Index

---

C++ debugging in gdb : 12.7

minphaseir : 14.11.1.4

acceleration due to gravity : 16.1.4

acoustic echo simulation : 2.2.6

acoustic energy density : 16.5.10

acoustic intensity : 16.5.9

acoustic kinetic energy density : 16.5.10

acoustic potential energy density : 16.5.10

acoustic wave simulation : 2.2

acoustical ohms : 18.7.3

acoustics : 16

adaptor : 27.2

series, reflection free : 27.2.4.4

two-port parallel : 27.2.1

unit element : 27.1.7

admittance : 22.1

aerofoil : 16.5.7

air absorption : 3.1.1 | 16.5.13

frequency-dependent : 2.3.1

frequency-independent : 2.3.1

air jets : 16.5.8

air pressure : 16.5.3

airfoil : 16.5.7

aliasing : 30.1.5

aliasing due to nonlinearity : 30.1.5

all-vowels pedal : 14.11.5

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 : 21.2

nested : 2.8.2 | 3.4.3

Thiran : 21.2

waveguide : 2.9

allpass phase shifter : 25.2.1

second-order case : 25.2.2

alpha parameters : 27.2.2.1

amplification factor : 24.4

amplifier cabinet filter : 5.14

amplifier feedback in Faust : 14.3

amplifier feedback simulation : 5.14

amplitude complementary : 7.1.1

amplitude envelopes : 5.11.1

arctangent nonlinearity : 30.1.2

area moment of inertia : 16.4.4

artificial reverberation : see reverberation

bandlimited interpolation : 21.3

bell models : 9.2

bending angle : 5.8

Bernoulli effect : 16.5.7

Bernoulli equation : 9.1 | 16.5.6

Bessel filter : 21.2

beta parameters : 27.2.4.1

bidirectional delay line : 2.4

bilinear transform : 22.4

Bode plot : 14.8.1 | 25.2.1.1

body factoring

by sinusoidal modeling : 29.1.4

body factoring example : 29.6

body-resonator factoring : 29

bowed strings : 8

bow-string junction : 8.2

linear commuted synthesis of : 8.4

brass instruments : 9

brass mouthpiece : 9.1

break frequency : 14.2.5 | 25.2.1.1 | 25.2.1.1

capacitor : 22.1.3

cardinal sine : 21.3.1

causal : 2.5.4 | 2.8.3

center of mass : 16.1.2

centered finite difference approximations : 26.1.1

centroid : 16.1.2

chain rule : 18.3.2 | 18.3.2

characteristic impedance : 18.7.3 | 22.1 | see wave impedancetextbf

characteristic polynomial equation : 24.2.2.1 | 24.3

chorus effect : 2 | 4.4.6

citations by topic : 33

clarinet tonehole as a two-port junction : 7.2.1

clipping : 30.1.1

clipping function : 5.13

hard : 5.13

soft : 5.13

clipping nonlinearity : 30.1.1

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

pick-position illusion : 14.2.2

commuted piano synthesis : 6 | 6.3

commuted synthesis : 5.15 | 6

piano : 6

commuted waveguide synthesis

bowed strings : 8.4

compatible port connection : 27.2.1.1

compiling from emacs : 11.5

compliance : 22.1.3

compression velocity : 22.1.3

computational physical model : 2.6.1

cone-cylinder intersection : 18.14.3

conical acoustic tubes : 18.14.2

conical cap reflectance : 18.14.3.2

conical tube junction : 18.14.3.1

conservation of energy : 16.2.5

conservation of momentum : 16.1.1 | 16.3.1

conservative forces : 16.2

consistency of finite differences : 24.2.1

convergence of finite difference schemes : 24.2

Coulomb force : 16.1.4

coupled strings : 5.12 | 18.11

coupled strings eigenanalysis : 18.11.2

coupling of horizontal and vertical transverse waves : 5.12.2

coupling of two ideal strings : 18.11.1

crests : 16.5.4

CryBaby : 14.11

CryBaby in Faust : 14.11.1.5

CryBaby wah pedal : 14.11.1

cubic nonlinearity : 5.13 | 14.3.1

cubic soft clipper : 30.1.3

cylinder with conical cap : 18.14.3

daemon : 12.6.1

damping filter design : 5.11.1 | 5.11.2

dashpot : 22.1.1 | 22.1.1

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 : 21

