Index for this Document

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3-dB bandwidth : 9.5 | 18.6

abstraction (pd) : 24.5.1

additive synthesis : 8.6.5

affine function : 11.5

allpass condition : 16

allpass filter : 15.2

biquad case : 15.2.1

examples : 16.1

general case : 16

allpass filter design : 15.2.2

Amperes : 18.2 | 18.3

amplifier modeling : 19.7

amplitude : 14.1.1

amplitude envelope : 8.6.5

amplitude response : 2.2 | 2.3.1 | 8.2

analog filters : 18 | 22.2

allpass : 18.8

capacitor impedance : 18.2

example : 18.1

example RC analysis : 18.4

example RLC analysis : 18.5

inductor impedance : 18.3

poles and zeros : 18.4.5

RL impulse response : 18.4.3

RLC impulse response : 18.5.4

second-order poles and zeros : 18.5.3

second-order transfer function : 18.5.2

transfer function : 18.4.2

analog prototype : 22.3.3

analytic continuation : 7.2 | 17.2 | 17.2 | 22.2.1

anticausal : 9.8

anticausal exponentials : 9.7

antiresonance frequency : 15.1.4 | 15.1.6

antiresonator : 15.1.4

antisymmetric impulse responses : 11.5

antisymmetric linear-phase filters : 11.5

banded Toeplitz filter matrix : 19.3

bandwidth of a pole : 9.5

bandwidth of a pole : 18.6

bilateral z transform : 7.1

bilateral Laplace transform : 17

bilinear transformation : 22.3.1

frequency warping : 22.3.2

prototype analog filters : 22

binomial coefficient : 20.10.1

biquad filter section : 7.8.3 | 15.1.6

blocking capacitor : 15.3

boost : 15.5

Butterworth filters : 22.2

Butterworth lowpass example : 10.2.4

Butterworth lowpass filter design example : 22.2.2

canonical with respect to delay : 6.11.6

capacitor : 18.2

capacitor driving point impedance : 18.4.1

capacitors as springs : 18.2.1

carrier frequency : 8.6.3.1

carrier term : 14.3.3

carrier wave : 8.6.5

causal : 5.3 | 6.3 | 16

causal filters : 6.3

causal signal : 7.1 | 24.1

center frequency of a resonator : 15.1.3

cepstrum

complex : 9.8

minimum phase : 9.9

poles and zeros : 9.8

real : 9.8

characteristic polynomial : 20.6

circulant matrix : 19.4

clipping : 5.1

clipping dB magnitude : 23.10

coefficients, difference equation : 6.1

comb filter : 4

commutativity of series filters : 7.7.2.1

companding : 5.7

complete response : 6.12.5 | 20.3

complex amplitude : 2.4.2

complex analysis : 5.1

complex and trig identities : 14.2

complex cepstrum : 9.8

complex exponential : 2.4.1 | 7.8.4

complex filter : 5.3 | 6.1

complex numbers summary : 14.2

complex one-pole sections : 10.2.2.1

complex resonator : 15.1.5 | 18.6

complex signal : 5.1

complex sinusoid : 2.4.1

complex sinusoidal oscillator : 15.1.5

condition number : 20.10

conformal map : 22.3.2

constant peak-gain resonator : 15.6.4

constant resonance-gain resonator : 15.6.2

continuous-time complex one-pole resonator : 18.6

controllability and observability : 20.7.3

controllable modes : 20.7.1

controller canonical form : 19.6.1 | 20.7.1

convex optimization : 22.1

convolution : 7.8.10.2 | 20.1

convolution filter representation : 6.9 | 6.10

convolution is commutative : 7.7.2.1

convolution theorem for z transforms : 7.3

convolution theorem for z transforms : 7.3.2

convolution theorem for z transforms : 7.3.2

Coulombs : 18.2

cps : 14.1.1

critically damped : 18.7

current : 18.2

cut filter : 15.5

cut-off frequency : 2.2

cycles per second : 14.1.1

cyclic convolution : 19.4

damping constant : 18.7

dB clipping : 23.10

dc blocker : 15.3

dc blocker frequency response : 15.3.1

dc blocking filter : 15.3

decay response : 6.12.4 | 6.12.4

decay time : 6.12.1

decay time-constant : 9.6

deconvolution : 7.8.10.3

degeneracy : 7.8.7

delay equalization : 8.6.4

delta function : 18.4.4

design of recursive digital filters : 22

determinant : 20.6

DFT matrix : 19.4

diagonalizing a state-space model : 20.9.1

difference equation : 6.1

differentiation theorem for Laplace transforms : 17.4.2

digital filter theory : 5

direct form filter implementation : 15.1.6

direct form filter implementations : 10.1

discrete Fourier transform (DFT) : 8.5.1

discrete time Fourier transform (DTFT) : 8.1

discrete-time sinusoid : 14.1.2

doublet : 17.5.1

driving point impedance

RLC network : 18.5.1

driving-point impedance : 18.2 | 18.3

DTFT : 8.1

Durbin recursion : 9.4.1 | 9.4.1

dynamic convolution : 5.9

dynamic range compression : 5.7

eigenvalues : 20.6 | 20.6

eigenvector : 20.9.1

electrical equivalent circuit : 17.5.1

equation error : 22.4.1

definition : 22.4.1

minimization : 22.4

equiripple : 8.6.4

error weighting function : 22.4.2

Euler's identity : 2.4

even impulse-response filter : 11.2

example elementary audio filters : 15

existence of the z transform : 7.2

explicit finite difference scheme : 6.1

exponential function summary : 14.2.1

exponential order : 17.1

exponentially swept sine analysis : 2.3.1

exponentially windowed : 17

externals (pd) : 24.5.1

factorial notation : 17.2

Farads : 18.2

Fast Fourier Transform (FFT) : 8.5.1

Faust programming language : 24

feedback coefficients : 6.1

feedback signal : 5.3

feedforward coefficients : 6.1

FFT convolution : 6.11.7 | 19.4

filter

allpass biquad : 15.2.1

allpass examples : 16.1

allpass sections : 15.2

amplitude response : 8.2

antiresonator : 15.1.4

antisymmetric impulse response : 11.5

biquad : 15.1.6

causal : 6.3

checking stability : 9.4.1

coefficients : 6.1

complete response : 6.12.5

complex : 6.1

complex one-pole resonator : 15.1.5

constant gain at resonance : 15.6.1

converting to minimum phase : 12.7

converting to parallel form : 7.8

dc blocker : 15.3

definition : 5.2 | 5.2

difference equation : 6.1

direct-form I : 6.2 | 6.5

direct-form II : 6.2 | 10.1.2

estimation from input/output data : 19.7

even impulse response : 11.2

examples : 5.3

feedback : 6.1

finite impulse response (FIR) : 6.11

first and second-order sections : 15.1

forming real second-order sections from two complex one-poles : 7.8.3

forward and backward : 11.6

frequency response : 8.1

frequency response in matlab : 8.5.1

general form of finite-order, causal, linear, time-invariant case : 6.4

graphical amplitude-response calculation from poles and zeros : 9.2

graphical phase response : 9.3

imaginary frequency response : 11.3

implementation structures : 6.2 | 10

complex resonators : 10.2.2.1

