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 synthesis
loop 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