Index for this Document

3D sound : 13.8.5

acceleration due to gravity : 13.1.4

acoustic

echo simulation : 3.2.7

energy density : 13.7.8

intensity : 13.7.7

wave simulation : 3.2

acoustic guitars : 10.2

acoustic tube

nonuniform : 14.18

waveguide model : 7.2

acoustical ohms : 14.7.3

acoustics : 13

action : 13.4

action force : 10.3.1

adaptor : 17.2

series, reflection free : 17.2.4.4

two-port parallel : 17.2.1

unit element : 17.1.7

additive synthesis : 2.4.3

adiabatic gas constant : 13.7.12

admittance : 8.1

aerofoil : 13.7.5

air absorption : 4.1.1 | 13.7.15

frequency-dependent : 3.3.2

frequency-independent : 3.3.1

air jets : 13.7.6

air pressure : 13.7.3

airfoil : 13.7.5

aliasing : 7.13.1.6

allpass comb filter : 3.8.1

allpass condition

equivalence to losslessness : 3.8.3

allpass filter : 3.8 | 3.8.1

examples : 3.8.4

general case : 3.8.3

Gerzon nested MIMO : 3.8.5

maximally flat group delay : 5.3

nested : 3.8.2 | 4.4.3

Thiran : 5.3

waveguide : 3.9

allpass phase shifter : 9.9.1

second-order case : 9.9.2

allpass reflectance : 14.11.1

alpha parameters : 17.2.2.1 | 17.2.2.1

amplification factor : 15.4

amplifier

cabinet filter : 10.1.8

distortion : 10.1.10

feedback simulation : 10.1.7

amplitude complementary : 10.5.1.1

amplitude envelopes : 7.11.1

analog circuit : 2.5.10

angular acceleration : 13.4.19

angular momentum : 13.4.13

general case : 13.4.20.2

vector : 13.4.14

angular velocity vector : 13.4.11

arctangent nonlinearity : 7.13.1.2

area moment of inertia : 13.4.8

artificial reverberation : 4.5

backward difference : 2.5.5 | 8.3.1

backward Euler method : 8.4.3

bandlimited interpolation : 5.4

Bark scale : 9.6.2

beaded strings : 10.4.3

bell models : 10.7.2

Bernoulli effect : 13.7.5

Bernoulli equation : 10.7.1 | 13.7.4

Bessel filter : 5.3

beta parameters (WDF) : 17.2.4.1

bidirectional delay line : 3.4

bilinear transform : 8.3.2

bilinear transform vs. finite differences : 8.3.2.1

Bode plot : 9.9.1.1

body factoring : 9.8

by sinusoidal modeling : 9.8.1.4

example : 9.8.6

resonator extraction : 9.8

body-fixed frame : 13.4.10.2 | 13.4.20.1 | 13.4.20.1

Boltzmann's constant : 13.7.10

boundary conditions : 13.8.4

boundary element method : 14.18.1.1

boundary losses : 13.7.15

bowed strings : 10.6

bow-string junction : 10.6.2

linear commuted synthesis of : 10.6.4

brass instruments : 10.7

brass mouthpiece : 10.7.1

break frequency : 9.9.1.1 | 9.9.1.1

bridge power splitting : 14.11.1.2

bridge velocity transmittance : 14.11.1.1

butterflies : 4.7.9

cabinet filtering : 10.1.8

capacitor : 8.1.3

cardinal sine : 5.4.1

causal : 3.5.4 | 3.8.3

center of gravity : 13.4.1

center of mass : 13.4.1

center of mass, momentum : 13.4.1.1

center-of-mass frame : 13.4.10.2

centered finite difference : 8.3.1.2 | 12.5.2 | 16.1.1

centroid : 13.4.1

cepstral method : 9.6.4.3

chain rule : 14.3.2 | 14.3.2

change of coordinates: : 2.5.9.3

characteristic impedance : see wave impedancetextbf

characteristic polynomial equation : 15.2.2.1 | 15.3

Chebyshev optimality : 5.2.3

chorus effect : 3 | 6.8

clarinet tonehole two-port junction : 10.5.4.1

classical mechanics : 13.4

clipping distortion : 10.1.6.3 | 10.1.6.4

clipping nonlinearity : 7.13.1.1

closed waveguide networks : 3.9

coefficient of inharmonicity : 7.11.4.3 | 10.4.1.3

collision detection : 10.3.3.2

comb filter : 3.6

amplitude response : 3.6.3 | 3.6.4

feedback : 3.6.2

feedforward : 3.6.1

filtered feedback : 3.6.5

lowpass feedback : 4.6.2

Schroeder-Moorer : 3.6.5 | 4.6.2

commuted waveguide synthesis : 9.7

bowed strings : 10.6.4

excitation synthesis : 10.4.4.6

piano : 10.4.4

compatible port connection : 17.2.1.1

complete response : 2.5.7.2

compliance of springs : 8.1.3

compression velocity : 8.1.3

cone wave impedance : 14.18.4

cone-cylinder intersection : 14.18.8

conformal map interpretation of damping : 4.7.4.1

conical acoustic tubes : 14.18.2

conical cap reflectance : 14.18.8.2

conical diffuser : 6.9.1