parallel second-order sections : 10.2.2

real second-order sections : 10.2.2.2

repeated pole : 10.2.2.3

second-order sections : 10.2

series second-order sections : 10.2.1

transposed direct-form II : 10.1.4

implementations

direct-form I : 10.1.1

direct-form II : 10.1.2

transposed direct forms : 10.1.3

internal overflow : 10.1.2

inverse : 19.5

linear : 5.4.2

linear phase : 11 | 11.4

linear time-varying : 21

linear, time invariant : 5

lossless : 16

LTI : 5.5

LTI matrix representation : 19.3

matrix representation : 19

minimum phase : 12

multi-input, multi-output (MIMO) allpass filters : 16.3

nonlinear example : 5.7

notch : 15.1.4

null : 15.1.4

odd impulse response : 11.3

one complex pole : 15.1.5

one pole : 15.1.2

one zero : 15.1.1

order : 6.4 | 6.4 | 9.1

paraconjugate : 16.2

parallel combination : 7.7

paraunitary, MIMO case : 16.3.1

paraunitary, SISO case : 16.2

partial fraction expansion : 7.8

peaking eq : 15.5

phase : 8.3

phase preserving : 11

phase response : 8.3

polar form of freq. response : 8.4

poles : 4.11

poles and zeros : 9

Q (quality factor) : 18.7

real : 6.1

real, digital : 5.2 | 5.2

recursive : 6.1

reflection coefficients : 9.4.1

resonance bandwidth of a pole : 18.6

resonator : 15.1.3

resonator bandwidth in terms of pole radius : 15.1.3.1

resonator center frequency : 15.1.3

series combination : 7.7

shelf : 15.4

shift-invariance : 5.5

signal flow graph (system diagram) : 6.2

simplest lowpass : 2

stability : 6.7 | 9.4

state space realization : 19.6

symmetric impulse response : 11.4

time-domain representations : 6

time-invariance : 5.5

transfer function : 7

transposition : 10.1.3

tunable resonator : 15.6.1

two pole : 15.1.3

two zero : 15.1.4

zero phase : 11.2

zeros : 4.11

filter design

analog prototype : 22.3.3

analog to digital conversion via bilinear transform : 22.3

Butterworth : 8.6.4 | 22.2

Chebyshev : 8.6.4

elliptic : 8.5.2 | 8.6.4

equation error method : 22.4

equation error minimization in the frequency domain : 22.4.4

frequency warping : 22.3.2

lowpass filter : 22.1

maximally flat amplitude response : 22.2

Padè-Prony method : 22.4.6

Prony's method : 22.4.5

Finite Impulse Response (FIR) digital filter : 6.11

finite support : 6.11.3

Finite-Impulse-Response (FIR) digital filter : 6.1

finite-order causal LTI digital filters : 6.4

FIR filter : 6.11 | 6.11

FIR filter design : 11.4.2

FIR part : 7.8.5

flip theorem for z transforms : 11.6

flow graph : 6.2

flow graph reversal : 10.1.3

folding a signal about index zero : 23.9

formant : 10.2.3

formant filtering : 10.2.3

forward-backward filtering : 11.6

frequencies : 14.1.1

frequency domain : 14.1.3

frequency response : 8.1

computation in matlab : 8.5.1

example in matlab : 8.5.2

imaginary : 11.3

frequency warping : 22.3.2 | 22.4.2

frequency-domain equation-error minimization : 22.4.4

frequency-response

measurement : 2.3

plotting in matlab : 23.4

gain at resonance : 15.6

generalized eigenvectors : 20.10

generalized function : 18.4.4

geometric sequence : 7.8.4

graphical computation of amplitude response from transfer-function poles and zeros : 9.2