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 : 22.3

dependent port : 27.2.2.1

differential equation : 16.1.5

differentiator : 22.1.3

diffuse field : 3.7.3.1

diffuse reflection : 2.2.5

diffusers : 3.5

digital state variable filter : 20.2

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

digitar : 14.1

directional derivative : 16.5.5

dispersion : 2.3.2 | 2.4

dispersion filter design : 5.11.3 | 6.2.2

dispersion filtering : 5.8.1

dispersion relation : 24.3

dispersive 1D wave equation : 18.6

dispersive wave propagation : 2.3.2 | 5.8

displacement waves : 23.2

distortion in Faust : 14.3

Doppler effect : 4.4.4

Doppler shift : 4.4.4

doubling effect : 4.4.9.1

driving point impedance : 22.1

driving-point impedance : 3.4.2

DSSI plugin : 12.6.1

DSSI/LADSPA plugin debugging : 12.6

dynamic level filter in Faust : 14.2.5.3

dynamic level lowpass filter : 14.2.5

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 : 16.4

elliptic norm : 18.13.3

energy conservation : 16.2.5

energy conservation in volumes : 16.5.11

energy decay curve (EDC) : 3.2.2.1

energy decay relief (EDR) : 3.2.2.2

energy density : 16.5.10

energy density waves : 18.7.6

energy in a vibrating string : 18.7.8

energy of a mass : 16.2.2

energy of a mass-spring system : 16.2.4

equilibrium : 16.1.4

evanescent : 18.8.2.2

evanescent wave : 18.8.2.2

even part : 30.1.4.1

example .gdbinit file : 12.1

excess air pressure : 9.1

excitation noise substitution : 29.5

experimental fact : 16.1.3

explicit finite difference scheme : 24.1

Extended Karplus Strong (EKS) in Faust : 14.2.8

Extended Karplus-Strong (EKS) algorithm

Faust program : 14.2

Extended Karplus-Strong algorithm : 5.7.5

F0 : 5.11.4

F0 estimation : 5.11.4

Farrow structure : 21.1.7

Faust

amplifier feedback : 14.3

coupled strings : 14.6

CryBaby wah pedal : 14.11.1.5

distortion : 14.3

speaker model

low frequency : 14.8.2.1

Faust examples

Extended Karplus Strong : 14.2

Karplus-Strong digitar : 14.1

stiffness allpass : 14.2.7

tuning allpass : 14.2.6

Faust programming language : 14

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 : 18.8.4

one-multiply section : 18.8.5

lattice section : 2.8.2

lossless : 2.8.3

transposition : 2.5.2

vectorized comb : 2.7

filter design : 28.4

dispersion filter : 6.2.2

filtered feedback comb filter : 2.6.5

filtered node variables : 18.5.5.1

filtered-feedback comb filter : 2.6.5

filtering per sample : 2.3.1 | 3.7.4

finite difference approximation : 18.2 | 18.2 | 22.3

finite difference scheme

consistency : 24.2.1

convergence : 24.2

explicit : 24.1

implicit : 24.1

passivity : 24.2.5

stability : 24.2.3

well posed initial-value problem : 24.2.2

finite difference schemes : 24

finite difference string model

frequency-dependent losses : 18.5.5.1

lossless : 18.4.3

lossy : 18.5.5

finite difference time domain scheme : 26

finite-difference time-domain : 18.5.5

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 : 16.1.3

force of gravity : 16.1.3

force reflectance : 5.10.2

force times distance : 16.2

force transmittance : 5.10.2

force wave variable : 18.7.2

force waves : 5.1.5 | 18.7.2

frequency shift : 4.4.3

friction force : 22.1.1

function inverse : 30.1

fundamental frequency

estimation : 5.11.4

gas pressure : 16.5.3

gases : 16.5

gdb debugging : 12.2

gdb in emacs : 12.4

generalized scattering coefficients : 18.14.2.2

gradient : 16.5.5

gravitation : 16.1.3

gravitation constant : 16.1.3

group-delay filters : 21.2

GUI generation : 14

guitar bridge : 23.3

guitar modeling : 5.15

gyration : 16.4.5

Hadamard matrix : 3.7.1

