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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
ambisonics : 13.8.6
order : 13.8.6
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
dipole term : 13.8.6
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
lateral quadrupoles : 13.8.6
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 quadrupoles : 13.8.6
longitudinal wave : 7.12.5 | 13.6.2
in rods : 14.8.3
loop filter : see waveguide synthesisloop 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
monopole term : 13.8.6
moving notches : 6.3
multipole expansion : 13.8.6
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
quadrupoles : 13.8.6
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
spherical-harmonic expansion : 13.8.6
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


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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4.
Copyright © 2014-03-23 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA