Ch1 EE412 Introduction to DSP and .ppt
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About This Presentation
DSP stands for Digital Signal Processing. It's a branch of engineering that deals with the manipulation of digital signals using algorithms and mathematical techniques. DSP is used in a wide range of applications such as audio and speech processing, image and video processing, communications, ra...
Slide Content
Digital Signal Processing (DSP)
Fundamentals
Fundamentals
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Copyright (C) 2005
Güner Arslan
351M Digital Signal Processing
(Spring 2005)
3
Signal Processing
Humans are the most advanced signal processors
speech and pattern recognition, speech
synthesis,…
We encounter many types of signals in various
applications
Electrical signals: voltage, current, magnetic and
electric fields,…
Mechanical signals: velocity, force,
displacement,…
Acoustic signals: sound, vibration,…
Other signals: pressure, temperature,…
Güner Arslan
351M Digital Signal Processing
(Spring 2005)
3
Signal Processing
Humans are the most advanced signal processors
speech and pattern recognition, speech
synthesis,…
We encounter many types of signals in various
applications
Electrical signals: voltage, current, magnetic and
electric fields,…
Mechanical signals: velocity, force,
displacement,…
Acoustic signals: sound, vibration,…
Other signals: pressure, temperature,…
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DSP’s process signals
Signal–a detectablephysical
quantityor impulse (as a voltage,
current, or magnetic field strength)
by which messages or information
can be transmitted (Webster
Dictionary)
DSP’s process signals
Signal–a detectablephysical
quantityor impulse (as a voltage,
current, or magnetic field strength)
by which messages or information
can be transmitted (Webster
Dictionary)
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Introduction to DSP
Signal Characteristics:
Signals are Physical Quantities:
Signals are Measurable
Signals are Analog
Signals Contain Information.
Examples:
Temperature[
o
C]
Pressure [Newtons/m
2
] or [Pa]
Mass [kg]
Speed [m/s]
Acceleration[m/s
2
]
Torque [Newton*m]
Voltage [Volts]
Current [Amps]
Power [Watts]
Introduction to DSP
Signal Characteristics:
Signals are Physical Quantities:
Signals are Measurable
Signals are Analog
Signals Contain Information.
Examples:
Temperature[
o
C]
Pressure [Newtons/m
2
] or [Pa]
Mass [kg]
Speed [m/s]
Acceleration[m/s
2
]
Torque [Newton*m]
Voltage [Volts]
Current [Amps]
Power [Watts]
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Why Processing Signals?
Extraction of Information
Amplitude
Phase
Frequency
Spectral Content
Transform the Signal
FDMA (Frequency Division
Multiple Access)
TDMA (Time Division Multiple
Access)
CDMA (Code Division Multiple
Access)
Compress Data
ADPCM (Adaptive Differential
Pulse Code Modulation)
CELP (Code Excited Linear
Prediction)
MPEG (Moving Picture Experts
Group)
HDTV (High Definition TV)
Generate Feedback
Control Signal
Robotics (ASIMOV)
Vehicle Manufacturing
Process Control
Extraction of Signal in
Noise
Filtering
Autocorrelation
Convolution
Store Signals in Digital
Format for Analysis
FFT
…
Why Processing Signals?
Extraction of Information
Amplitude
Phase
Frequency
Spectral Content
Transform the Signal
FDMA (Frequency Division
Multiple Access)
TDMA (Time Division Multiple
Access)
CDMA (Code Division Multiple
Access)
Compress Data
ADPCM (Adaptive Differential
Pulse Code Modulation)
CELP (Code Excited Linear
Prediction)
MPEG (Moving Picture Experts
Group)
HDTV (High Definition TV)
Generate Feedback
Control Signal
Robotics (ASIMOV)
