Index

3D sound : 15.5.6

C++ debugging in gdb : 12.7

acceleration due to gravity : 15.1.4

acoustic echo simulation : 2.2.6

acoustic energy density : 15.5.11

acoustic intensity : 15.5.10

acoustic kinetic energy density : 15.5.11

acoustic potential energy density : 15.5.11

acoustic wave simulation : 2.2

acoustical ohms : 17.7.3

acoustics : 15

adaptor : 26.2

series, reflection free : 26.2.4.4

two-port parallel : 26.2.1

unit element : 26.1.7

admittance : 21.1

aerofoil : 15.5.8

air absorption : 3.1.1 | 15.5.14

frequency-dependent : 2.3.1

frequency-independent : 2.3.1

air jets : 15.5.9

air pressure : 15.5.3

airfoil : 15.5.8

aliasing : 29.1.5

aliasing due to nonlinearity : 29.1.5

allpass comb filter : 2.8.1

allpass condition

equivalence to losslessness : 2.8.3

allpass filter : 2.8 | 2.8.1

examples : 2.8.4

general case : 2.8.3

Gerzon nested MIMO : 2.8.5

maximally flat group delay : 20.2

nested : 2.8.2 | 3.4.3

Thiran : 20.2

waveguide : 2.9

allpass phase shifter : 24.2.1

second-order case : 24.2.2

alpha parameters : 26.2.2.1

amplification factor : 23.4

amplifier cabinet filter : 5.14

amplifier feedback simulation : 5.14

amplitude complementary : 7.1.1

amplitude envelopes : 5.11.1

arctangent nonlinearity : 29.1.2

area moment of inertia : 15.4.4

artificial reverberation : see reverberation

bandlimited interpolation : 20.3

bell models : 9.2

bending angle : 5.8

Bernoulli effect : 15.5.8

Bernoulli equation : 9.1 | 15.5.7

Bessel filter : 20.2

beta parameters : 26.2.4.1

bidirectional delay line : 2.4

bilinear transform : 21.4

Bode plot : 24.2.1.1

body factoring

by sinusoidal modeling : 28.1.4

body factoring example : 28.6

body-resonator factoring : 28

bowed strings : 8

bow-string junction : 8.2

linear commuted synthesis of : 8.4

brass instruments : 9

brass mouthpiece : 9.1

break frequency : 24.2.1.1 | 24.2.1.1

capacitor : 21.1.3

cardinal sine : 20.3.1

causal : 2.5.4 | 2.8.3

center of mass : 15.1.2

centered finite difference approximations : 25.1.1

centroid : 15.1.2

chain rule : 17.3.2 | 17.3.2

characteristic impedance : 17.7.3 | 21.1 | see wave impedancetextbf

characteristic polynomial equation : 23.2.2.1 | 23.3

chorus effect : 2 | 4.4.6

citations by topic : 32

clarinet tonehole as a two-port junction : 7.2.1

clipping : 29.1.1

clipping function : 5.13

hard : 5.13

soft : 5.13

clipping nonlinearity : 29.1.1

closed waveguide networks : 2.9

coefficient of inharmonicity : 5.11.4.3 | 6.2.2

comb filter : 2.6

amplitude response, feedback case : 2.6.4

amplitude response, feedforward case : 2.6.3

feedback : 2.6.2

feedforward : 2.6.1

filtered feedback : 2.6.5

lowpass feedback : 3.6.2

Moorer : 3.6.2

commuted piano synthesis : 6 | 6.3

commuted synthesis : 5.15 | 6

piano : 6

commuted waveguide synthesis

bowed strings : 8.4

compatible port connection : 26.2.1.1

compiling from emacs : 11.5

compliance : 21.1.3

compression velocity : 21.1.3

computational physical model : 2.6.1

cone-cylinder intersection : 17.14.3

conical acoustic tubes : 17.14.2

conical cap reflectance : 17.14.3.2

conical tube junction : 17.14.3.1

conservation of energy : 15.2.5

conservation of momentum : 15.1.1 | 15.3.1

conservative forces : 15.2

consistency of finite differences : 23.2.1

convergence of finite difference schemes : 23.2

Coulomb force : 15.1.4

coupled strings : 5.12 | 17.11

coupled strings eigenanalysis : 17.11.2

coupling of horizontal and vertical transverse waves : 5.12.2

coupling of two ideal strings : 17.11.1

