Introduction to Adaptive Signal Processing (II)

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EECS0712 Adaptive Signal Processing 2 Introduction to Adaptive Signal Processing (II) Processing (II) Assoc. Prof. Dr. Peerapol Yuvapoositanon Dept. of Electronic Engineering EECS0712 Adaptive Signal Processing http://embedsigproc.wordpress.com/eecs0712 Assoc. Prof. Dr. P.Yuvapoositanon ASP2-1

Transcript of Introduction to Adaptive Signal Processing (II)

Page 1: Introduction to Adaptive Signal Processing (II)

EECS0712 Adaptive Signal Processing2

Introduction to Adaptive SignalProcessing (II)

EECS0712 Adaptive Signal Processing2

Introduction to Adaptive SignalProcessing (II)

Assoc. Prof. Dr. Peerapol YuvapoositanonDept. of Electronic Engineering

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Assoc. Prof. Dr. P.YuvapoositanonASP2-1

Page 2: Introduction to Adaptive Signal Processing (II)

Content

• Digital Filters• Overview of Adaptive Signal Processing

Applications

• Digital Filters• Overview of Adaptive Signal Processing

Applications

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Page 3: Introduction to Adaptive Signal Processing (II)

Noise Cancellation

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Page 4: Introduction to Adaptive Signal Processing (II)

Ex 2.1 ECG Noise Cancellation

time index0 500 1000 1500

ECG

-1

-0.5

0

0.5

1ECG Noise Canceller

ECG

plus

Filte

red

Noi

se

3

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time index0 500 1000 1500

ECG

plus

Filte

red

Noi

se

-2

-1

0

1

2

time index0 500 1000 1500

ECG

with

Cle

aned

Noi

se

-2

-1

0

1

2

3

Page 5: Introduction to Adaptive Signal Processing (II)

Ex 2.1 ECG Noise Cancellation(cont.)

time index0 500 1000 1500

Noi

se

-2

-1

0

1

2

2

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time index0 500 1000 1500

Filte

red

Noi

se

-2

-1

0

1

time index0 500 1000 1500

Erro

rSqu

ared

0

0.5

1

1.5

2

2.5

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Prediction

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Page 7: Introduction to Adaptive Signal Processing (II)

Ex 2.2 Chirp Signal Prediction

time index0 200 400 600 800 1000 1200 1400 1600 1800 2000

Ampl

itude

-1

-0.5

0

0.5

1Desired signal d(t)

2Desired signal d(t) with noise

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time index0 200 400 600 800 1000 1200 1400 1600 1800 2000

Ampl

itude

-2

-1

0

1

time index0 200 400 600 800 1000 1200 1400 1600 1800 2000

Ampl

itude

-2

-1

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2Predicted signal y(t)

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Ex 2.2 Chirp Signal Prediction

0.8

1

1.2Error Squared e2(t)

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time index0 200 400 600 800 1000 1200 1400 1600 1800 2000

Ampl

itude

0

0.2

0.4

0.6

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Ex 2.2 Chirp Signal Prediction

0.06

0.08

0.1Predictor Tap Weights

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Tap weight index0 10 20 30 40 50 60 70 80 90 100

Tap

wei

ghtv

alue

-0.02

0

0.02

0.04

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Inverse Modelling

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Ex 2.3 Channel Equalisation

Bits0 50 100 150 200 250 300 350 400 450 500

Ampl

itude

(V)

-1

-0.5

0

0.5

1Transmitted Signal

4Received Signal

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Bits0 50 100 150 200 250 300 350 400 450 500

Ampl

itude

(V)

-6

-4

-2

0

2

Bits0 50 100 150 200 250 300 350 400 450 500

Ampl

itude

(V)

-2

-1

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2Equalized Signal

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Ex 2.3 Channel Equalisation

1

1.2

1.4Error Squared

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Bits0 50 100 150 200 250 300 350 400 450 500

Ampl

itude

(V)

0

0.2

0.4

0.6

0.8

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System Identification

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Ex 2.4 System Identificationsi

gnal

valu

e

-1

-0.5

0

0.5

1

1.5System Identification of an FIR filter

Desired d(t)Estimated y(t)

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time index0 50 100 150 200 250 300 350 400 450 500

-1.5

time index0 50 100 150 200 250 300 350 400 450 500

Erro

rSqu

ared

0

0.2

0.4

0.6

0.8

1

1.2Error Squared e2(t)

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Digital Filters

• Digital Filters is a digital device adjustingfrequency and magnitude

• There are two types of Finite ImpulseResponse (FIR) and Infinite Impulse Response(IIR)– FIR has no feedback– IIR has feedback

• Digital Filters is a digital device adjustingfrequency and magnitude

• There are two types of Finite ImpulseResponse (FIR) and Infinite Impulse Response(IIR)– FIR has no feedback– IIR has feedback

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• An FIR filter has no feedback

Finite Impulse Response (FIR)

DelayDelay

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Infinite Impulse Response (IIR)

• An IIR filter has feedback

FeedbackFeedbackFeedbackFeedback

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Page 18: Introduction to Adaptive Signal Processing (II)

Transfer Function I

• Transfer function= A ratio of z-transform• Z-Transform• Transfer function= A ratio of z-transform• Z-Transform

z -Transform

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Page 19: Introduction to Adaptive Signal Processing (II)

Transfer Function

• Transfer function

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Page 20: Introduction to Adaptive Signal Processing (II)

Use z-Transform to find FrequencyResponse

• Replace z with ,

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Frequency Response from Poles andZeros Zk=

Zeros

Pk=Poles

Magnitude of

responseat omega

Example

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Pk=PolesExample

Page 22: Introduction to Adaptive Signal Processing (II)

Example for Frequency Response

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Example for Frequency Response

• Put together

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Page 24: Introduction to Adaptive Signal Processing (II)

To Summarise…

The coefficients of a DigitalFilter determine the desired

frequency response.