Vehicle Manufacturing
Process Control
Extraction of Signal in
Noise
Filtering
Autocorrelation
Convolution
Store Signals in Digital
Format for Analysis
FFT
…
M. J. Roberts -All Rights Reserved. Edited by Dr.
Robert Akl
8
In digital telephones, voice is sampled every 125μsec, or at a
sampling frequency of 8,000 Hz. Each sample is quantized into
an 8-bit word, or 256 levels. This gives an overall rate of 8x0008
= 64;000 bits per second. The
worldwide digital telephony network, therefore, is composed primarily of
channels
capable of carrying 64,000 bits per second, or multiples of this (so that
multiple
telephone channels can be carried together). In cellular phones, voice
samples are
further compressed to bit rates of 8,000 to 32,000 bits per second
Robert Akl
8
In digital telephones, voice is sampled every 125μsec, or at a
sampling frequency of 8,000 Hz. Each sample is quantized into
an 8-bit word, or 256 levels. This gives an overall rate of 8x0008
= 64;000 bits per second. The
worldwide digital telephony network, therefore, is composed primarily of
channels
capable of carrying 64,000 bits per second, or multiples of this (so that
multiple
telephone channels can be carried together). In cellular phones, voice
samples are
further compressed to bit rates of 8,000 to 32,000 bits per second
M. J. Roberts -All Rights Reserved. Edited by Dr.
Robert Akl
9
whose "phase" is now . It has been shifted by radians
Robert Akl
9
whose "phase" is now . It has been shifted by radians
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Robert Akl
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For infinitely long sinusoids, a change in is the same as a shift in time, such as a time delay. If is delayed (time-shifted) by of its cycle, it becomes:
whose "phase" is now . It has been shifted by radians
Robert Akl
10
For infinitely long sinusoids, a change in is the same as a shift in time, such as a time delay. If is delayed (time-shifted) by of its cycle, it becomes:
whose "phase" is now . It has been shifted by radians
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Robert Akl
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Calculation between phase angle φ°in degrees (deg), the time delay Δ
tand the
frequency fis:
Phase angle (deg)
(Time shift) Time difference
Frequency
λ = c/ fandc= 343 m/s at 20°C.
Calculation between phase angle φin radians (rad),
the time shift or time delay Δ t,
and the frequency fis:
Phase angle (rad)
"Bogen" means "radians". (Time shift) Time difference
Frequency
Time = path length /speed of sound
Robert Akl
11
Calculation between phase angle φ°in degrees (deg), the time delay Δ
tand the
frequency fis:
Phase angle (deg)
(Time shift) Time difference
Frequency
λ = c/ fandc= 343 m/s at 20°C.
Calculation between phase angle φin radians (rad),
the time shift or time delay Δ t,
and the frequency fis:
Phase angle (rad)
"Bogen" means "radians". (Time shift) Time difference
Frequency
Time = path length /speed of sound
M. J. Roberts -All Rights Reserved. Edited by Dr.
Robert Akl
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S(t) = A sin(ωot−ϕ)
Robert Akl
12
S(t) = A sin(ωot−ϕ)
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Robert Akl
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Robert Akl
13
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Robert Akl
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Robert Akl
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Robert Akl
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Robert Akl
15
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In this class, analog signals are electrical.
Sensors: are devices that convert other
physical quantities (temperature,
pressure, etc.) to electrical signals.
Sensor output is analog and need to be
converted to digital to be processed by
computer
In this class, analog signals are electrical.
Sensors: are devices that convert other
physical quantities (temperature,
pressure, etc.) to electrical signals.
Sensor output is analog and need to be
converted to digital to be processed by
computer
Data : student grades (80, 60, .., 90,
75), Temp’s over days of the month,
Information: process data : (grade
average, % success, ), ( today is hot,
average temp over month,..)
Knowledge: use data and information
to conclude / experience : if .., then..
(if it is hot use umbrella /..
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75), Temp’s over days of the month,
Information: process data : (grade
average, % success, ), ( today is hot,
average temp over month,..)
Knowledge: use data and information
to conclude / experience : if .., then..
(if it is hot use umbrella /..
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Signal : convert data/../ to volt/current
ready to be sent.
