**NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW
VERSION:** "Introduction to Digital
Filters with Audio Applications", by Julius O. Smith III,
Copyright © *2017-11-26* by Julius O. Smith III -
Center for Computer Research
in Music and Acoustics (CCRMA), Stanford University

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## Index

-transform- Convolution Representation
norms- Specific Norms
norms- Specific Norms
amplitude response- Frequency Response | Frequency Response
Banach Space- Vector Space Concepts
Cauchy sequence- Vector Space Concepts
causal- Difference Equation | Specific Norms
Chebyshev norm- Specific Norms
cluster point- Concavity (Convexity)
concave- Concavity (Convexity)
concave error surface- Concave Norms
concave functional- Concavity (Convexity)
concave hull- Concavity (Convexity)
convergence, existence of minimizer- Concave Norms
convergence, global- Concave Norms
difference equation- Difference Equation
difference equation coefficients- Difference Equation
filter- Introduction to Digital Filter
filter coefficients- Difference Equation
filter delay for amplitude envelopes- Phase Delay and Group
filter order- Difference Equation
filter power response- Frequency Response
filter time delay- Phase Delay and Group
frequency response- Frequency Response
Frobenious norm- Specific Norms
functional- Concavity (Convexity)
global convergence, conditions for- Concave Norms
global minimizer- Concavity (Convexity)
gradient- Gradient Descent
Gradient Method- Gradient Descent
group delay- Phase Delay and Group
Hankel matrix- Specific Norms
Hankel norm- Specific Norms
Hessian- Gradient Descent
impulse- Difference Equation
impulse response- Difference Equation
induced norm- Specific Norms
linear- Linearity and Time-Invariance
linear filter- Linearity and Time-Invariance
linear functional- Concavity (Convexity)
linear space- Vector Space Concepts
local minimizer- Concavity (Convexity)
LTI filters- Linearity and Time-Invariance
metric space- Vector Space Concepts
Newton's method- Newton's Method
norm- Vector Space Concepts
normed linear space- Vector Space Concepts
outer disk- Positive Real Functions
phase delay- Phase Delay and Group
phase response- Frequency Response | Frequency Response
phase response at zero frequency- Phase Delay and Group
positive real- Positive Real Functions
pseudo-norm- Vector Space Concepts
real filter- Difference Equation
root mean square norm- Specific Norms
Schur function- Relation to Schur Functions
signal- Introduction to Digital Filter
spectral norm- Specific Norms
stable- Difference Equation
stationary point- Gradient Descent
strictly concave functional- Concavity (Convexity)
time-invariant- Linearity and Time-Invariance
transfer function- Convolution Representation
uniform norm- Specific Norms
uniformly concave- Concavity (Convexity)
weighted norms- Specific Norms