conical tube junction : 14.18.8.1

conservation of energy : 13.2.6

conservation of momentum : 13.1.1 | 13.3.1 | 13.3.1

conservative forces : 13.2

consistency of finite differences : 15.2.1

convergence of finite-difference schemes : 15.2

Coulomb force : 13.1.4

coupled strings : 7.12 | 14.13

coupled strings eigenanalysis : 14.13.2

coupling of horizontal and vertical transverse waves : 7.12.2

coupling of two ideal strings : 14.13.1

crests : 13.8.1

cubic nonlinearity : 10.1.6.4

cubic soft clipper : 7.13.1.3

cylinder with conical cap : 14.18.8

damping filter design : 7.11.1 | 7.11.2

damping, plectrum : 10.3.3.4

dashpot : 2.5.3 | 8.1.1 | 8.1.1

degree of freedom : 2.5.6.4

delay effects : 3 | 6 | 6

delay line : 3.1 | 3.1

bidirectional : 3.4

interpolation : 5.1

software : 3.1.1

tapped : 3.5

time varying : 6.1

time-varying reads : 6.7.2

delay loop expansion : 9.5.2

delay operator notation : 8.3.1.2

delay-line lengths, reverberation : 4.7.3

dependent port : 17.2.2.1

diatomic gas : 13.7.12

difference equation : 2.5.2

differential equation : 13.1.5

differentiator : 8.1.3 | 9.6.1

diffuse field : 4.2.1 | 4.3 | 4.7.3.1

diffuse reflection : 3.2.6

diffusers : 4.5

digital waveguide

mesh : 10.8.3

digital sinusoid generators : 14.17.2

digital state variable filter : 14.17.2

digital waveguide : 3.4

animation : 7.4.2

equivalent forms : 7.10.1

history : 12.9

mesh : 4.7.11.4 | see mesh

synthesis : see waveguide synthesis

digital waveguide filter : 12.6.3 | 14.9

digitization of lumped models : 8.3

digitizing systems : 2.5.2

directional derivative : 13.8.2

dispersion : 3.3.3 | 3.4

dispersion filter design : 7.11.3 | 10.4.1.3

dispersion filtering : 7.9.1

dispersion relation : 13.8.3 | 15.3

dispersive : 3.2.3

dispersive 1D wave equation : 14.6

dispersive wave propagation : 3.3.3 | 7.9

displacement waves : 10.2.1

distributed mass : 13.4

distributed parameters : 2.5.10

Doppler effect : 6.6

doubling effect : 6.2 | 6.2

driving force : 10.3.1

driving-point impedance : 4.4.2 | 8.1

dualizer : 14.16.1

duty-cycle modulation : 10.1.9

DWF : see digital waveguide filtertextbf

dynamic scattering junction : 10.3.1.6

dynamically balanced : 13.4.14.1

early reflections : 4.2.1 | 4.3

echo : 3.2.7

Echoplex : 6.7

EDC : see energy decay curvetextbf

EDR : see energy decay relieftextbf

EDR-based loop filter design : 7.11.5

eigenpolarizations : 7.12.2

elastic collision : 10.3.1

elastic solids : 13.5

electric guitars : 10.1

elliptic norm : 14.15.3

energy conservation : 13.2.6

energy conservation in volumes : 13.7.9

energy decay curve (EDC) : 4.2.2.1

energy decay relief (EDR) : 4.2.2.2

energy density : 13.7.8

energy density waves : 14.7.6

energy in a vibrating string : 14.7.8

energy of a mass : 13.2.2

energy of a mass-spring system : 13.2.5

equations of motion, rigid bodies : 13.4.20

equilibrium : 13.1.4

equivalent circuit : 2.5.10

ERB scale : 9.6.2

Euler method

backward : 8.4.3

forward : 8.4.2

semi-implicit backward : 8.4.7

Euler's equations, rotations : 13.4.20.3

evanescent wave : 14.8.2.2

even part : 7.13.1.5

excess air pressure : 10.7.1

excitation factoring : 10.4.4.5

excitation noise substitution : 9.8.5

excitation table : 10.4.4.3

exciting a string : 10.3

experimental fact : 13.1.3

explicit finite-difference scheme : 10.4.3.3 | 15.1

explicit method : 8.4.2

Extended Karplus-Strong (EKS) : 10.1.5

F0 estimation : 7.11.4

factoring excitations : 10.4.4.5

factoring resonators : 9.8

Farrow structure : 5.2.15.3 | 5.2.15.3

coefficients formula : 5.2.15.4

FDN : see feedback delay networktextbf

FDN reverberation in Faust : 4.7.9

FDTD : see finite difference time domaintextbf

feedback comb filter : 3.6.2 | 3.6.2 | 4.6.2

feedback delay network : 3.7 | 4.7

as a digital waveguide network : 4.7.8

relation to state space : 3.7.1

single input : 3.7.2

stability : 3.7.3

feedback howl : 10.1.7

feedforward comb filter : 3.6.1 | 3.6.1

filter

allpass : 3.8 | 3.9

allpass examples : 3.8.4

allpass from two combs : 3.8.1