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Text
data
Binary
data
Digital signal
3 011
7 111
ready to be sent.
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Text
data
Binary
data
Digital signal
3 011
7 111
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What is DSP?0
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Analog-to-Digital and Digital-to-Analog
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Digital Telephone Communication System Example:
Digital Telephone Communication System Example:
Signal Types
M. J. Roberts -All Rights Reserved. Edited by Dr.
Robert Akl
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M. J. Roberts -All Rights Reserved. Edited by Dr.
Robert Akl
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Conversions Between Signal
Types
Sampling
Quantizing
Encoding
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Robert Akl
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Types
Sampling
Quantizing
Encoding
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Robert Akl
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Message Encoded in ASCII
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Robert Akl
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M. J. Roberts -All Rights Reserved. Edited by Dr.
Robert Akl
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Noisy Message Encoded in ASCII
Progressively
noisier
signals
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Robert Akl
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Progressively
noisier
signals
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Robert Akl
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Bit Recovery in a Digital Signal
Using Filtering
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Robert Akl
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Using Filtering
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Robert Akl
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Assignment 1 (Matlabimplementation) signal regeneration
-Generate noiseless clean signal X(n) :pulse train of 0’s and 1’s
-Generate discrete random noise N(n) (or Gaussian noise) using
random generate
-Noisy signal Y(n) = x(n) + n(n)
-Select a threshold level TH
-Apply condition: if y(n) >=TH; then y1(n) =1;
- else; y1(n) =0
-Compare x(n) to y1(n); and find error bits
-Change noise amplitude (higher/ lower) and repeat signal
regeneration
-Put your conclusion on the effect of high noise level on bit error
rate ( higher noise ; higher error bits).
Assignment 1 (Matlabimplementation) signal regeneration
-Generate noiseless clean signal X(n) :pulse train of 0’s and 1’s
-Generate discrete random noise N(n) (or Gaussian noise) using
random generate
-Noisy signal Y(n) = x(n) + n(n)
-Select a threshold level TH
-Apply condition: if y(n) >=TH; then y1(n) =1;
- else; y1(n) =0
-Compare x(n) to y1(n); and find error bits
-Change noise amplitude (higher/ lower) and repeat signal
regeneration
-Put your conclusion on the effect of high noise level on bit error
rate ( higher noise ; higher error bits).
Image Filtering to Aid
Perception
Original X-Ray ImageFiltered X-Ray Image
M. J. Roberts -All Rights Reserved. Edited by Dr.
Robert Akl
38
Perception
Original X-Ray ImageFiltered X-Ray Image
M. J. Roberts -All Rights Reserved. Edited by Dr.
Robert Akl
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Discrete-Time Systems
In a discrete-timesystem events occur atpoints in time but not
betweenthose points. The most important example is a digital
computer. Significant events occur at the end of each clock
cycle and nothing of significance (to the computer user) happens
between those points in time.
Discrete-time systems can be described by difference(not
differential) equations. Let a discrete-time system generate an
excitation signal y[n] where nis the number of discrete-time
intervals that have elapsed since some beginning time n= 0.
Then, for example a simple discrete-time system might beyn[]=1.97yn-1[]-yn-2[]
M. J. Roberts -All Rights Reserved. Edited by Dr.
Robert Akl
39
In a discrete-timesystem events occur atpoints in time but not
betweenthose points. The most important example is a digital
computer. Significant events occur at the end of each clock
cycle and nothing of significance (to the computer user) happens
between those points in time.
Discrete-time systems can be described by difference(not
differential) equations. Let a discrete-time system generate an
excitation signal y[n] where nis the number of discrete-time
intervals that have elapsed since some beginning time n= 0.
Then, for example a simple discrete-time system might beyn[]=1.97yn-1[]-yn-2[]
M. J. Roberts -All Rights Reserved. Edited by Dr.
Robert Akl
39
Discrete-Time Systems
The equationyn[]=1.97yn-1[]-yn-2[]
says in words “The signal value at any time nis 1.97 times the signal value at the
previous time [n-1] minus the signal value at the time before that
[n-2].”