crests : 15.5.4

cubic nonlinearity : 5.13

cubic soft clipper : 29.1.3

cylinder with conical cap : 17.14.3

daemon : 12.6.1

damping filter design : 5.11.1 | 5.11.2

dashpot : 21.1.1 | 21.1.1

debugging software in gdb : 12

delay effects : 2 | 4 | 4.4

delay line : 2.1 | 2.1

bidirectional : 2.4

interpolation : 4.2

interpolation, high order : 20

software : 2.1.1

tapped : 2.5

time varying : 4.1

time-varying reads : 4.4.5.2

delay lines, time-varying applications : 4.4

delay operator notation : 21.3

dependent port : 26.2.2.1

differential equation : 15.1.5

differentiator : 21.1.3

diffuse field : 3.7.3.1

diffuse reflection : 2.2.5

diffusers : 3.5

digital state variable filter : 19.2

digital waveguide : 2.4 | see waveguide

animation : 5.3.2

digital waveguide mesh : 3.7.8.5 | see mesh

digital waveguide model : see waveguide synthesis

digital waveguide models

equivalent forms : 5.9.1

directional derivative : 15.5.5

dispersion : 2.3.2 | 2.4

dispersion filter design : 5.11.3 | 6.2.2

dispersion filtering : 5.8.1

dispersion relation : 23.3

dispersive 1D wave equation : 17.6

dispersive wave propagation : 2.3.2 | 5.8

displacement waves : 22.2

Doppler effect : 4.4.4

Doppler shift : 4.4.4

doubling effect : 4.4.9.1

driving point impedance : 21.1

driving-point impedance : 3.4.2

DSSI plugin : 12.6.1

DSSI/LADSPA plugin debugging : 12.6

dynamic scattering junction : 5.10.2

early reflections : 3.2.1 | 3.3

echo : 2.2.6

Echoplex : 4.4.5

EDR-based loop filter design : 5.11.5

eigenpolarizations : 5.12.2

elastic collision : 5.10

elastic solids : 15.4

elliptic norm : 17.13.3

energy conservation : 15.2.5

energy conservation in volumes : 15.5.12

energy decay curve (EDC) : 3.2.2.1

energy decay relief (EDR) : 3.2.2.2

energy density : 15.5.11

energy density waves : 17.7.6

energy in a vibrating string : 17.7.8

energy of a mass : 15.2.2

energy of a mass-spring system : 15.2.4

equilibrium : 15.1.4

evanescent : 17.8.2.2

evanescent wave : 17.8.2.2

even part : 29.1.4.1

example .gdbinit file : 12.1

excess air pressure : 9.1

excitation noise substitution : 28.5

experimental fact : 15.1.3

explicit finite difference scheme : 23.1

Extended Karplus-Strong algorithm : 5.7.5

F0 : 5.11.4

F0 estimation : 5.11.4

Farrow structure : 20.1.7

feedback comb filter : 2.6.2 | 2.6.2 | 3.6.2

feedback delay network : 2.7 | 3.7

as a digital waveguide network : 3.7.7

relation to state space description : 2.7.1

single input : 2.7.2

stability : 2.7.3

feedback howl : 5.14

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 : 17.8.4

one-multiply section : 17.8.5

lattice section : 2.8.2

lossless : 2.8.3

transposition : 2.5.2

vectorized comb : 2.7

filter design : 27.4

dispersion filter : 6.2.2

filtered feedback comb filter : 2.6.5

filtered node variables : 17.5.5.1

filtered-feedback comb filter : 2.6.5

filtering per sample : 2.3.1 | 3.7.4

finite difference approximation : 17.2 | 17.2 | 21.3

finite difference scheme

consistency : 23.2.1

convergence : 23.2

explicit : 23.1

implicit : 23.1

passivity : 23.2.5

stability : 23.2.3

well posed initial-value problem : 23.2.2

finite difference schemes : 23

finite difference string model

frequency-dependent losses : 17.5.5.1

lossless : 17.4.3

lossy : 17.5.5

finite difference time domain scheme : 25

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 reflectance : 5.10.2

force times distance : 15.2

force transmittance : 5.10.2

force wave variable : 17.7.2

force waves : 5.1.5 | 17.7.2

