- 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