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Index


acceleration due to gravity : 15.1.4
acoustic echo simulation : 2.2.6
acoustic kinetic energy density : 15.20
acoustic potential energy density : 15.20
acoustical ohms : 17.7.3
acoustics : 15
adaptor
series, reflection free : 24.2.4.4
two-port parallel : 24.2.1
unit element : 24.1.7
admittance : 20.1
aerofoil : 15.17
air absorption : 3.1.1
frequency-dependent : 2.3.1
frequency-independent : 2.3.1
air pressure : 15.15
airfoil : 15.17
aliasing : 28.1.5
aliasing due to nonlinearity : 28.1.5
allpass comb filter : 2.8.1
allpass condition
equivalence to losslessness : 2.8.3
allpass filter : 2.8.1
examples : 2.8.4
general case : 2.8.3
Gerzon nested MIMO : 2.8.5
nested : 2.8.2 | 3.4.3
allpass phase shifter : 4.4.3
second-order case : 4.4.4
alpha parameters : 24.2.2.1
amplification factor : 22.4
amplifier cabinet filter : 5.13
amplitude complementary : 7.1.1
amplitude envelopes : 5.10.1
arctangent nonlinearity : 28.1.2
artificial reverberation : see reverberation
bending angle : 5.8
Bernoulli equation : 9.1
beta parameters : 24.2.4.1
bidirectional delay line : 2.4
Bode plot : 4.4.3.1
body factoring
by sinusoidal modeling : 27.1.4
body-resonator factoring : 27
bowed strings : 8
linear commuted synthesis of : 8.4
brass instruments : 9
break frequency : 4.4.3.1 | 4.4.3.1
capacitor : 20.1.3
cardinal sine : 19.3.1
causal : 2.5.4 | 2.8.3
center of mass : 15.1.2
centered finite difference approximations : 23.1.1
centroid : 15.1.2
chain rule : 17.3.2 | 17.3.2
characteristic impedance : 17.7.3 | 20.1 | see wave impedancetextbf
characteristic polynomial equation : 22.2.2.1
chorus effect : 2 | 4.4.8
citations by topic : 31
clarinet tonehole as a two-port junction : 7.2.1
clipping : 28.1.1
clipping function : 5.12
hard : 5.12
soft : 5.12
clipping nonlinearity : 28.1.1
closed waveguide networks : 2.9
coefficient of inharmonicity : 5.10.4.3 | 6.2.1
comb filter
amplitude response, feedback case : 2.6.4
amplitude response, feedforward case : 2.6.3
feedback : 2.6.2
feedforward : 2.6.1
commuted piano synthesis : 6
commuted synthesis : 5.14 | 6
piano : 6
compatible port connection : 24.2.1.1
compliance : 20.1.3
compression velocity : 20.1.3
computational physical model : 2.6.1
conservation of energy : 15.5.1
conservation of momentum : 15.1.1 | 15.7
conservative forces : 15.2
consistency of finite differences : 22.2.1
Coulomb force : 15.1.4
coupled strings eigenanalysis : 17.11.2
coupling of horizontal and vertical transverse waves : 5.11.2
coupling of two ideal strings : 17.11.1
cubic nonlinearity : 5.12
cubic soft clipper : 28.1.3
damping filter design : 5.10.1 | 5.10.2
dashpot : 20.1.1 | 20.1.1
debugging software in gdb : 12
delay effects : 2 | 4 | 4.4
delay line : 2.1
bidirectional : 2.4
interpolation, high order : 19
software : 2.1.1
tapped : 2.5
time-varying reads : 4.4.7.2
delay operator notation : 20.3
dependent port : 24.2.2.1
differential equation : 15.1.5
differentiator : 20.1.3
diffuse field : 3.6.3.1
diffuse reflection : 2.2.5
diffusers : 3.5
digital waveguide : see waveguide
digital waveguide mesh : 3.6.8.5 | see mesh
digital waveguide model : see waveguide synthesis
digital waveguide models
equivalent forms : 5.9.1
dispersion : 2.3.2 | 2.4
dispersion filter design : 5.10.3 | 6.2.1
dispersion filtering : 5.8.1