half-rate waveguide filter : 19.2

hard clipper : 5.13

Heaviside unit step function : 21.5.2.1

Hermitian conjugate : 3.7.2.2

Hermitian transpose : 2.7.3 | 2.8.5

history of ideas : 15

Hooke's law : 16.1.4 | 16.1.5

horizontal & vertical transverse waves : 5.12.1

horns : 18.14

Householder feedback matrix, FDNs : 3.7.2.1

Householder reflection : 3.7.2.1

Huygens' principle : 2.2.4

Huygens-Fresnel principle : 18.14.1

ideal bar : 16.4.1.1 | 18.6

ideal mass : 22.1.2

ideal spring : 22.1.3

ideal string

digital waveguide model : 18.4.1

ill posed PDE : 18.5.2 | 24.2.2.2 | 24.3

image method : 3.2.1

immittance : 22.1

impedance : 22.1 | 22.1

impedance analysis : 22.2.3

implicit finite difference scheme : 24.1

impulse expanders : 3.4.2

impulse response sampling : 28.2

impulse-invariant method : 28.2.1

incompressible flow : 9.1

index of refraction : 18.8.2.1

induced norm : 2.7.3

inductor : 22.1.2

inelastic collision : 5.10

inertia : 16.1 | 16.1.2

initial conditions : 16.1.5

instantaneous nonlinearity : 30.1

integrator : 22.1.2

intensity, acoustic : 16.5.9

International Standard Units (``SI units'') : 16.1.3

interpolated delay line : 4.2

interpolation

allpass : 4.2.2

by filter bank of differentiators : 21.1.7

for delay lines : 4.2

linear : 4.2.1

inverse filtering : 29.2.2

inverse filtering matlab code : 29.2.2

inverse square law : 2.2.4

inviscid : 9.1

JCRev : 3.5 | 3.6

jets : 16.5.8

Joules : 16.2

Karplus-Strong algorithm : 5.7.4

Faust program : 14.1

Karplus-Strong history : 15.8

Karplus-Strong, extended : 5.7.5

Kelly-Lochbaum scattering junction : 18.8.4

kinetic energy : 16.2.3

kinetic energy of a mass : 16.2.2

kinetic theory of ideal gases : 16.5.3

L2 norm : 2.7.3

ladder filter : 19.3

ladder waveguide filters : 19.1

LADSPA plugin : 12.6.1

Lagrange interpolation : 14.2.6.3 | 21.1

equivalence to since interpolation : 21.1.1

Matlab function : 21.1.4

maxima function : 21.1.5

optimality : 21.1.2

Lagrange interpolation frequency response : 21.1.6

Lagrange interpolation, explicit coefficient formula : 21.1.3

Laplace transform : 22.1.2

late reverberation : 3.2.1 | 3.4

lattice filter

two-multiply section : 2.8.2

law of inertia : 16.1.1

Lax-Richtmyer equivalence theorem : 24.2.4

Legendre sequence : 18.12.6

Leslie effect : 4.4.7

LFO : 4.4.1

linear interpolation : 4.2.1 | 14.2.6.1

analysis : 21.5

loaded waveguide junction : 18.10

longitudinal wave : 17.2

longitudinal waves : 5.12.5

longitudinal waves in rods : 18.8.3

loop filter : see waveguide synthesis
loop filter

lossless : 18.13.3

lossless filter : 2.8.3

lossless prototype : 3.7.2

losslessness of FDNs : 18.13.3

lossy wave propagation : 2.3

low-frequency oscillator (LFO) : 4.4.1.1

lumped models : 22

lumped-parameter analysis : 22

lumping distributed losses : 2.2.2

marginally stable : 24.2.2 | 24.2.3

Mason's gain formula : 2.5.2

mass : 16.1.2

mass moment of inertia : 16.4.3

mass-spring oscillator, energy : 16.2.3

matched z transformation : 28.2.1

matrix norm : 2.7.3

matrix, triangular : 3.7.2.3

maximally flat : 21.1.7

mean free path : 3.7.3.1

mechanical impedance analysis : 22.2.3

mechanics : 16

memoryless nonlinearity : 30.1

mesh

2D rectilinear : 18.12.1

2D, lossy : 18.12.5

wave equation obeyed : 18.12.4

MIMO allpass filter : 2.9

mixing matrix : 3.5

modal expansion : 28.5

modal synthesis : 29.1

mode extraction techniques : 29.1

modulated delay line : 4.4.3

moment of inertia : 16.4.3

circular disk : 16.4.3.1

momentum : 16.3

momentum conservation : 16.3.1

Moog VCF wah pedal : 14.11.2