frequency shift : 4.4.3

friction force : 21.1.1

function inverse : 29.1

fundamental frequency

estimation : 5.11.4

gas pressure : 15.5.3

gases : 15.5

gdb debugging : 12.2

gdb in emacs : 12.4

generalized scattering coefficients : 17.14.2.2

gradient : 15.5.5

gravitation : 15.1.3

gravitation constant : 15.1.3

group-delay filters : 20.2

guitar bridge : 22.3

guitar modeling : 5.15

gyration : 15.4.5

Hadamard matrix : 3.7.1

half-rate waveguide filter : 18.2

hard clipper : 5.13

Heaviside unit step function : 20.5.2.1

Hermitian conjugate : 3.7.2.2

Hermitian transpose : 2.7.3 | 2.8.5

history of ideas : 14

Hooke's law : 15.1.4 | 15.1.5

horizontal & vertical transverse waves : 5.12.1

horns : 17.14

Householder feedback matrix, FDNs : 3.7.2.1

Householder reflection : 3.7.2.1

Huygens' principle : 2.2.4

Huygens-Fresnel principle : 17.14.1

ideal bar : 15.4.1.1 | 17.6

ideal mass : 21.1.2

ideal spring : 21.1.3

ideal string

digital waveguide model : 17.4.1

ill posed PDE : 17.5.2 | 23.2.2.2 | 23.3

image method : 3.2.1

immittance : 21.1

impedance : 21.1 | 21.1

impedance analysis : 21.2.3

implicit finite difference scheme : 23.1

impulse expanders : 3.4.2

impulse response sampling : 27.2

impulse-invariant method : 27.2.1

incompressible flow : 9.1

index of refraction : 17.8.2.1

induced norm : 2.7.3

inductor : 21.1.2

inelastic collision : 5.10

inertia : 15.1 | 15.1.2

initial conditions : 15.1.5

instantaneous nonlinearity : 29.1

integrator : 21.1.2

intensity, acoustic : 15.5.10

International Standard Units (``SI units'') : 15.1.3

interpolated delay line : 4.2

interpolation

allpass : 4.2.2

by filter bank of differentiators : 20.1.7

for delay lines : 4.2

linear : 4.2.1

inverse filtering : 28.2.2

inverse filtering matlab code : 28.2.2

inverse square law : 2.2.4

inviscid : 9.1

JCRev : 3.5 | 3.6

jets : 15.5.9

Joules : 15.2

Karplus-Strong algorithm : 5.7.4

Karplus-Strong history : 14.8

Karplus-Strong, extended : 5.7.5

Kelly-Lochbaum scattering junction : 17.8.4

kinetic energy : 15.2.3

kinetic energy of a mass : 15.2.2

kinetic theory of ideal gases : 15.5.3

L2 norm : 2.7.3

ladder filter : 18.3

ladder waveguide filters : 18.1

LADSPA plugin : 12.6.1

Lagrange interpolation : 20.1

equivalence to since interpolation : 20.1.1

Matlab function : 20.1.4

maxima function : 20.1.5

optimality : 20.1.2

Lagrange interpolation frequency response : 20.1.6

Lagrange interpolation, explicit coefficient formula : 20.1.3

Laplace transform : 21.1.2

late reverberation : 3.2.1 | 3.4

lattice filter

two-multiply section : 2.8.2

law of inertia : 15.1.1

Lax-Richtmyer equivalence theorem : 23.2.4

Legendre sequence : 17.12.6

Leslie effect : 4.4.7

LFO : 4.4.1

linear interpolation : 4.2.1

analysis : 20.5

loaded waveguide junction : 17.10

longitudinal wave : 16.2

longitudinal waves : 5.12.5

longitudinal waves in rods : 17.8.3

loop filter : see waveguide synthesis
loop filter

lossless : 17.13.3

lossless filter : 2.8.3

lossless prototype : 3.7.2

losslessness of FDNs : 17.13.3

lossy wave propagation : 2.3

low-frequency oscillator (LFO) : 4.4.1.1

lumped models : 21

lumped-parameter analysis : 21

lumping distributed losses : 2.2.2

marginally stable : 23.2.2 | 23.2.3

Mason's gain formula : 2.5.2

mass : 15.1.2

mass moment of inertia : 15.4.3

mass-spring oscillator, energy : 15.2.3

matched z transformation : 27.2.1

matrix norm : 2.7.3

matrix, triangular : 3.7.2.3

maximally flat : 20.1.7

mean free path : 3.7.3.1

