introduction to adaptive signal processing (ii)
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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
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Content
• Digital Filters• Overview of Adaptive Signal Processing
Applications
• Digital Filters• Overview of Adaptive Signal Processing
Applications
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Noise Cancellation
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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
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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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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
0
1
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
0
1
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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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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Transfer Function
• Transfer function
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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
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Example for Frequency Response
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Example for Frequency Response
• Put together
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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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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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Multipath in Wireless Communications
• Signal from transmitter may reach receiverwith multipath signals
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Multipath
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Channel Equalisation
Without multipath
Channel
11 00 11 00
11 0011..33
..66
Without multipath
With multipath
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Loss ofInfo.
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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
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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)
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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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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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LMS Algorithm Block
• บลอ็ก LMS
Normalization
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Example of Adaptive Equalization
• Least Mean Square (LMS) for AdaptiveEqualizer
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Signal+Noise, Signal and Error2
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Trend ofError2
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Equalizer Response
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Final Tap weights
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• Anti phase =Cancellation
Basic of Noise Cancellation
Quiet zoneQuiet zonenn--nn
• Anti phase =Cancellation
FeedbackFeedbackANCANC
NoiseNoisePilot MicPilot Mic
LoudspeakerLoudspeakernn
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Active Noise Cancellation Headphones
• ANC Headphones
LXLX--1818 Active Noise Cancelling HeadphonesActive Noise Cancelling Headphones
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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
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ANC
LoudspeakerLoudspeaker
Exterior MicExterior Mic
yynn
Pilot MicPilot Mic
nn
FIRFIR
AlgorithmAlgorithm
++ee
yynn
ANCANC
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ANC Simulink Model
• Dspanc.
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