The coefficients of a DigitalFilter determine the desired

frequency response.

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Page 25: Introduction to Adaptive Signal Processing (II)

Overview of AdaptiveSignal Processing

Overview of AdaptiveSignal Processing

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Why we need adaptive?

• Because environment is always changing.• System needs to be adaptable.• In electrical engineering, the environment is

systems defined by transfer function.

• Because environment is always changing.• System needs to be adaptable.• In electrical engineering, the environment is

systems defined by transfer function.

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Page 27: Introduction to Adaptive Signal Processing (II)

Multipath in Wireless Communications

• Signal from transmitter may reach receiverwith multipath signals

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Multipath

Page 28: Introduction to Adaptive Signal Processing (II)

Channel Equalisation

Without multipath

Channel

11 00 11 00

11 0011..33

..66

Without multipath

With multipath

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Loss ofInfo.

Page 29: Introduction to Adaptive Signal Processing (II)

Frequency fading channel• Multipath Channel is also called Frequency

fading channel

H(f)=1Without multipath

• Multipath Channel is also called Frequencyfading channel

fftt

FourierTransform

fftt

H(f)

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With multipath

Fading

Page 30: Introduction to Adaptive Signal Processing (II)

Channel Equalization

Channel

H(z)=1

11 00 11 00

11 00EECS0712 Adaptive Signal Processing

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ff

ff

H(z)=1

H(z)11..33

..66

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Basic Equalization II

• If we knew the channel H(z), we put a filterW(z) at the receiver

Channel DigitalFilter

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Channel DigitalFilter

H(z)

xx11 00 11 00

11..33

..66W(z)

H(z) x W(z) = 1

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Basic Equalization III

• Equaliser is an inverse channel estimation

Channel EqualizerChannel Equalizer

H(z) W(z)=1/H(z)

xx

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11 00 11 00

11..33

..66

W(z)= H-1(z)

Page 33: Introduction to Adaptive Signal Processing (II)

Basic Equalization II

• Adaptive Equaliser finds H-1(z) automatically

Channel AdaptiveEqualizer ++ ee

dd

yy++

--xxChannel AdaptiveEqualizer

H(z)

xx

++ ee--

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11 00 ..6611..33

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LMS Adaptive Algorithm

• error= d-yNew value = Old Value + Step * Error* Input

For n=1:N

AlgorithmAlgorithm

w(n)=w(n-1) + mu*e(n)*x(n)

For n=1:N

end

e(n)= d(n)-y(n)

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Page 35: Introduction to Adaptive Signal Processing (II)

To Summarise…

The coefficients of AdaptiveEqualiser are adapted to the

inverse channel H-1(z).

The coefficients of AdaptiveEqualiser are adapted to the

inverse channel H-1(z).

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Page 36: Introduction to Adaptive Signal Processing (II)

LMS Algorithm Block

• บลอ็ก LMS

Normalization

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Page 37: Introduction to Adaptive Signal Processing (II)

Example of Adaptive Equalization

• Least Mean Square (LMS) for AdaptiveEqualizer

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Page 38: Introduction to Adaptive Signal Processing (II)

Signal+Noise, Signal and Error2

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Trend ofError2

Page 39: Introduction to Adaptive Signal Processing (II)

Equalizer Response

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Page 40: Introduction to Adaptive Signal Processing (II)

Final Tap weights

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Page 41: Introduction to Adaptive Signal Processing (II)

• Anti phase =Cancellation

Basic of Noise Cancellation

Quiet zoneQuiet zonenn--nn

• Anti phase =Cancellation

FeedbackFeedbackANCANC

NoiseNoisePilot MicPilot Mic

LoudspeakerLoudspeakernn

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Page 42: Introduction to Adaptive Signal Processing (II)

Active Noise Cancellation Headphones

• ANC Headphones

LXLX--1818 Active Noise Cancelling HeadphonesActive Noise Cancelling Headphones

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Page 43: Introduction to Adaptive Signal Processing (II)

Diagram of Active Noise CancellationHeadphones

nn nn11 22Pilot Mic

Quiet Zone

DSPAdaptiveAlgorithm

H(z)H(z)

yy

33

H(z) =Acoustic Transfer Function

Ext.MicExt.Mic

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Speaker

DSPAdaptiveAlgorithm

Page 44: Introduction to Adaptive Signal Processing (II)

ANC

LoudspeakerLoudspeaker

Exterior MicExterior Mic

yynn

Pilot MicPilot Mic

nn

FIRFIR

AlgorithmAlgorithm

++ee

yynn

ANCANC

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Page 45: Introduction to Adaptive Signal Processing (II)

ANC Simulink Model

• Dspanc.

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