mechanical impedance analysis : 21.2.3

mechanics : 15

memoryless nonlinearity : 29.1

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 expansion : 27.5

modal synthesis : 28.1

mode extraction techniques : 28.1

modulated delay line : 4.4.3

moment of inertia : 15.4.3

circular disk : 15.4.3.1

momentum : 15.3

momentum conservation : 15.3.1

moving notches : 4.4.1

mutually prime : 3.7.3

nested allpass filters : 2.8.2

nested MIMO allpass filter : 2.8.5

Newton's laws of motion : 15.1

Newton's laws of motion, examples : 15.1.5

non-cylindrical acoustic tubes : 17.14

nonlinear distortion : 5.13

nonlinear element : 29

nonlinear phase distortion : 4.2.2.1

nonlinearity

aliasing : 29.1.5

cubic soft clipper : 29.1.3

memoryless : 29.1

nonparametric representation : 27.2

nonparametric resonator factoring : 28

normalized scattering junction : 17.8.6

normalized waveguide filter : 18.4

notch : 4.4.1

null : 4.4.1

nulls : 2.6.3

odd functions : 29.1.4.1

Ohm's law for traveling waves : 5.1.5 | 17.7.3

one ports

parallel combination : 21.2.2

passivity condition : 21.2.5

series combination : 21.2.1

one-filter dynamic scattering junction : 5.10.2

one-multiply scattering junction : 17.8.5

one-port network : 21.2

one-to-one : 29.1

order of a state-space system : 2.7.1

orthogonal matrix : 3.7.2.2

outer disk : 22.4

parallel axis theorem : 15.4.3.2

parallel combination of one-ports : 21.2.2

parallel connection : 26.2.1

paraunitary matrix transfer function : 2.8.5

paraunitary matrix transfer functions : 2.8.5

particle velocity : 9.1 | 15.5.1 | 21.1

passive finite difference scheme : 23.2.5

passive one-ports : 21.2.5

passive reflectance : 22.1

passive string terminations : 22.2

passive system properties : 22

phase shifter : 24.2.1

analog : 24.2.1.1

digital : 24.2.1.2

phase shifter, phaser : 4.4.2

phase velocity : 17.3.4 | 23.3

phaser : 4.4.2 | 24.2 | 24.2.1

phasing : 2 | 4.4.2

phasing effect, phaser : 24.2

phasing, allpass chain : 24.2

physical state : 15.1.2

physical units : 15.1.3

physics and mechanics : 15

piano

commuted synthesis : 6.3

string : 6.2

piano modeling : 6

piano synthesis : 5.8

pitch estimation : 5.11.4

plane wave : 15.5.4

plane wave scattering

oblique incidence : 17.8.2

plane-wave scattering

normal incidence : 17.8.1

plucked string synthesis model : 5.4

plugin : 12.6.1

plugin architectures : 13.1

point mass : 5.10

point source : 2.2.4

polarizations : 5.1.2

pole-zero cancellation : 4.2.2

polynomial growth : 23.2.2

polynomial interpolation : 20.1

positive real : 22.2 | 22.3.1

positive real functions : 22.4

positive real impedance : 21.2.5

potential energy : 15.2.1 | 15.2.3

potential energy of a spring : 15.2.1

power waves : 17.7.5 | 17.7.5

power-normalized waveguide filters : 18.4

preemphasis : 28.2.1

pressure in a gas : 15.5.3 | 21.1

pressure recovery : 9.1 | 15.5.9

quadratic residue sequence : 17.12.6

radius of gyration : 15.4.5

circular cross-section : 15.4.5.2

rectangular cross-section : 15.4.5.1

reactance : 21.1

rectangular pulse : 20.5.2.1

reed instruments : 7.1

reed modeling : 7.1.3

reference directions : 5.10

reflectance : 5.10.1 | 5.10.2 | 22.2.1

conical cap : 17.14.3.2

reflection

from a yielding termination : 22.2

sound waves : 2.2.5

reflection transfer function : 22.2.1

reflection coefficient : 2.9.1 | 21.6.1 | 26.2.2.2

plane waves : 17.8.1.2

velocity waves : 26.2.4.2

reflection free port : 26.2.2.4

reflection transfer function : 22.1 | 22.2.1

reflection-free port : 26.2.2.4