dispersion relation : 22.3
dispersive wave propagation : 2.3.2 | 5.8
displacement waves : 21.2
Doppler effect : 4.4.6
Doppler shift : 4.4.6
doubling effect : 4.4.11.1
driving-point impedance : 3.4.2
early reflections : 3.2.1
echo : 2.2.6
eigenpolarizations : 5.11.2
elliptic norm : 17.13.3
energy conservation : 15.5.1
energy decay curve (EDC) : 3.2.2.1
energy decay relief (EDR) : 3.2.2.2
energy density : 15.20
energy density waves : 17.7.6
energy in a vibrating string : 17.7.8
energy of a mass : 15.3.1
equilibrium : 15.1.4
even part : 28.1.4.1
excess air pressure : 9.1
experimental fact : 15.1.3
explicit finite difference scheme : 22.1
Extended Karplus-Strong algorithm : 5.7.5
F0 : 5.10.4
F0 estimation : 5.10.4
Farrow structure : 19.1.6
feedback comb filter : 2.6.2 | 2.6.2
feedback delay network
as a digital waveguide network : 3.6.7
relation to state space description : 2.7.1
single input : 2.7.2
stability : 2.7.3
feedback howl : 5.13
feedforward comb filter : 2.6.1 | 2.6.1
filter
allpass : 2.8 | 2.9
allpass examples : 2.8.4
allpass from two combs : 2.8.1
allpass, Gerzon nested MIMO : 2.8.5
allpass, nested : 2.8.2
ladder structure
Kelly-Lochbaum section : 17.8.1
one-multiply section : 17.8.2
lattice section : 2.8.2
lossless : 2.8.3
transposition : 2.5.2
vectorized comb : 2.7
filter design : 26.4
dispersion filter : 6.2.1
filtered node variables : 17.5.5.1
filtering per sample : 2.3.1 | 3.6.4
finite difference approximation : 17.2
finite difference scheme
consistency : 22.2.1
convergence : 22.2
explicit : 22.1
implicit : 22.1
passivity : 22.2.5
stability : 22.2.3
well posed initial-value problem : 22.2.2
finite difference schemes : 22
finite difference string model
frequency-dependent losses : 17.5.5.1
lossless : 17.4.3
lossy : 17.5.5
finite difference time domain scheme : 23
finite-difference time-domain : 17.5.5
finite-impulse-response filter : 2.5.4
FIR filter : 2.5.4 | 2.5.4
flanger : 4.4.1 | 4.4.1.5
depth : 4.4.1
feedback : 4.4.1.4
rate : 4.4.1.1
regeneration : 4.4.1.4
speed : 4.4.1.1
flangers : 2.6.3
flanging : 2
flare constant : 9
flow-graph reversal theorem : 2.5.2
force : 15.1.3
force of gravity : 15.1.3
force times distance : 15.2
force wave variable : 17.7.2
force waves : 5.1.5 | 17.7.2
frequency shift : 4.4.5
friction force : 20.1.1
function inverse : 28.1
fundamental frequency estimation : 5.10.4
gas pressure : 15.15
gravitation : 15.1.3
gravitation constant : 15.1.3
Hadamard matrix : 3.6.1
hard clipper : 5.12
Heaviside unit step function : 19.5.2.1
Hermitian conjugate : 3.6.2.2
Hermitian transpose : 2.8.5
history of ideas : 14
Hooke's law : 15.1.4 | 15.1.5
horizontal and vertical transverse waves : 5.11.1
Householder feedback matrix for FDNs : 3.6.2.1
Householder reflection : 3.6.2.1
Huygens' principle : 2.2.4
ideal bar : 15.9 | 17.6
ideal mass : 20.1.2
ideal spring : 20.1.3
ideal string
digital waveguide model : 17.4.1
ill posed PDE : 17.5.2 | 22.2.2.2 | 22.3
image method : 3.2.1
immittance : 20.1
impedance : 20.1
implicit finite difference scheme : 22.1
impulse expanders : 3.4.2
impulse invariant method : 26.2
incompressible flow : 9.1
inductor : 20.1.2
inertia : 15.1 | 15.1.2
initial conditions : 15.1.5
instantaneous nonlinearity : 28.1
integrator : 20.1.2
intensity, acoustic : 15.19
International Standard Units (``SI units'') : 15.1.3
interpolated delay line : 4.2