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 : 16.1

Newton's laws of motion, examples : 16.1.5

non-cylindrical acoustic tubes : 18.14

nonlinear distortion : 5.13

nonlinear element : 30

nonlinear phase distortion : 4.2.2.1

nonlinearity

aliasing : 30.1.5

cubic soft clipper : 30.1.3

memoryless : 30.1

nonparametric representation : 28.2

nonparametric resonator factoring : 29

normalized scattering junction : 18.8.6

normalized waveguide filter : 19.4

notch : 4.4.1

null : 4.4.1

nulls : 2.6.3

odd functions : 30.1.4.1

Ohm's law for traveling waves : 5.1.5 | 18.7.3

one ports

parallel combination : 22.2.2

passivity condition : 22.2.5

series combination : 22.2.1

one-filter dynamic scattering junction : 5.10.2

one-multiply scattering junction : 18.8.5

one-port network : 22.2

one-to-one : 30.1

order of a state-space system : 2.7.1

orthogonal matrix : 3.7.2.2

outer disk : 23.4

parallel axis theorem : 16.4.3.2

parallel combination of one-ports : 22.2.2

parallel connection : 27.2.1

paraunitary matrix transfer function : 2.8.5

paraunitary matrix transfer functions : 2.8.5

particle velocity : 9.1 | 16.5.1 | 22.1

passive finite difference scheme : 24.2.5

passive one-ports : 22.2.5

passive reflectance : 23.1

passive string terminations : 23.2

passive system properties : 23

phase shifter : 25.2.1

analog : 25.2.1.1

digital : 25.2.1.2

phase shifter, phaser : 4.4.2

phase velocity : 18.3.4 | 24.3

phaser : 4.4.2 | 25.2 | 25.2.1

phasing : 2 | 4.4.2

phasing effect, phaser : 25.2

phasing, allpass chain : 25.2

physical state : 16.1.2

physical units : 16.1.3

physics and mechanics : 16

piano

commuted synthesis : 6.3

string : 6.2

piano modeling : 6

piano synthesis : 5.8

pick modeling : 14.10

pick-position comb filter : 14.2.2

pitch estimation : 5.11.4

plane wave : 16.5.4

plane wave scattering

oblique incidence : 18.8.2

plane-wave scattering

normal incidence : 18.8.1

plucked string synthesis model : 5.4

plugin : 12.6.1

plugin architectures : 13.1

plugins : 14

point mass : 5.10

point source : 2.2.4

polarizations : 5.1.2

pole-zero cancellation : 4.2.2

polynomial growth : 24.2.2

polynomial interpolation : 21.1

positive real : 23.2 | 23.3.1

positive real functions : 23.4

positive real impedance : 22.2.5

potential energy : 16.2.1 | 16.2.3

potential energy of a spring : 16.2.1

power waves : 18.7.5 | 18.7.5

power-normalized waveguide filters : 19.4

preemphasis : 29.2.1

pressure in a gas : 16.5.3 | 22.1

pressure recovery : 9.1 | 16.5.8

quadratic residue sequence : 18.12.6

radius of gyration : 16.4.5

circular cross-section : 16.4.5.2

rectangular cross-section : 16.4.5.1

reactance : 22.1

rectangular pulse : 21.5.2.1

reed instruments : 7.1

reed modeling : 7.1.3

reference directions : 5.10

reflectance : 5.10.1 | 5.10.2 | 23.2.1

conical cap : 18.14.3.2

reflection

from a yielding termination : 23.2

sound waves : 2.2.5

reflection transfer function : 23.2.1

reflection coefficient : 2.9.1 | 22.6.1 | 27.2.2.2

plane waves : 18.8.1.2

velocity waves : 27.2.4.2

reflection free port : 27.2.2.4

reflection transfer function : 23.1 | 23.2.1

reflection-free port : 27.2.2.4

refraction : 18.8.2.1

resistor : 22.1.1

resonator factoring : 29

resources on the Internet : 31

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 : 18.12.6

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 : 23.2

root-power waves : 18.7.7

rounding : 14.2.2

running two-point average : 14.1 | 14.1

scattering : 2.9.1 | 2.9.1

at impedance changes : 18.8

scattering coefficients

at a change in conical taper angle : 18.14.2.2