allpass, Gerzon nested MIMO : 3.8.5

allpass, nested : 3.8.2

ladder structure

Kelly-Lochbaum section : 14.8.4

one-multiply section : 14.8.5

lattice section : 3.8.2

lossless : 3.8.3

transposition : 3.5.2

vectorized comb : 3.7

filter bank : 4.7.5.3

filter design : 9.6

differentiator : 9.6.3

dispersion filter : 10.4.1.3

invfreqz : 9.6.4

minimum phase conversion : 9.6.4.3

reading : 9.6.5

summary : 9.6.2

filtered node variables : 14.5.5.1

filtered-feedback comb filter : 3.6.5

filtering per sample : 3.3.2 | 4.7.4

finite difference approximation : 8.3.1 | 14.2 | 14.2

finite difference approximation vs. bilinear transform : 8.3.2.1

finite difference scheme

centered : 8.3.1.2 | 12.5.2 | 16.1.1

finite difference string model

frequency-dependent losses : 14.5.5.1

lossless : 14.4.3

lossy : 14.5.5

finite state machines : 2.5.6.3

finite-difference equations : 8.3

finite-difference scheme : 15 | 15.1

consistency : 15.2.1

convergence : 15.2

explicit : 15.1

FDTD and digital waveguides : 16

implicit : 15.1

passivity : 15.2.5

stability : 15.2.3

well posed initial-value problem : 15.2.2

finite-difference time-domain : 16

finite-impulse-response (FIR) filter : 3.5.4

flanger : 6.3 | 6.3.5

depth : 6.3

feedback : 6.3.4

rate : 6.3.1

regeneration : 6.3.4

speed : 6.3.1

flanging : see flangertextbf

flare constant : 10.7

flow-graph reversal theorem : 3.5.2

flute synthesis : 10.8.2

FM synthesis : 2.4.3

force : 13.1.3

force of gravity : 13.1.3

force reflectance : 10.3.1.3

force times distance : 13.2

force transmittance : 10.3.1.5 | 14.11.1.1

force wave variable : 14.7.2

force waves : 7.1.5 | 14.7.2

forced response : 2.5.7.2

formant synthesis : 9.5

forward Euler method : 8.4.2

fractional delay : 5.1.1.2

fractional delay filter : 5.1.1.2 | 5.2.1

fractional-delay filter : 5.2.2

frame of reference : 13.4.20.1

frequency shift : 6.5

friction force : 8.1.1

fundamental frequency

estimation : 7.11.4

gas

heat capacity : 13.7.13

pressure : 13.7.3

properties : 13.7

temperature : 13.7.10

gas law, ideal : 13.7.10

generalized eigenvector : 2.5.9.3

generalized scattering coefficients : 14.18.6

gradient : 13.8.2

gravitation : 13.1.3

group-delay filters : 5.3

guitar

acoustic : 10.2

bridge : 10.2.1

distortion modeling : 10.1.6

electric : 10.1

modeling : 9.7

string damping model : 10.1.2

string modeling : 7

gyration : 13.4.9

gyrator : 14.16.1 | 14.16.1

Hadamard matrix : 4.7.2.1

half-rate waveguide filter : 14.9.3

hard clipping : 10.1.6.3

heat capacity : 13.7.12

Heaviside unit step function : 5.1.3.3

Helmholtz motion : 10.6.4

Hermitian conjugate : 4.7.2.4

Hermitian transpose : 3.7.3 | 3.8.5

history of ideas : 12

Hooke's law : 13.1.4 | 13.1.5

Horner's rule : 5.2.15.3

horns : 14.18

Householder FDN feedback matrix : 4.7.2.2

Householder reflection : 4.7.2.2

Huygens-Fresnel principle : 3.2.5 | 14.18.1.2

hysteresis : 10.3.2.2

ideal bar : 13.5.1.1 | 14.6

ideal gas law : 13.7.10

ideal mass : 8.1.2

ideal spring : 8.1.3

ideal string

digital waveguide model : 14.4.1

idempotent : 13.4.12.1

ill posed PDE : 14.5.2 | 15.2.2.2 | 15.3

image method : 4.2.1

imedance of a terminated string : 7.4.3

immittance : 8.1

impedance : 8.1 | 8.1

impedance analysis : 8.2.5

implicit finite difference scheme : 15.1

implicit method : 8.4.2

impulse expanders : 4.4.2

impulse response sampling : 9.1

impulse-invariant method : 9.2

incompressible flow : 10.7.1

index of refraction : 14.8.2.1

induced norm : 3.7.3

inductor : 8.1.2

inelastic collision : 10.3.1

inertia : 13.1 | 13.1.2

inertial frame : 13.4.20.1

initial conditions : 2.5.7.2 | 13.1.5

initial state : 2.5.7.2

instantaneous nonlinearity : 7.13.1

integrator : 8.1.2

intensity, acoustic : 13.7.7

International Standard (SI) Units : 13.1.3

Internet links : 18

interpolated delay line : 5.1 | 5.2.2

interpolated table lookup : 5.1.1.2

interpolating read : 5

interpolation

allpass : 5.1.2

by differentiator filter bank : 5.2.15.5

