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

---

Previous: Bibliography
Next: Book Series Overview

Order a Hardcopy of Physical Audio Signal Processing

---

About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.