scattering filter : 18.14.3.1

scattering junction : 2.9.1 | 5.10.2

N waveguides : 18.10

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 : 23.4.2

semitone : 4.4.3

series combination of one-ports : 22.2.1

series connection : 27.2.3

series reflection-free port : 27.2.4.4

shift operator notation : 24.2.1

signal scattering : 27.2

simulation diagram : 22.2.6

sinc function : 21.3.1

sine cardinal : 21.3.1

sinusoidal modeling : 5.8

slap back : 4.4.9.2

Snell's Law : 18.8.2.1

soft clipper : 5.13 | 30.1.3

software : 13

C++

acoustic echo simulation : 2.2.7

plucked string (simple) : 13.1

delay line : 2.1.1

Faust

electric guitars : 14

sound examples : 32

sound speed : 16.5.12

sparse state space model : 2.7

spatial derivatives : 18.7.1

spatial impression : 3.3

spatial phase : 16.5.5

spatial sampling interval : 18.4

speaker model

high frequency : 14.8.3

low frequency : 14.8.2

spectral norm : 2.7.3

specular reflection : 2.2.5

speed of sound : 16.5.12

spherical spreading loss : 2.2.4

spherical wave : 2.2.4

spring and free mass : 27.3.4

spring constant : 16.1.4

spring force : 16.1.4

square law nonlinearity : 30.1.5.1

stability of a finite difference scheme : 24.2.3 | 24.2.3

stability proof for a conical cap : 18.14.3.3

stable system : 24.2.2

Standard Model : 16.1.3

standard temperature and pressure : 16.5.12

state conversions : 18.7.4

state of an ideal string : 18.3.6

state transformation, vibrating string : 18.3.6

state transition matrix : 2.7.1

state variable filter : 14.11.1.1

state variables : 2.7.1

state-space analysis, digital waveguide oscillator : 20.6

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 : 16.1.4

stiffness allpass in Faust : 14.2.7

stiffness term : 5.8

STK introduction : 11

STK project, creating : 11.4

STK tutorials : 11.3

strain : 18.8.3

strictly stable : 24.2.3

string

dispersion filter design : 6.2.2

dispersive (stiff) : 6.2 | 18.6

dispersive wave propagation : 5.8

EDR-based loop-filter design : 5.11.5

externally excited : 5.9

finite difference approximation : 18.2.1

frequency-dependent losses : 18.5.2

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 : 17 | 18.1

wave momentum : 17.2

string coupling : 5.12

string damping filter

one zero : 14.2.3

two zeros : 14.2.4

string tuning

Lagrange interpolation : 14.2.6.3

allpass interpolation : 14.2.6.2

linear interpolation : 14.2.6.1

string-mass model : 5.10.1

stringed instruments

bowed : 8

bridge reflectance : 23.2.1

commuted synthesis of : 5.15

coupled : 18.11

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 : 23.2

struck string

digital waveguide model : 5.10.3

ideal mass : 5.10

impedance analysis : 5.10.2

struck string synthesis model : 5.5

subtractive synthesis : 25.1

susceptance : 22.1

symmetric FIR filters : 5.7

synthesis : see waveguide synthesis

synthesizer plugin : 12.6.1

tap : 2.5

tapped delay line : 2.5 | 2.5

equivalence to parallel comb filters : 2.6.6

equivalence to series comb filters : 2.6.7

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

tension of a string : 16.4.2

termination, moving : 5.3

Thiran allpass interpolation : 21.2

time domain finite difference scheme : 24

time-domain difference operators : 22.3

tonal correction filter : 3.7.6

tone stack : 14.7

tonehole modeling : 7.2

total internal reflection : 18.8.2.2

transfer function models : 28

transfer-function matrix : 3.1.1

transmission coefficient : 2.9.1 | 27.2.2.2

velocity waves : 27.2.4.2

transmittance : 5.10.2

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 : 5.12.1