by the Farrow structure : 5.2.15

delay and signals : 5

delay lines : 5.1

linear : 5.1.1

intrinsic momentum : 13.4.20

inverse filtering : 9.8.2.2

matlab code : 9.8.2.2

inverse square law : 3.2.5

invfreqz example : 9.6.4

inviscid : 10.7.1

isentropic : 13.7.11

isothermal : 13.7.11

JCRev : 4.5 | 4.6

jets : 13.7.6

joules : 13.2

Karplus-Strong algorithm : 10.1.4

Karplus-Strong history : 12.8

Karplus-Strong, extended : 10.1.5

Kelly-Lochbaum scattering junction : 14.8.4

kinetic energy : 2.5.6.4 | 13.2.4

of a mass : 13.2.2

of rotation : 13.4.3

of translation : 13.4.2

kinetic theory of ideal gases : 13.7.3 | 13.7.10

L2 norm : 3.7.3

ladder filter : 14.9.4 | 14.9.4

normalized : 14.9.5

ladder waveguide filter : 14.9.1

ladder, reflecting termination : 14.9.2

Lagrange interpolation : 5.2

coefficient formula : 5.2.4

coefficient symmetry : 5.2.5

differentiator bank : 5.2.15.5

equivalence to sinc interp. : 5.2.17

Farrow structure : 5.2.15.3

faust function : 5.2.8

fractional-delay filtering : 5.2.2

frequency response : 5.2.9

matlab function : 5.2.6

maxima function : 5.2.7

optimality : 5.2.3

recent developments : 5.2.16

uniform samples : 5.2.1

Laplace transform : 8.1.2

Laplacian operator : 13.8

late reverberation : 4.2.1 | 4.4

lattice filter : 14.9.4

two-multiply section : 3.8.2

law of inertia : 13.1.1

Lax-Richtmyer equivalence theorem : 15.2.4

left wing (FIR filter) : 5.4.3

Leslie block diagram : 6.7.6

Leslie effect : 6.9

lever arm : 13.4.18

leverage : 13.4.18

LFO : see low-frequency oscillatortextbf

linear interpolation : 5.1.1

resampling interpretation : 5.1.3

linear prediction : 9.6.2

loaded waveguide junction : 14.12

longitudinal attack pulse : 10.4.2

longitudinal wave : 7.12.5 | 13.6.2

in rods : 14.8.3

loop filter : see waveguide synthesis
loop filter

lossless : 14.15.3

FDN : 14.15.3

filter : 3.8.3

reverberator prototype : 4.7.2

lossy wave propagation : 3.3

low-frequency oscillator (LFO) : 6.3.1

lumped

elements : 2.5.10

model : 8

model digitization : 8.3

lumped-parameter analysis : 8

lumping distributed losses : 3.2.2

magnetic pickup : 7.10.1.2

marginally stable : 15.2.2 | 15.2.3

Mason's gain formula : 3.5.2

mass : 13.1.2

of piano hammer : 10.3.2.3

mass density : 13.4.1

mass disk : 10.4.3.1

mass moment of inertia : 13.4.4

circular disk

about center : 13.4.4.1

about diameter : 13.4.4.2

mass moment of inertia tensor : 13.4.15 | 13.4.15

mass-spring chain : 10.4.3

mass-spring oscillator, energy : 13.2.4

mass-spring-wall : 8.2.2

mass-string collision : 10.3.1

matched z transformation : 9.3 | 9.3.1

matlab

amplitude-response

extrapolation : 9.6.4.1

interpolation : 9.6.4.1

coherence function : 10.2.1.7

inverse filtering : 9.8.2.2

invfreqz example : 9.6.4

Lagrange interpolation : 5.2.6

linear regression : 9.8.1.4

minimum-phase computation : 9.6.4.3

quadratic residue sequence : 14.14.6

sinusoid generators : 14.17.9

time-aliasing check : 9.6.4.2

matrix

determinant : 13.4.12

norm : 3.7.3

matrix, triangular : 4.7.2.5

matrix-pencil method : 9.5

maxima, the symbolic math program : 5.2.7

maximally flat : 5.2.15.5

mean free path : 4.7.3.1

mechanical impedance : 8.2.5

mechanics : 13

membrane wave equation : 14.14.4

memoryless nonlinearity : 7.13.1

mesh

2D, lossy : 14.14.5

2D, rectilinear : 14.14.1

wave equation obeyed : 14.14.4

MIMO allpass filter : 3.9

minimum phase : 9.6.4.3

computation in matlab : 9.6.4.3

mixing matrix : 4.5

modal

expansion : 9.5 | 12.2

extraction techniques : 9.8.1

representation : 2.5.9

from state space : 9.5.1

modal synthesis : 2.5.9 | 9.5 | 9.8.1

mode conversion : 7.2

mode of vibration : 9.5

model : 2.2

modulated delay line : 6.5

molar mass : 13.7.10

moment arm : 13.4.18

moment of force : 13.4.18

moment of inertia : see mass moment of inertiatextbf

momentum : 13.3

angular versus linear : 13.4.13.1

linear+angular : 13.4.10

momentum of center-of-mass : 13.4.1.1

momentum of waves : 13.6.2

moving notches : 6.3

musical acoustics : 12.1