interpolation
allpass : 4.2.2
by filter bank of differentiators : 19.1.6
for delay lines : 4.2
linear : 4.2.1
inverse filtering : 27.2.2
inverse filtering matlab code : 27.2.2
inverse square law : 2.2.4
inviscid : 9.1
JCRev : 3.5
jets : 15.18
Joules : 15.2
Karplus-Strong algorithm : 5.7.4
Karplus-Strong, extended : 5.7.5
Kelly-Lochbaum scattering junction : 17.8.1
kinetic energy : 15.4
kinetic energy of a mass : 15.3.1
kinetic theory of ideal gases : 15.15
L2 norm : 2.7.3
Lagrange interpolation
equivalence to since interpolation : 19.1.1
optimality : 19.1.2
Lagrange interpolation, explicit coefficient formula : 19.1.3
Laplace transform : 20.1.2
late reverberation : 3.2.1
lattice filter
two-multiply section : 2.8.2
law of inertia : 15.1.1
Lax-Richtmyer equivalence theorem : 22.2.4
Legendre sequence : 17.12.6
Leslie effect : 4.4.9
linear interpolation : 4.2.1
analysis : 19.5
longitudinal wave : 16.2
longitudinal waves : 5.11.5
loop filter : see waveguide synthesisloop filter
lossless : 17.13.3
lossless filter : 2.8.3
lossless prototype : 3.6.2
losslessness of FDNs : 17.13.3
low-frequency oscillator (LFO) : 4.4.1.1
lumped models : 20
lumped-parameter analysis : 20
lumping distributed losses : 2.2.2
marginally stable : 22.2.2 | 22.2.3
Mason's gain formula : 2.5.2
mass : 15.1.2
matrix, triangular : 3.6.2.3
maximally flat : 19.1.6
mean free path : 3.6.3.1
mechanics : 15
memoryless nonlinearity : 28.1
mesh
2D rectilinear : 17.12.1
2D, lossy : 17.12.5
wave equation obeyed : 17.12.4
MIMO allpass filter : 2.9
mixing matrix : 3.5
modal synthesis : 27.1
modulated delay line : 4.4.5
moment of inertia : 15.11
moving notches : 4.4.1
mutually prime : 3.6.3
nested allpass filters : 2.8.2
nested MIMO allpass filter : 2.8.5
Newton's laws of motion, examples : 15.1.5
nonlinear element : 28
nonlinear phase distortion : 4.2.2.1
nonlinearity
aliasing : 28.1.5
cubic soft clipper : 28.1.3
nonparametric representation : 26.2
nonparametric resonator factoring : 27
normalized scattering junction : 17.8.3
normalized waveguide filter : 18.4
notch : 4.4.1
null : 4.4.1
nulls : 2.6.3
odd functions : 28.1.4.1
Ohm's law for traveling waves : 5.1.5 | 17.7.3
one ports
parallel combination : 20.2.2
passivity condition : 20.2.4
series combination : 20.2.1
one-multiply scattering junction : 17.8.2
one-to-one : 28.1
order of a state-space system : 2.7.1
orthogonal matrix : 3.6.2.2
outer disk : 21.4
parallel axis theorem : 15.11.1
parallel combination of one-ports : 20.2.2
parallel connection : 24.2.1
paraunitary matrix transfer function : 2.8.5
paraunitary matrix transfer functions : 2.8.5
particle velocity : 9.1 | 20.1
passive finite difference scheme : 22.2.5
passive one-ports : 20.2.4
passive string terminations : 21.2
passive system properties : 21
phase shifter : 4.4.3
analog : 4.4.3.1
digital : 4.4.3.2
phase shifter, phaser : 4.4.2
phase velocity : 17.3.3 | 22.3
phaser : 4.4.2 | 4.4.3
phasing : 2 | 4.4.2
physical state : 15.1.2
physical units : 15.1.3
physics and mechanics : 15
piano
commuted synthesis : 6.3
piano modeling : 6
piano synthesis : 5.8
pitch estimation : 5.10.4
point source : 2.2.4
polarizations : 5.1.2
pole-zero cancellation : 4.2.2
polynomial growth : 22.2.2
polynomial interpolation : 19.1
positive real : 21.2 | 21.3.1
positive real impedance : 20.2.4
potential energy : 15.3 | 15.4
