Proportional Bandwidth Filter Banks

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Proportional Bandwidth Filter Banks

• fred harris
• San Diego State University

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PHOBIA GLOSSARY Authorities say a seemingly
endless variety of objects or phenomenon can
trigger phobias. Most of them like fear of
heights, or fear of water do not incapacitate
an individual Others do. Some phobias are unique
to individuals most others have appeared
frequently enough to have been given a name.
Below is a list of medically recognized phobias,
with their Latin or Greek names presented first,
followed by their English translation. ARACHNEPHO
BIA - Fear of Spiders.
GYNEPHOBIA Fear of women. AMAXOPHOBIA
HELIOPHOBIA Fear of sun. or
HAMAXOPHOBIA Fear of vehicles.
HODCPHOBIA Fear of traveling. ANDROPHOBIA
Fear of Males. HYGROPHOBIA
Fear of dampness. AUTOPHOBIA Fear of
Self. HYPNOPHOBIA Fear of
sleep. AUTOMYSOPHOBIA Fear of being dirty.
ICHTHYOPHOBIA Fear of fish
or BELONEPHOBIA Fear of pins.
MYSOPHOBIA. BROMIDOSIPHOBIA
or RHYPOPHOBIA Fear of dirt.. or
OSPHRESIOPHOBIA OMBROPHOBIA
Fear of rain. or OSMOPHOBIA Fear of
odors. PANPHOBIA
Fear of everything. CYNOPHOBIA Fear of
dogs. PENIAPHOBIA Fear of
poverty. ENTOMOPHOBIA Fear of Insects.
PHARMACOPHOBIA Fear of
drugs. ERGASIOPHOBIA PHOBOPHOBIA
Fear of phobias. or PONOPHOBIA
Fear of work. SIDERODROMOPHONIA
Fear of trains.. GAMOPHOBIA Fear of
marriage. SPECTRAPHOBIA
Fear of Fourier GEPHYROPHOBIA Fear of
crossing a bridge.
transforms. GRAPHOPHOBIA
Fear of writing.
VACCINOPHOBIA Fear of vaccination
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Why Proportional Bandwidth?

• The Ear-Brain System Performs a Proportional
  Bandwidth Spectral Decomposition.
• Signal Enhancement and Source Coding of Acoustic
  Signals are matched to the Ear-Brain Resolution
• Examples MP-3 Filter Bank
• ISO Graphic
  Equalizers
• Sound Pressure
  Level Analyzers
• Matched Filter For Harmonically Related Spectral
  Lines
• Acoustic Signature and Synchronous Spectrum
• for Vibration and Rotating Machinery
  Diagnostics

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Proportional Bandwidth Filter Bank With Step And
Repeat Processing
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2-to-1 Down Sampling to Shift Octaves By Aliasing
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Half-Band Filter and 2-to-1 Downsampler
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Half Band Filter Polyphase Partition
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Noble Identity Applied to Half Band Polyphase
Partition
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Half Band Down Sample Filter Operating at Output
Rate
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Prototype Filter For Recursive All-Pass Structure
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Fundamental All-Pass Filter Building Block
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Pole Zero Diagram of All Pass Filter Building
Block
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Phase Response of Fundamental All-Pass Filter
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Two Path Filter Each Path is Cascade of
Fundamental Stages
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Phase Response of Two paths of Two-Path Recursive
Filter
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4-Coefficient, Two-Path Filter
Path-0 Polynomial Coefficients Filter-0
1 0 0.101467517 Filter-2 1 0
0.612422841   Path-1 Polynomial Coefficients
Filter-1 1 0 0.342095596 Filter-3 1
0 0.867647439
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Characterization of 2-Path Half-Band Filter
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Frequency response of Successive Half Band Filters
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Very Efficient Cascade of Half-Band Filters
Workload 21 1/2 1/4 1/8....
lt 4 Multiples for Entire
Cascade of Half-Band Filters
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Proportional Bandwidth Filter Bank
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Can Change Bandwidth of 2-Path Recursive Filter
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Pole-Zero Plot of Low Pass Filter With Reduced
Bandwidth
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Low-Pass to Low-Pass Transformation
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Effect on Signal Flow Diagram of Low-Pass to
Low-Pass Transformation

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Pole-Zero Shift Due to LP-to-LP Transformation
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Can Change Center Frequency of 2-Path Recursive
Filter
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Pole-Zero Plot of Low Pass Filter With Tuned to
New Center FRequency
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Low-Pass to Band-Pass Transformation
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All Together Now
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Effect on Signal Flow Diagram of Low-Pass to
Band-Pass Transformation
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Pole-Zero Change Due to LP-to-BP Transformation
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Six-Proportional Bandwidth Filters Spanning
3/16-to-3/8 fs
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An Octave Spanned by 6-Proportional Bandwidth
Filters
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ISO Standard Frequencies for 15-band Proportional
Filter Bank
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ISO 15-Band Proportional BW Filter Bank
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Frequency Response 10-bands of 15-Stage
Proportional BW Filter Bank
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Work Load
First Stage Half Band 2-Ops/Input
Filter A 19-Ops/Input
Filter B
19-Ops/Input Total First Stage
40-Ops/Input All Ten Octaves lt
80-OPs/Input
or lt 6-Ops/Input Per Filter
(15-Filters)
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1/12-Octave Proportional BW Filter Bank
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Work Load
First Stage Half Band
3-Ops/Input 12 Proportional
Bandwidth Filters 72 -
Ops/Input Total First Stage
75 - Ops/Input All Ten
Octaves lt 750 - Ops/Input
or lt 6.25 -
Ops/Input Per Filter
(120 Filters)
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