mutually prime : 4.7.3

nested allpass filter : 3.8.2

nested MIMO allpass filter : 3.8.5

Newton's laws of motion : 13.1

examples : 13.1.5

Newton's method

nonlinear minimization : 8.4.5

Newton's second law, rotational : 13.4.19

nodes : 9.5

nonlinear

distortion : 10.1.6

element : 7.13

finite differences : 8.4

length modulation : 10.1.6.2

tension modulation : 10.1.6.1

nonlinear-phase distortion : 5.1.2.1

nonlinearity

aliasing : 7.13.1.6

cubic soft clipper : 7.13.1.3

memoryless : 7.13.1

nonparametric representation : 9.1

normal mode : 9.5

normalized ladder filter : 14.9.4

normalized scattering junction : 14.8.6

normalized waveguide filter : 14.9.5

notch : 6.3

null : 3.6.3 | 6.3

numerical integration : 2.5.6.3 | 8.4

backward Euler : 8.4.3

forward Euler : 8.4.2

semi-implicit : 8.4.6

semi-implicit backward Euler : 8.4.7

semi-implicit trapezoidal : 8.4.8

trapezoidal rule : 8.4.4

odd functions : 7.13.1.5

ODE : see ordinary differential equationtextbf

Ohm's Law : 2.5.11

Ohm's law for traveling waves : 7.1.5 | 14.7.3

one ports

parallel combination : 8.2.3

passivity condition : 8.2.7

series combination : 8.2.1

one-filter scattering junction : 10.3.1.6

one-multiply scattering junction : 14.8.5

one-parameter waves : 14.18.1

one-port network : 8.2

one-to-one : 7.13.1

order of a state-space system : 3.7.1

ordinary differential equation : 2.5.3

orthogonal basis : 13.8.4

orthogonal matrix : 4.7.2.4

oscillator

algorithms : 14.17.2

mass spring : 17.3.6

wave digital : 17.3.6

waveguide : 14.17

outer disk : 14.11.2

parallel axis theorem : 13.4.6

parallel combination of one-ports : 8.2.3

parallel connection : 8.2.3 | 17.2.1

parallel second-order filter bank : 2.5.9

parametric spectrum analysis : 9.5

paraunitary matrix transfer function : 3.8.5

partial derivative : 2.5.4 | 2.5.13

partial differential equation : 8.4.10

partial fraction expansion : 2.5.9

particle velocity : 8.1 | 10.7.1 | 13.7.1

passive : 14.11

finite-difference scheme : 15.2.5

one-port : 8.2.7

reflectance : 14.11.1

string termination : 10.2.1

system properties : 14.11

PDE : see partial differential equationtextbf

percussion synthesis : 10.8.3

perpendicular axis theorem : 13.4.5

PFE : see partial fraction expansiontextbf

phantom partials : 10.4.2

phase shifter : see phasertextbf

phase velocity : 14.3.4 | 15.3

phase vocoder : 2.4.3

phaser : 6.4

allpass chain : 9.9

analog : 9.9.1.1

digital : 9.9.1.2

phasing : see phasertextbf

physical models : 2 | 2.5

physical signal model : 2.3 | 2.5

physical state : 13.1.2

physical units : 13.1.3

physics and mechanics : 13

piano

acoustics : 10.4.5

commuted synthesis : 10.4.4

longitudinal attack pulse : 10.4.2

longitudinal vibrations : 10.4.2

phantom partials : 10.4.2

string : 10.4.1

synthesis : 10.4

piano hammer

hysteresis : 10.3.2.2

mass : 10.3.2.3

models : 10.3.2

nonlinear spring : 10.3.2.1

piano string

damping filter : 10.4.1.2

nonlinear synthesis : 10.4.2.1

nonlinearities : 10.4.2

piano synthesis : 7.9 | 10.4.5

pipe organs : 10.8.2

pitch estimation : 7.11.4

plane wave : 13.8.1

plane-wave scattering

normal incidence : 14.8.1

oblique incidence : 14.8.2

plasmas : 13.7.10

plectrum

damping : 10.3.3.4

impedance : 10.3.3

model : 10.3.3

pluck control : 10.3.3.2

pluck modeling : 10.3.3 | 10.3.3.3

plucked string

digital waveguide model : 10.3.3.1

plucked string synthesis model : 7.5

point mass : 10.3.1

point source : 3.2.5

polarizations (of waves) : 7.1.2

pole mapping : 9.4

pole-zero cancellation : 5.1.2

polynomial growth : 15.2.2

polynomial interpolation : 5.2

port : 3.4.3

positive real : 10.2.1.1 | 10.2.1.8

positive real functions : 14.11.2

positive real impedance : 8.2.7

potential energy : 13.2.1 | 13.2.4

potential energy of a spring : 13.2.1

power complementary : 14.11.1.2

power reflection frequency response : 14.11.1.2

power waves : 14.7.5 | 14.7.5

power-normalized waveguide filters : 14.9.5

preemphasis : 9.8.2.1

pressure in a gas : 8.1 | 13.7.3