power waves : 17.7.5 | 17.7.5
preemphasis : 27.2.1
pressure in a gas : 20.1
pressure recovery : 9.1 | 15.18
quadratic residue sequence : 17.12.6
radius of gyration
circular cross-section : 15.12.2
rectangular cross-section : 15.12.1
reactance : 20.1
rectangular pulse : 19.5.2.1
reed modeling : 7.1.3
reflectance : 21.2.1
reflection
from a yielding termination : 21.2
sound waves : 2.2.5
reflection transfer function : 21.2.1
reflection coefficient : 2.9.1 | 20.6.1 | 24.2.2.2
velocity waves : 24.2.4.2
reflection free port : 24.2.2.4
reflection transfer function : 21.1 | 21.2.1
reflection-free port : 24.2.2.4
resistor : 20.1.1
resonator factoring : 27
resources on the Internet : 29
reverberation : 2 | 3
allpass : 3.4.2 | see allpass filters
desired qualities : 3.4.1
energy decay curve (EDC) : 3.2.2.1
energy decay relief (EDR) : 3.2.2.2
feedback delay network : 2.7 | 3.6
first-order delay filters : 3.6.5.1
mesh diffusion : 17.12.6
perception of echo and mode density : 3.2.1
perceptual metrics : 3.2.2
Schroeder : 3.4.2
waveguide : 3.6.8.4
rigid string terminations : 21.2
root-power waves : 17.7.7
scattering : 2.9.1 | 2.9.1
scattering junction : 2.9.1
N waveguides : 17.10
scattering theory : 2.9.1
Schroeder allpass : 2.8
waveguide interpretation : 3.4.2
Schroeder reverberator : 3.4.2
Schur function : 21.4.2
semitone : 4.4.5
series combination of one-ports : 20.2.1
series connection : 24.2.3
series reflection-free port : 24.2.4.4
shift operator notation : 22.2.1
signal scattering : 24.2
simulation diagram : 20.2.5
sinc function : 19.3.1
sine cardinal : 19.3.1
sinusoidal modeling : 5.8
slap back : 4.4.11.2
soft clipper : 5.12 | 28.1.3
software : 13
C++
acoustic echo simulation : 2.2.7
plucked string (simple) : 13.1
delay line : 2.1.1
sound examples : 30
sound speed : 15.21
sparse state space model : 2.7
spatial derivatives : 17.7.1
spatial impression : 3.3
spatial sampling interval : 17.4
specular reflection : 2.2.5
spherical spreading loss : 2.2.4
spherical wave : 2.2.4
spring and free mass : 24.3.4
spring constant : 15.1.4
spring force : 15.1.4
square law nonlinearity : 28.1.5.1
stability of a finite difference scheme : 22.2.3 | 22.2.3
stable system : 22.2.2
Standard Model : 15.1.3
standard temperature and pressure : 15.21
state conversions : 17.7.4
state of an ideal string : 17.3.5
state transformation, vibrating string : 17.3.5
state transition matrix : 2.7.1
state variables : 2.7.1
state-space description : 2.7.1
stiff string F0 estimation : 5.10.4.3
stiff string synthesis : 5.8.1
stiffness : 15.1.4
stiffness term : 5.8
STK introduction : 11
strain : 17.8
strictly stable : 22.2.3
string
dispersion filter design : 6.2.1
dispersive (stiff) : 6.2 | 17.6
dispersive wave propagation : 5.8
finite difference approximation : 17.2.1
frequency-dependent losses : 17.5.2
fundamental frequency estimation : 5.10.4
modeling for synthesis : 5
piano : 6.2
pitch detection : 5.10.4
stiff : 5.8
wave equation : 16
wave momentum : 16.2
stringed instruments
bowed : 8
bridge reflectance : 21.2.1
commuted synthesis of : 5.14
coupled : 17.11
frequency-dependent damping : 5.7
guitar : 5.14
guitars : 5
nonlinear : 5.12
susceptance : 20.1
symmetric FIR filters : 5.7
synthesis : see waveguide synthesis
tap : 2.5
tapped delay line : 2.5
equivalence to parallel comb filters : 2.6.5
