.
Master's thesis, University of Notre Dame, 1996.
Available as Technical Report CSE-TR-26-94.

211

C. Q. Xu, S. Bass, and X. Wang.
Accommodating linear and nonlinear boundary conditions in wave digital simulations of PDE systems.
J. of Circuits Systems and Computers, 7(6):563-597, Dec. 1997.

212

C. Q. Xu, S. Bass, and X. Wang.
Accomodating boundary conditions in the wave digital simulations of PDE systems.
In Proc. of the 40th Midwest Symp. on Circuits and Systems, volume 2, pages 694-697. IEEE Press, 1997.

213

A. E. Yagle.
Fast algorithms for estimation and signal processing: An inverse scattering formulation.
IEEE Trans. on Acoust., Speech, and Signal Proc., 37(6):957-9, 1989.

214

K. S. Yee.
Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media.
IEEE Trans. Antennas and Propagation, 14:302-7, 1966.

215

B. Yegnanarayana.
Design of recursive group delay filters by autoregressive modeling.
IEEE Trans. on Acoust., Speech, and Signal Proc., ASSP-30:632-7, Aug. 1982.

216

L. Zhao and C. Cangellaris.
A general approach for the development of unsplit-field time domain implementations of perfectly matched layers for FDTD grid truncation.
IEEE Microwave and Guided Wave Letters, 6(5):209-11, May 1996.

217

R. Ziolkowski.
Time-derivative Lorentz material model-based absorbing boundary condition.
IEEE Trans. Antennas and Propagation, 45(10), Oct. 1997.