pressure recovery : 10.7.1 | 13.7.6

prime-power delay-line lengths : 4.7.3.3

principal axes of rotation : 13.4.16

principal direction : 13.4.16

principal moment of inertia : 13.4.16 | 13.4.16

principle of least action : 13.4

products of inertia : 13.4.16.1

quadratic convergence : 8.4.5

quadratic form : 8.4.5

quadratic residue sequence : 14.14.6

quasi-harmonic series of modes : 9.5.2

radius of gyration : 13.4.9

circular cross-section : 13.4.9.2

rectangular cross-section : 13.4.9.1

reactance : 7.4.3 | 8.1

reaction force : 10.3.1

real-time finite difference schemes : 8.4.10

recorder : 10.8.2

recording-based models : 2.4.1

rectangular pulse : 5.1.3.3

reed instruments : 10.5.1

reed modeling : 10.5.3

reference directions : 10.3.1

reflectance : 10.3.1.2 | 10.3.1.3 | 14.10.1 | 14.11.1

conical cap : 14.18.8.2

reflection

from a yielding termination : 10.2.1

sound waves : 3.2.6

reflection coefficient : 3.9.1 | 7.2 | 17.2.2.2

plane waves : 14.8.1.2

velocity waves : 17.2.4.2

reflection filter : see reflectancetextbf

reflection-free port : 17.2.2.4

refraction : 14.8.2.1

resistor : 8.1.1

resonator factoring : 9.8

resources on the Internet : 18

resultant moment : 13.4.20

reverberation : 3 | 4

delay-line damping : 4.7.4.2

desired qualities : 4.4.1

echo and mode density : 4.2.1

energy decay curve (EDC) : 4.2.2.1

energy decay relief (EDR) : 4.2.2.2

feedback delay network : 3.7 | 4.7

first-order delay filters : 4.7.5.1 | 4.7.5.2

freeverb : 4.6

mesh diffusion : 14.14.6

multiband delay filters : 4.7.5.3

perception of : 4.2

perceptual metrics : 4.2.2

Schroeder : 4.5

Schroeder allpass comb filter : 4.4.2

waveguide : 4.7.11.3

zita-rev1 : 4.7.10

reverberation time : 4.1.2

set by contracting poles : 4.7.4

vs. frequency : 4.7.5.3

reversible adiabatic process : 13.7.11

right wing (FIR filter) : 5.4.3

right-hand rule : 13.4.12

right-hand screw : 13.4.11

rigid body

dynamics : 13.4

equations of motion : 13.4.20

rigid string terminations : 7.3 | 10.2.1

root-power waves : 14.7.7

rotary inertia : 10.4.2.4

rotational dynamics : 13.4

rotational kinetic energy : 13.4.3

rotational relaxation : 13.7.15

sampling an instrument : 2.4.1

sampling synthesis : 2.4.1

scalar product : 13.4.12

scattering : 3.9.1 | 3.9.1

at impedance changes : 14.8

scattering coefficients

at conical taper-angle change : 14.18.6

scattering filter : 14.18.8.1

scattering junction : 3.9.1 | 10.3.1.6

N waveguides : 14.12

scattering theory : 3.9.1

Schroeder allpass comb filter : 3.8 | 4.4.2

waveguide interpretation : 4.4.2

Schroeder reverberators : 4.5 | 4.5.1

Schroeder-Moorer comb filter : 3.6.5 | 4.6.2 | 4.6.2

Schur function : 14.11.1 | 14.11.2.2

semi-implicit

backward Euler : 8.4.7

finite-difference : 2.5.5

numerical integration : 8.4.6

trapezoidal rule : 8.4.8

semitone : 6.5

series combination of one-ports : 8.2.1

series connection : 8.2.1 | 17.2.3

series reflection-free port : 17.2.4.4

shift operator notation : 15.2.1

short-time Fourier transform : 2.4.3

shufflers : 4.7.9

signal models : 2.2.2 | 2.4

signal scattering : 17.2

similarity transformation matrix : 2.5.9.3

similarity transformations : 2.5.7

sinc function : 5.4.1

sine cardinal : 5.4.1

singing voice synthesis : 10.8.1

sinusoid generators : 14.17.2

sinusoidal modeling : 7.9

slap-back effect : 6.2

Snell's Law : 14.8.2.1

soft clipper : 7.13.1.3 | 10.1.6.4

software : see matlabtextbf

acoustic echo simulation : 3.2.8

delay line : 3.1.1

solid of revolution : 13.4.16.1

sound examples : 19

sound speed : 13.7.14

source-filter synthesis : 9.5

space-fixed frame : 13.4.20.1 | 13.4.20.1

sparse state-space model : 3.7

spatial derivatives : 14.7.1

spatial impression : 4.3

spatial phase : 13.8.2

spatial sampling interval : 14.4

specific heat : 13.7.12

spectral modeling synthesis : 2.4.3

spectral norm : 3.7.3

spectral signal models : 2.3 | 2.4.3

specular reflection : 3.2.6

speed of sound : 13.7.14

spherical spreading loss : 3.2.5