graphical phase response calculation : 9.3

group delay : 8.6.3

computation : 8.6.6

example : 8.6.4

matlab function 1 : 23.8

matlab function 2 : 23.6

group delay equals modulation delay : 8.6.3.1

guard bits : 10.1.2.1

GUI generation : 24

Haar filter bank : 16.3.2

half-angle tangent identities : 14.2.3.1

half-open interval : 3.2

half-power bandwidth : 9.5 | 18.6

harmonic distortion : 5

Heaviside unit step function : 18.4.3

Henrys : 18.3

Hermitian : 11.2 | 11.3

Hertz (Hz) : 14.1.1

high shelf : 15.4

Hilbert transform relations : 9.10

Hooke's law for ideal springs : 18.2.1

Hurwitz polynomial : 18.8

impedance analysis : 18.4 | 18.5

implicit finite difference schemes : 6.1

impulse : 6.6

impulse invariant transformation : 18.6

impulse response : 6.6 | 6.11.1 | 12.2

example : 6.8

state-space model : 20.1

impulse signal : 4.6 | 6.6 | 6.11.1

impulse, continuous time : 18.4.4

inductor : 17.5.1 | 18.3

inductors as masses : 18.3.1

infinite-impulse-response (IIR) : 6.1

initial conditions : 20.2

initial state : 20.2

initial-condition response : 6.12.5

instantaneous frequency : 14.1.2

instantaneous phase : 14.1.2

intermodulation distortion : 5

interreciprocal : 10.1.3

inverse filter : 19.5

irreducible : 7.8.8

Jordan block : 20.10.1

Jordan canonical form : 20.10.1

Jordan form of a matrix : 20.10.1

ladder filter : 10.2.3

LADSPA plugins : 24.6

Laplace transform

analysis

linear systems : 17.5

mass-spring oscillator : 17.5.2

moving mass : 17.5.1

definition : 17

differentiation theorem : 17.4.2

existence : 17.1

linearity : 17.4.1

relation to z transform : 17.3

response to initial conditions : 17.5.1

theorems : 17.4

least-squares : 19.7

level-dependent gain : 5.7.1

Levinson recursion : 9.4.1

limiter : 5.7

linear algebra : 5.1

linear filter : 5.4.2

linear operator : 5.2

linear phase in audio applications : 12.6

linear prediction : 9.4.1

linear systems theory : 5

linear transformation : 5.2

linear, time-invariant filters : 5

linear-phase filter : 11 | 11.4

design : 11.4.2

examples : 11.4.1

linearity and time invariance : 5

log-swept sine-wave analysis : 2.3.1

logarithmic derivative : 8.6.6

long division : 7.8.5

lossless analog filters : 18.8.1

lossless filter : 15.2 | 16

examples : 16.1

lossless transfer function matrix : 16.3

losslessness implies allpass : 16

low shelf : 15.4

LTI filter matrix : 19.3

LTI filters : 5.5 | 5.10

LTI implications : 6.9

magnitude frequency response : 2.2 | 8.2

marginally stable : 9.4 | 9.4.2

Markov parameters : 20.1

Mason's gain formula : 10.1.3

Mason's gain theorem : 20.5

matched z transformation : 18.6

math summary : 14

matlab : 3

Matlab software : see softwaretextbf

matrices : 19.1 | 20

matrix : 5.2

matrix fraction descriptions : 5.2

matrix representations : 19

maximum-phase filters : 12.3

maximum-phase sequence : 12.3

median smoother : 5.3

memoryless nonlinearity : 5.3

message box (pd) : 24.5.1

MIMO digital filter : 5.2

minimum-delay sequence : 12.4

minimum-delay signals : 12.4

minimum-phase

filter : 12

polynomial : 12.2

sequence : 12.2

minimum-phase = fastest decay : 12.4

minimum-phase allpass decomposition : 12.5

minimum-phase computation from spectral magnitude data : 12.7

minimum-phase conversion of a spectrum : 23.11

minimum-phase filter design : 12.7

minimum-phase filters and signals : 12.7

minimum-phase sequence : 12.7

mixed-phase filter : 12.3

modal representation : 20.9 | 20.9 | 20.9.1

mode of vibration : 20.7.3

Moog VCF : 15.6.5

Moore-Penrose pseudoinverse : 19.7

moving average : 5.6

multi-input, multi-out (MIMO) digital filter : 5.2

multiplicity of a pole : 7.8.7.1

Muse Receptor : 24.7

negative-frequency component : 2.4.4

Newton's second law : 18.3.1

nonlinear distortion : 19.7

nonlinear filter : 5.7

analysis : 5.9

nonparametric signal processing : 12.7

nonrecursive digital filter : 6.1

normalized second-order resonator : 20.4.1

notch : 15.1.6

notch filter : 2.3.2

notch frequency : 15.1.4

null : 2.3.2

numerical issues : 10

observable modes : 20.7.3

observer canonical form : 20.7.1 | 20.7.2

Octave software : see softwaretextbf

odd impulse response : 11.3

one-off subpatch (pd) : 24.5.1

one-pole filter : 15.1.2

