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Brandon RumbergBrandon RumbergWest Virginia UniversityWest Virginia Universitybrumberg@mix.wvu.edubrumberg@mix.wvu.edu

Analog Filter BanksAnalog Filter Banks

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Themes of this talk

• Analog VLSI–Analog audio

processing

• Analog filter-bank –Relation to wavelets

–Relation to cochlea

• Computation based on physics of devices

Analog Front-end

FeatureExtraction

FeatureExtraction

FeatureExtraction

Filterbank

A/D

Digital Back-end

Higher-LevelProcessing

A/D

A/D

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Ubiquitous Sensors

• Sensors are extremely:–Small

–Cheap

• Devices are:–Small

–Battery powered

–Always on

• With bench top sensors it wouldn't be an issue

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Analog VLSI

• Relation to traditional analog–Not just op-amps and data converters

–Perform computation

• Standard CMOS–Piggy-back on digital developments

–Weak inversion (sub-threshold)

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Analog VLSI

• Low power–Subthreshold

• Fewer transistors

• Small

• Complex operations based on physics

• Lack of precision–Resolution <=>

dynamic range

–Noise

–Nonlinearity

–Biases

• Lack of programming–Hard to reuse earlier

work

• Difficult to design

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Subthreshold

• Weak inversion–Exponential relationship

–Low currents• 0.1pA <-> 1μA I=I0

WLe

κV gsUT

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Floating Gates

• Nonvolatile memory

• Biasing problem

• Add some reconfigurability–Program bias currents

• Adaptation–Learning

–Neural Nets

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Neuromorphic

• Biologically inspired–Humans great at:

• Perception

• Adaptation

• Efficient

• Historically related to Analog VLSI

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Analog VLSI for Audio ProcessingAnalog VLSI for Audio Processing

Analog Front-end

FeatureExtraction

FeatureExtraction

FeatureExtraction

Filterbank

A/D

Digital Back-end

Higher-LevelProcessing

A/D

A/D

Analog/Digital Synergy•Analog: General Tasks•Digital: Specific Tasks

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Analog Filter Bank

• Array of resonators

• Relation to wavelets–Constant relative

bandwidth

–Similar algorithms?

• Time resolution vs. frequency resolution–Resonance

101

102

103

104

-60

-40

-20

0

Frequency (Hz)

Gai

n (d

B)

out1 out2 out3 out4 out5outn

Vin

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CochleaCochlea

Frequency Decomposition•Position dependent

frequency response•Exponential tap spacing

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Silicon CochleaeSilicon Cochleae

•Cochlea resonators aren't independent

outnout2 out3 out4 out5

Vin

out1

101

102

103

104

-60

-40

-20

0

Frequency (Hz)

Gai

n (d

B)

W W W

W W W

Vin

out1 out2 out3 outn

101

102

103

104

105

-30

-25

-20

-15

-10

-5

0

5

10

15

20

Frequency (Hz)

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Quality Factor

• Resonance

• Possibility to do

adaptive Q

C4

101

102

103

104

105

-60

-50

-40

-30

-20

-10

0

10

Frequency (Hz)

Mag

nitu

de (

dB)

C4 Tuning; Gmratio

= 7 -- 1500

100

102

104

106

108

-100

-80

-60

-40

-20

0

20

Frequency (Hz)

Mag

nitu

de (

dB)

Tow Thomas Tuning

Q=f cBW

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BPF Design

• Struggle for high precision–Limited by noise and

nonlinearities

• Has to work across audio range–3 orders of magnitude change in

frequency

–3 orders of magnitude change in current

• Limited by programming precision and transition to strong inversion

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Filter Bank Questions

• How many taps?

• How much Q?

• Phase?

• Orthogonal

filters?

• Reconstruction?

• What is the output?

101

102

103

104

105

-70

-60

-50

-40

-30

-20

-10

0

10

20

Frequency (Hz)

Mag

nitu

de (

dB)

8 taps; Q = 1.2583; Ripple = 0.81347

101

102

103

104

105

-70

-60

-50

-40

-30

-20

-10

0

10

20

Frequency (Hz)

Mag

nitu

de (

dB)

18 taps; Q = 2.033; Ripple = 0.23548

101

102

103

104

105

-40

-30

-20

-10

0

10

20

30

40

Frequency (Hz)M

agni

tude

(dB

)

8 taps; Q = 2.1536; Ripple = 2.7323

101

102

103

104

105

-50

-40

-30

-20

-10

0

10

20

30

40

Frequency (Hz)

Mag

nitu

de (

dB)

18 taps; Q = 5.6143; Ripple = 2.0548

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Response to Sine

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Two Tones

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Response to Speech

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Response to Pulse

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Speech Spectrogram

Circuit ModelFFT

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Frequency Response

101

102

103

104

105

-80

-70

-60

-50

-40

-30

-20

-10

0

10

Frequency (Hz)

Mag

nitu

de (

dB)

16 taps

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Analog Sub-band Processing

• Peak detector

• Vector-matrix multiplier

• Comparator

• Rectifier

• Differentiator

• Nonlinear– tanh

–sinh

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To do...

• Analytic characterization of analog filter banks

• Full portfolio of sub-band processing structures

• DSP back-ends–Full system

–Algorithms

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