spherical wave : 3.2.5

spring and free mass : 17.3.4

spring constant : 13.1.4

spring force : 13.1.4

spring, nonlinear : 10.3.2.1

spring-mass system : 8.2.4

square law nonlinearity : 7.13.1.7

stability margin : 9.6.2

stability of finite differences : 15.2.3

stability of nonlinear delay loops : 7.13.1.11

stability proof for a conical cap : 14.18.8.3

stable system : 15.2.2

standard model (physics) : 13.1.3

standing wave : 13.8.3

state conversions : 14.7.4

state definition : 2.5.6.4

state machines : 2.5.6.3

state of an ideal string : 14.3.6

state space model : 2.5.6

digitization : 2.5.6.3

force-driven mass : 2.5.6.2

linear : 2.5.7

outputs : 2.5.6.1

state space to modal representation : 9.5.1

state transformation, vibrating string : 14.3.6

state transition matrix : 3.7.1

state variable : 2.5.6.4

state variables : 3.7.1

state-space analysis, digital waveguide oscillator : 14.17.6

state-space model : 3.7.1

statistical mechanics : 13.7.10

statistical thermodynamics : 13.7.12

Steiglitz-McBride iterations : 9.6.2

STFT : see short-time Fourier transformtextbf

stiff string F0 estimation : 7.11.4.3

stiff string simulation : 7.9

stiff string synthesis : 7.9.1

stiffness : 13.1.4

stiffness term : 7.9

strain : 14.8.3

stretch rule for moment of inertia : 13.4.7

strictly stable : 15.2.3

string

collision with mass : 10.3.1

coupling : 7.12

dispersion filter design : 10.4.1.3

dispersive (stiff) : 10.4.1 | 14.6

dispersive wave propagation : 7.9

EDR-based loop-filter design : 7.11.5

excitation : 10.3

externally excited : 7.10

finite difference approx. : 14.2.1

frequency-dependent losses : 14.5.2

fundamental freq. estimation : 7.11.4

length modulation : 10.1.6.2

loop filter design : 7.11

modeling for synthesis : 7

moving termination : 7.4

piano : 10.4.1

pitch detection : 7.11.4

plectrum damping : 10.3.3.4

stiff : 7.9

wave equation : 13.6 | 14.1

wave momentum : 13.6.2

waveguide model : 7.1

string-mass

force-wave model : 10.3.1.5

model : 10.3.1.1

reflectance : 10.3.1.2

summary : 10.3.1.6

transmittance : 10.3.1.4

stringed instruments

body models : 10.2.2

bowed : 10.6

bridge reflectance : 10.2.1

commuted synthesis of : 9.7

coupled : 14.13

damping : 7.7

frequency-dep. damping : 7.8

guitar : 7 | 9.7

nonlinear : 10.1.6

yielding terminations : 10.2.1 | 10.2.1.1

struck string

digital waveguide model : 10.3.1.7

ideal mass : 10.3.1

impedance analysis : 10.3.1.3

synthesis model : 7.6

structured sampling : 2.1 | 2.4.2

Sturm-Liouville formulation : 14.18.1.1

susceptance : 8.1

symmetric FIR filters : 7.8

symmetric top : 13.4.16.1

synthesis, modal : see modal synthesis

synthesis, sampling : 2.4.1

synthesis, waveguide : see waveguide synthesis

tangential speed : 13.4.13.1

tapped delay line : 3.5 | 3.5 | 4.1

equiv. to parallel comb filters : 3.6.6

equiv. to series comb filters : 3.6.7

example : 3.5.1

parallel adds : 3.5.3

transposed : 3.5.2

temperature : 13.7.10

tension modulation : 10.1.6.1 | 10.1.6.1

tension of a string : 13.5.2

termination, moving : 7.4

thermal diffusion : 13.7.15

Thiran allpass interpolation : 5.3

time-domain difference operators : 8.3.1.2

Timoshenko beam theory : 10.4.2.4

tonal correction filter : 4.7.7

tonehole modeling : 10.5.4

torque : 13.4.18

total internal reflection : 14.8.2.2

transfer function

matrix : 2.5.8 | 4.1.1

models : 9

transformer, waveguide : 14.16

translational kinetic energy : 13.4.2

transmission coefficient : 3.9.1 | 7.2 | 17.2.2.2

velocity waves : 17.2.4.2

transmission filter : see transmittancetextbf

transmittance : 10.3.1.3

transposed tap : 3.4.2

transposed tapped delay line : 3.5.2

transposition of a flow graph : 3.5.2

transversal filter : 3.5.4

transverse displacement : 2.5.4

transverse waves : 7.12.1

trapezoidal rule : 8.4.4

traveling sinusoidal plane waves : 13.8.3

traveling waves : 3.2.1 | 3.2.1

damped : 3.2.2

dispersive : 3.2.3 | 3.3.3

in lumped systems : 14.10

partial derivatives : 14.3.1

plane waves : 3.3.1