one-pole resonator, complex : 15.1.5

one-sided Laplace transform : 17

one-zero filter : 15.1.1

operator : 5.2

operator theory : 5.1

optimality in the Chebyshev sense : 8.6.4

order of a

filter : 6.4 | 9.1

pole : 17.2

polynomial : 9.1

rational function : 9.1

orthogonality principle : 19.7.1

output error minimization : 22.4.1

overdamped : 18.7

Padé-Prony method for filter design : 22.4.6

para-Hermitian conjugate : 8.6.6

paraconjugate transfer function : 16.2

parallel and series filter sections : 10.2.5

parallel combination : 7.7.2 | 18.5.1

parallel complex resonator : 10.2.2.1

parallel second-order filter sections : 4.12

parallel sos in matlab : 23.7

parametric equalizer : 15.5

paraunitary filter bank : 16.3.1.4

paraunitary MIMO filters : 16.3.1

partial fraction expansion : 4.12 | 7.8 | 10.2.2 | 15.1.5.1

alternate methods : 7.8.6

complex poles : 4.12.1

FIR part : 7.8.5

in matlab : 23.5

inversion : 7.8.4

repeated pole : 7.8.7 | 7.8.7.1

second order sections : 7.8.3

software : 7.8.10

summary : 7.8.9

passband : 2.2 | 8.5.2 | 11.2

pd

abstraction : 24.5.1

externals : 24.5.1

plugins : 24.5

subpatch : 24.5.1

peak filter : 15.5

peak gain : 15.6 | 15.6.3

peak gain versus resonance gain : 15.6.3

peaking eq filters : 15.5

perfect reconstruction filter bank : 16.3.1.4

periodic signal : 14.1.1

phase : 14.1.2

phase delay : 8.6.1

phase dispersion : 8.6.3 | 11.7

phase offset : 14.1.2

phase quadrature : 20.11.2

phase response : 2.3.1 | 8.3

phase unwrapping : 8.6.2

phasor : 2.4.3 | 14.3.3

phasor analysis : 2.4.3 | 14.3.2 | 14.3.3

phasor representation : 2.4.3

piecewise constant-phase filters : 11.2.2

plot

frequency data : 23.2

saving to disk : 23.3

plugin wrapper (pd) : 24.5.2

plugins : 24

LADSPA : 24.6

pd : 24.5

VST : 24.7

polar form of freq. response : 8.4

pole : 17.2

bandwidth : 9.5

frequency : 15.1.3

order : 17.2

time-constant : 9.6

pole-zero analysis : 4.11

poles : 4.11 | 7.6 | 7.8 | 9

poles and zeros : 9

poles of a state-space model : 20.6

poles outside unit circle : 9.7

polynomial

division in matlab : 7.8.10.3

long division : 7.8.10.3

multiplication : 7.8.10.2

multiplication in matlab : 7.8.10.2

order : 9.1

polynomial amplitude envelopes : 7.8.7.3

positive-frequency sinusoid : 2.4.4

predelay : 7.8.5

problems : see exercisestextbf

projection error : 19.7.1

Prony's method : 22.4.5

pseudoinverse : 19.7

Q (quality factor) : 18.7

relation to decay time : 18.7.1

radians per second : 14.1.1

ratio test : 17.2

rational function : 9.1

RC time constant : 18.4.2

real filter : 2.3.2 | 5.2 | 6.1 | 7.8.3

real signal : 5.1

real, even-impulse-response filter : 11.2

real-frequency-response filter : 11.2

Receptor : 24.7

recursive filter : 5.3 | 6.1

reflecting zeros inside unit circle : 9.9

reflection coefficients : 9.4.1

region of convergence : 9.7

repeated pole : 20.10

impulse response : 7.8.7.3

residue : 7.8

resonance : 15.1.3

resonant frequency : 18.7

resonator : 15.1.3

resonator bandwidth : 18.6

response to initial conditions : 6.12.4

right-half plane : 17

ring time : 6.12.1

ripple : 8.5.2

rms level : 5.7.1

roll-off : 8.5.2

running weighted sum : 5.6

samples : 14.1.1

sampling interval : 14.1.1

scalars : 5.1

scaling property of linear systems : 5.4.2

Schur recursion : 9.4.1

Schur-Cohn stability test : 9.4.1 | 9.4.1

seconds : 14.1.1

series and parallel filter sections : 10.2.5

series and parallel transfer functions : 7.7

series connection : 7.7.1

series second-order sections : 10.2.1

set notation : 5.1

shelving filters : 15.4

shift operator : 5.5

shift theorem for z transforms : 7.3

shift theorem for z transforms : 7.3.1

shift-invariant filter : 5.5

sideband images : 5

sifting property : 18.4.4

signal

complex, discrete-time : 5.1 | 5.1

definition : 5.1

flow graph : 6.2

operator : 5.4.2

plotting in matlab : 23.1 | 23.13

real, discrete-time : 5.1 | 5.1

representation : 14.1

signal flow graph : 4.2

signal space : 5.1

similarity transformation : 20.8 | 20.9.1

simple lowpass filter

analysis in matlab : 3 | 3.2 | 3.3 | 3.4

matlab implementation : 3.1

simulation diagram : 2.2.1 | 6.2

sinc function : 11.2.2

sine-wave analysis : 2.3.1 | 2.3.2 | 2.4.5

single-input, single-output (SISO) digital filters : 5.2