refraction : 17.8.2.1

resistor : 21.1.1

resonator factoring : 28

resources on the Internet : 30

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 | 3.7

first-order delay filters : 3.7.5.1

freeverb : 3.6

mesh diffusion : 17.12.6

perception of : 3.2

perception of echo and mode density : 3.2.1

perceptual metrics : 3.2.2

Schroeder : 3.4.2

Schroeder reverb JCRev : 3.5

waveguide : 3.7.8.4

reverberation time, set by contracting poles : 3.7.4

rigid string terminations : 22.2

root-power waves : 17.7.7

scattering : 2.9.1 | 2.9.1

at impedance changes : 17.8

scattering coefficients

at a change in conical taper angle : 17.14.2.2

scattering filter : 17.14.3.1

scattering junction : 2.9.1 | 5.10.2

N waveguides : 17.10

scattering theory : 2.9.1

Schroeder allpass : 2.8

waveguide interpretation : 3.4.2

Schroeder reverberator : 3.4.2

Schroeder-Moorer comb filter : 3.6.2

Schur function : 22.4.2

semitone : 4.4.3

series combination of one-ports : 21.2.1

series connection : 26.2.3

series reflection-free port : 26.2.4.4

shift operator notation : 23.2.1

signal scattering : 26.2

simulation diagram : 21.2.6

sinc function : 20.3.1

sine cardinal : 20.3.1

sinusoidal modeling : 5.8

slap back : 4.4.9.2

Snell's Law : 17.8.2.1

soft clipper : 5.13 | 29.1.3

software : 13

C++

acoustic echo simulation : 2.2.7

plucked string (simple) : 13.1

delay line : 2.1.1

sound examples : 31

sound speed : 15.5.13

sparse state space model : 2.7

spatial derivatives : 17.7.1

spatial impression : 3.3

spatial phase : 15.5.5

spatial sampling interval : 17.4

spectral norm : 2.7.3

specular reflection : 2.2.5

speed of sound : 15.5.13

spherical spreading loss : 2.2.4

spherical wave : 2.2.4

spring and free mass : 26.3.4

spring constant : 15.1.4

spring force : 15.1.4

square law nonlinearity : 29.1.5.1

stability of a finite difference scheme : 23.2.3 | 23.2.3

stability proof for a conical cap : 17.14.3.3

stable system : 23.2.2

Standard Model : 15.1.3

standard temperature and pressure : 15.5.13

state conversions : 17.7.4

state of an ideal string : 17.3.6

state transformation, vibrating string : 17.3.6

state transition matrix : 2.7.1

state variables : 2.7.1

state-space analysis, digital waveguide oscillator : 19.6

state-space description : 2.7.1

stiff string F0 estimation : 5.11.4.3

stiff string simulation : 5.8

stiff string synthesis : 5.8.1

stiffness : 15.1.4

stiffness term : 5.8

STK introduction : 11

STK project, creating : 11.4

STK tutorials : 11.3

strain : 17.8.3

strictly stable : 23.2.3

string

dispersion filter design : 6.2.2

dispersive (stiff) : 6.2 | 17.6

dispersive wave propagation : 5.8

EDR-based loop-filter design : 5.11.5

externally excited : 5.9

finite difference approximation : 17.2.1

frequency-dependent losses : 17.5.2

fundamental frequency estimation : 5.11.4

loop filter design : 5.11

modeling for synthesis : 5

moving termination : 5.3

physical diagram : 5.1

piano : 6.2

pitch detection : 5.11.4

stiff : 5.8

wave equation : 16 | 17.1

wave momentum : 16.2

string coupling : 5.12

string-mass model : 5.10.1

stringed instruments

bowed : 8

bridge reflectance : 22.2.1

commuted synthesis of : 5.15

coupled : 17.11

damping in : 5.6

frequency-dependent damping : 5.7

frequency-dependent damping in : 5.7

guitar : 5.15

guitars : 5

nonlinear : 5.13

yielding terminations : 22.2

struck string

digital waveguide model : 5.10.3

ideal mass : 5.10

impedance analysis : 5.10.2

struck string synthesis model : 5.5