wave equation solution : 14.3 | 14.3.5

tremolo : 6.5 | 10.3.3.3

triangular matrices : 4.7.2.5

tube, waveguide model : 7.2

tunneling : 14.8.2.2

two-multiplier lattice filter : 3.8.2

unit element : 17.1.7

unit-delay operator : 3.8.5

unitary frequency-response matrix : 3.8.5

unitary matrix : 4.7.2.4

feedback : 3.7

Univibe : 6.4 | 9.9.1

vector calculus : 13.4.12

vector cosine : 13.4.12.1

vector cross product : 13.4.12

vector equation of motion : 10.4.3

vector feedback comb filter : 3.7

vector product : 13.4.12

vector wavenumber : 13.8.2 | 13.8.2

velocity

particle : 13.7.1

reflection coefficient : 17.2.4.2

transmission coefficient : 17.2.4.2

volume : 13.7.2

velocity reflectance : 10.3.1.3

velocity reflection transfer function : 10.3.1.2

vibrating string : see string

vibration relaxation : 13.7.15

vibrato simulation : 6.5

virtual analog : 8.4.10 | 9.1 | 9.9.1.2

virtual displacement : 13.2.3

virtual musical instrument : 2 | 10

virtual work : 13.2.3 | 13.2.3

viscosity : 13.7.15

voice modeling history : 12.6.3

voice synthesis : 10.8.1

voltage divider : 8.2.5

voltage source : 2.5.10

voltage transfer interconnections : 3.4.3

volume velocity : 8.1 | 13.7.2

von Neumann analysis : 15.4

wave digital

model examples : 17.3

element : 17.1

filter : 17

mass : 17.3.1 | 17.3.4

mass-spring oscillator : 17.3.6

physical derivation : 17.1.1

spring : 17.3.4

wave digital filter : 17

alpha parameters : 14.12 | 17.2.2.1

beta parameters : 17.2.4.1

wave equation : 14.1

2D : 13.8.3 | 14.14.4

2D boundary conditions : 13.8.4

applications : 7.1.2

damped string : 14.5

in air : 13.8

piano string : 10.4.1.1

vibrating string : 7.1.1 | 13.6

wave momentum : 13.6.2

zero stiffness : 13.6.1

wave impedance : 7.1.5 | 7.1.5 | 8.1 | 14.7.3

arbitrary bore shapes : 14.18.5

cone : 14.18.4

wave momentum : 13.6.2

wave variables : 14.7 | 17.1

wave velocity : 14.3.4

waveform dispersion : 3.3.3

waveguide

collocated input/output : 3.4.3

cone-cylinder intersection : 14.18.8

conical : 14.18.2

conical cap reflectance : 14.18.8.2

conical cap reflectance stability : 14.18.8.3

conical wave impedance : 14.18.4

definition : 3.4

dispersive : 14.6

equivalence to FDTD scheme : 16

generalized impedance : 14.18.6

generalized scattering coefficients : 14.18.7

momentum conservation : 14.18.3

network : 3.9.2

nonuniform : 14.18 | 14.18.5

physical inputs : 3.4.2

physical outputs : 3.4.1

scattering : 3.9.1

scattering filter : 14.18.8.1

waveguide filter : 14.9

conventional ladder : 14.9.4

half-rate structure : 14.9.3

ladder structure : 14.9.1

normalized : 14.9.5

reflective termination : 14.9.2

waveguide junction

loaded : 14.12

N waveguides : 14.12

waveguide mesh : 4.7.11.4 | 14.14 | see mesh

waveguide mesh applications : 10.8.3

waveguide model

bowed strings : 10.6

ideal string : 14.4.1

reed instruments : 10.5.1

waveguide network : 3.9.2

FDN equivalence : 14.15

waveguide oscillator : 14.17 | 14.17

state-space analysis : 14.17.6

waveguide reverb : 4.7.11.3

waveguide synthesis

acoustic strings : 9.7

amplifier feedback simulation : 10.1.7

bowed strings : 10.6

brightness and sustain : 10.1.2

commuted : 9.7

commuted bowed strings : 10.6.4

damping filter design : 7.11.2

dispersion filter design : 7.11.3

distorted strings : 10.1.6

FIR(3) loop filter : 10.1.1

general bore shapes : 14.18

guitar body : 9.8

guitar bridge reflectance : 10.2.1

isolating resonant modes : 9.8.1

loop filter

one-zero : 10.1.3

three-tap : 10.1.1

loop filter design : 7.11.1

piano : 10.4

software : see softwaretextbf

waveguide theory : 14

waveguide transformer : 14.16

waves

longitudinal : 7.12.5

transverse : 13.6 | 14.1

WDF : see wave digital filtertextbf

Webster's horn equation : 14.18.2

wedge product : 13.4.14.1

well posed initial-value problem : 15.2.2

well posed PDE : 15.2.2.1

windowed sinc interpolation : 5.4

work : 13.2

yielding string terminations : 10.2.1

Young's modulus : 13.5.1

zita-rev1 reverberator : 4.7.10

Sign in