singular matrix : 20.10

sinusoid : 14.1.2

SISO digital filter : 5.2

sliding linear combination : 5.6

software : 23

Faust programming : 24

Matlab

frequency-response plot : 23.4 | 23.13

signal plots : 23.1

Matlab or Octave

clipping dB magnitude : 23.10

folding a signal about index zero : 23.9

frequency plots : 23.2

frequency-response computation : 8.5.1

group delay computation : 23.8

minimum phase conversion : 23.11

parallel second-order sections : 23.7

partial fraction expansion : 23.5 | 23.6

saving plots : 23.3

Octave

signal plots : 23.1

spectrum : 14.1.3

speech modeling : 9.4.1

speech synthesis : 10.2.3

split-radix FFT : 3.4

spring

compliance : 18.2.1

constant : 18.2.1

stiffness : 18.2.1

stability of a digital filter : 6.7 | 7.8.8 | 9.4

state space filter : 20

analysis : 20

analysis example

the digital waveguide oscillator : 20.11

complete response : 20.3

computation : 20.7.6

diagonalization : 20.9.1

example : 19.6.1

from difference equations : 20.7

impulse response : 20.1

matlab : 20.7.8

modal representation : 20.9

poles : 20.6

realization : 19.6 | 20

response from initial conditions : 20.2

similarity transformation : 20.8

transfer function : 20.4

transfer function example : 20.4.1

transposition : 20.5

state space realization : 7.8.6

steady state

analysis : 18.2

response : 6.12

signal : 6.12.3

Steinberg Media Technologies : 24.7

step-down procedure : 9.4.1

stopband : 2.2 | 8.5.2

strict right-half plane : 17

strictly proper transfer function : 7.8.3

subpatch (pd) : 24.5.1

sum of sinusoids : 14.3

superposition property : 5.4.2

superposition property of linear systems : 5.4.2 | 6.10

swanalmainplot : 23.13

swanalplot : 23.12

symmetric impulse response : 11.1 | 11.1

symmetric linear-phase FIR filter : 11.4

synthesis filter bank : 16.3.1.4

system diagram : 4.2 | 6.2

system function : 7

system identification : 19.7 | 19.7

tapped delay line : 6.11

Taylor series expansion : 2.4

Tellegen's theorem : 10.1.3

time constant : 9.6

time constant of a pole : 9.6

time domain : 14.1.3

time reversal inverts the locations of all zeros : 12.3

time-delay spectrometry : 2.3.1

time-invariant filter : 5.5 | 5.5

time-varying

filter coefficients : 15.6

filter example : 5.8

two-pole digital filters : 15.6

Toeplitz linear operator : 19.3

Toeplitz matrix : 19.3

transfer characteristics : 7

transfer function : 6.11.5 | 7

factored : 7.6

matrix : 20.4

of a state space filter : 20.4

to second-order-section matlab function tf2sos : 10.2.1

transient : 6.12.3 | 6.12.3

transient response : 6.12

transition band : 8.5.2

transition frequency : 15.4

transpose of a filter : 10.1.3 | 20.5

transposed direct form I (TDF-I) : 10.1.3

transposed direct form II (TDF-II) : 10.1.3

transposing the signal flow graph : 20.5

transversal filter : 6.11

tremolo : 5.8

trig identities : 14.2

trigonometric identity summary : 14.2.2

tunable two-pole digital filters : 15.6

two's complement wrap-around : 10.1.1.1

two-pole filter : 15.1.3

two-pole partial fraction expansion : 15.1.5.1

two-pole time-varying filter : 15.6

two-sided Laplace transform : 17

two-zero filter : 15.1.4

undamped : 18.7

underdamped : 18.7

unilateral z transform : 7.1

unilateral Laplace transform : 17

unit step function : 6.8 | 15.1.5

unstable poles : 9.7

unwrapping phase : 8.6.2

variable resonator : 15.6.1

variable two-pole digital filters : 15.6

VCF : 15.6

vector coordinate : 5.1

vector space : 5.1

vectorized algorithms : 3.1

virtual analog synthesis : 15.6.5

vocoder : 8.6.5

voltage divider rule : 18.4.2

voltage-controlled filters : 15.6

Volterra kernels : 5.9

vowel simulation : 10.2.3

VST plugins : 24.7

wave digital filters : 22.3.4

weighting function : 22.4.2

window method for FIR filter design : 22.1

z transform : 7.1

existence : 7.2

theorems

convolution : 7.3.2

shift : 7.3.1

zero at infinity : 18.4.5

zero initial state : 20.1

zero padding : 3.4 | 19.3 | 19.4

zero-input response : 19.6.1

zero-phase filter : 11.2

examples : 11.2.1 | 11.2.2

zero-state response : 6.12.5

zeros of a filter : 4.11

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About the Author: 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.