equivalence to series comb filters : 2.6.6
example : 2.5.1
tapped delay line FIR filter : 3.1
tapped delay line, parallel adds : 2.5.3
tapped delay line, transposed : 2.5.2
time domain finite difference scheme : 22
time-domain difference operators : 20.3
tonal correction filter : 3.6.6
transfer function models : 26
transfer-function matrix : 3.1.1
transmission coefficient : 2.9.1 | 24.2.2.2
velocity waves : 24.2.4.2
transposed tapped delay line : 2.5.2
transposition of a flow graph : 2.5.2
transversal filter : 2.5.4
transverse waves on a string : 5.11.1
traveling wave solution of the wave equation : 17.3.4
traveling waves : 2.2.1 | 2.2.1
damped : 2.2.2
dispersive : 2.3.2
lumped interpretation : 20.6.2
plane waves : 2.3.1
traveling-wave partial derivatives : 17.3.1
tremolo : 4.4.5
triangular matrices : 3.6.2.3
two-multiplier lattice filter : 2.8.2
unit element : 24.1.7
unit-delay operator : 2.8.5
unitary matrix : 3.6.2.2
unitary matrix feedback : 2.7
unitary matrix frequency response : 2.8.5
vector feedback comb filter : 2.7
velocity
particle : 15.13
reflection coefficient : 24.2.4.2
transmission coefficient : 24.2.4.2
volume : 15.14
vibrating string : see string
vibrato simulation : 4.4.5
virtual analog : 4.4.3.2
virtual displacement : 15.3.1
virtual work : 15.3.1
volume velocity : 15.14 | 20.1
wave digital
mass-spring oscillator : 24.3.6
wave digital elements
physical derivation : 24.1.1
wave digital filter : 24
wave digital mass : 24.3.1 | 24.3.4
wave digital spring : 24.3.4
wave equation : 17.1
applications : 5.1.2
vibrating string : 5.1.1 | 16
wave impedance : 5.1.5 | 17.7.3 | 20.1
wave variables : 24.1
wave velocity : 17.3.3
waveform dispersion : 2.3.2
waveguide
definition : 2.4
dispersive : 17.6
equivalence to FDTD scheme : 23
network : 2.9.2
physical outputs : 2.4.1
scattering : 2.9.1
waveguide filter : 18
conventional ladder : 18.3
half-rate structure : 18.2
ladder structure : 18.1
normalized : 18.4
waveguide junction, N waveguides : 17.10
waveguide mesh : 3.6.8.5 | see mesh
waveguide model
ideal string : 17.4.1
waveguide network : 2.9.2
waveguide oscillator : 25 | 25
state-space analysis : 25.6
waveguide reverb : 3.6.8.4
waveguide synthesis
acoustic strings : 5.14
amplifier feedback simulation : 5.13
bowed strings : 8
brightness and sustain parameters : 5.7.2
commuted : 5.14
commuted bowed strings : 8.4
damping filter design : 5.10.2
dispersion filter design : 5.10.3
distorted strings : 5.12
Extended Karplus-Strong algorithm : 5.7.5
FIR(3) loop filter : 5.7.1
guitar body : 27
guitar bridge reflectance : 21.2.1
isolating resonant modes : 27.1
Karplus-Strong algorithm : 5.7.4
loop filter
one-zero : 5.7.3
three-tap : 5.7.1
loop filter design design : 5.10.1
software : see softwaretextbf
waveguide theory : 17
waves
longitudinal : 5.11.5
transverse : 16 | 17.1
well posed initial-value problem : 22.2.2 | 22.2.2
well posed PDE : 22.2.2.1
windowed sinc interpolation : 19.3
work : 15.2 | 15.5
yielding string terminations : 21.2


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[How to cite and copy this work] 
``Physical Audio Signal Processing for Virtual Musical Instruments and Digital Audio Effects'', by Julius O. Smith III, (December 2005 Edition).
Copyright © 2006-07-01 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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