traveling wave solution of the wave equation : 18.3.5

traveling waves : 2.2.1 | 2.2.1

damped : 2.2.2

dispersive : 2.3.2

in lumped systems : 22.6

lumped interpretation : 22.6.2

plane waves : 2.3.1

traveling-wave partial derivatives : 18.3.1

traveling-wave solution of 1D wave equation : 18.3

tremolo : 4.4.3

triangular matrices : 3.7.2.3

truncation : 14.2.2

tuning allpass : 14.2.6.2

tuning allpass in Faust : 14.2.6

tunneling : 18.8.2.2

two-multiplier lattice filter : 2.8.2

unit element : 27.1.7

unit-delay operator : 2.8.5

unitary matrix : 3.7.2.2

unitary matrix feedback : 2.7

unitary matrix frequency response : 2.8.5

Univibe : 25.2.1

vector feedback comb filter : 2.7

vector wavenumber : 16.5.5 | 16.5.5

velocity

particle : 16.5.1

reflection coefficient : 27.2.4.2

transmission coefficient : 27.2.4.2

volume : 16.5.2

velocity reflectance : 5.10.2

velocity transmittance : 5.10.2

vibrating string : see string

vibrato simulation : 4.4.3

virtual analog : 25 | 25.2.1.2

virtual displacement : 16.2.2

virtual work : 16.2.2

voltage divider : 22.2.3

volume velocity : 16.5.2 | 22.1

volume velocity in a gas : 16.5.2

von Neumann analysis : 24.4

vowel pedal : 14.11.3

wah pedal : 14.11 | 14.11

wah-wah : 14.11

wave digital

mass-spring oscillator : 27.3.6

wave digital element : 27.1

wave digital elements

physical derivation : 27.1.1

wave digital examples : 27.3

wave digital filter : 27

wave digital mass : 27.3.1 | 27.3.4

wave digital spring : 27.3.4

wave equation : 18.1

applications : 5.1.2

damped string : 18.5

piano string : 6.2.1

vibrating string : 5.1.1 | 17

wave momentum : 17.2

zero stiffness : 17.1

wave impedance : 5.1.5 | 5.1.5 | 18.7.3 | 22.1

wave variables : 18.7 | 27.1

wave velocity : 18.3.4

waveform dispersion : 2.3.2

waveguide

cone-cylinder intersection : 18.14.3

conical : 18.14.2

conical cap reflectance : 18.14.3.2

conical cap reflectance stability proof : 18.14.3.3

definition : 2.4

dispersive : 18.6

equivalence to FDTD scheme : 26

generalized scattering coefficients : 18.14.2.2

network : 2.9.2

non-uniform : 18.14

physical outputs : 2.4.1

scattering : 2.9.1

scattering filter : 18.14.3.1

waveguide filter : 19

conventional ladder : 19.3

half-rate structure : 19.2

ladder structure : 19.1

normalized : 19.4

waveguide junction, N waveguides : 18.10

waveguide mesh : 3.7.8.5 | 18.12 | see mesh

waveguide model

ideal string : 18.4.1

waveguide network : 2.9.2

FDN equivalence : 18.13

waveguide oscillator : 20 | 20

state-space analysis : 20.6

waveguide reverb : 3.7.8.4

waveguide synthesis

acoustic strings : 5.15

amplifier feedback simulation : 5.14

bowed strings : 8

brightness and sustain parameters : 5.7.2

commuted : 5.15

commuted bowed strings : 8.4

damping filter design : 5.11.2

dispersion filter design : 5.11.3

distorted strings : 5.13

Extended Karplus-Strong algorithm : 5.7.5

FIR(3) loop filter : 5.7.1

general bore shapes : 18.14

guitar body : 29

guitar bridge reflectance : 23.2.1

isolating resonant modes : 29.1

Karplus-Strong algorithm : 5.7.4

loop filter

one-zero : 5.7.3

three-tap : 5.7.1

loop filter design design : 5.11.1

software : see softwaretextbf

waveguide theory : 18

waves

longitudinal : 5.12.5

transverse : 17 | 18.1

well posed initial-value problem : 24.2.2 | 24.2.2

well posed PDE : 24.2.2.1

windowed sinc interpolation : 21.3

work : 16.2 | 16.2.4

yielding string terminations : 23.2

Young's modulus : 16.4.1

yoyo pedal : 14.11.4

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written by 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.