If we know the signal value at any two times, we can compute its
value at all other (discrete) times. This is quite similar to a
second-order differential equation for which knowledge of two
independent initial conditions allows us to find the solution for all
time and the solution methods are very similar.
M. J. Roberts -All Rights Reserved. Edited by Dr.
Robert Akl
40
The equationyn[]=1.97yn-1[]-yn-2[]
says in words “The signal value at any time nis 1.97 times the signal value at the
previous time [n-1] minus the signal value at the time before that
[n-2].”
If we know the signal value at any two times, we can compute its
value at all other (discrete) times. This is quite similar to a
second-order differential equation for which knowledge of two
independent initial conditions allows us to find the solution for all
time and the solution methods are very similar.
M. J. Roberts -All Rights Reserved. Edited by Dr.
Robert Akl
40
Discrete-Time Systemsyn[]=1.97yn-1[]-yn-2[]
We could solve this equation by iteration using a computer.
yn=1;yn1=0;
while1,
yn2=yn1;yn1=yn;yn=1.97*yn1-yn2;
end
We could also describe the system
with a block diagram.
Initial Conditions
(“D”means delay one unit in discrete
time.)
M. J. Roberts -All Rights Reserved. Edited by Dr.
Robert Akl
41
We could solve this equation by iteration using a computer.
yn=1;yn1=0;
while1,
yn2=yn1;yn1=yn;yn=1.97*yn1-yn2;
end
We could also describe the system
with a block diagram.
Initial Conditions
(“D”means delay one unit in discrete
time.)
M. J. Roberts -All Rights Reserved. Edited by Dr.
Robert Akl
41
Discrete-Time Systemsyn[]=1.97yn-1[]-yn-2[]
With the initial conditions y[1] = 1 and y[0] = 0 the response
is
M. J. Roberts -All Rights Reserved. Edited by Dr.
Robert Akl
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With the initial conditions y[1] = 1 and y[0] = 0 the response
is
M. J. Roberts -All Rights Reserved. Edited by Dr.
Robert Akl
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Feedback Systems
In a feedbacksystem the response of the system is “fed back”
and combined with the excitation is such a way as to optimize
the response in some desired sense. Examples of feedback
systems are
1.Temperature control in a house using a thermostat
2.Water level control in the tank of a flush toilet.
3.Pouring a glass of lemonade to the top of the glass without overflowing.
4.A refrigerator ice maker that keeps the bin full of ice
but does not make extra ice.
5.Driving a car.
M. J. Roberts -All Rights Reserved. Edited by Dr.
Robert Akl
43
In a feedbacksystem the response of the system is “fed back”
and combined with the excitation is such a way as to optimize
the response in some desired sense. Examples of feedback
systems are
1.Temperature control in a house using a thermostat
2.Water level control in the tank of a flush toilet.
3.Pouring a glass of lemonade to the top of the glass without overflowing.
4.A refrigerator ice maker that keeps the bin full of ice
but does not make extra ice.
5.Driving a car.
M. J. Roberts -All Rights Reserved. Edited by Dr.
Robert Akl
43
Feedback Systems
Below is an example of a discrete-time feedback system. The
response y[n] is fed back through two delays and gains band c
and combined with the excitation x[n]. Different values of a,
band ccan create dramatically different responses to the same
excitation.
M. J. Roberts -All Rights Reserved. Edited by Dr.
Robert Akl
44
Below is an example of a discrete-time feedback system. The
response y[n] is fed back through two delays and gains band c
and combined with the excitation x[n]. Different values of a,
band ccan create dramatically different responses to the same
excitation.
M. J. Roberts -All Rights Reserved. Edited by Dr.
Robert Akl
44
Feedback Systems
Responses to an excitation that changes from 0 to 1 at n= 0.
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Robert Akl
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Responses to an excitation that changes from 0 to 1 at n= 0.
M. J. Roberts -All Rights Reserved. Edited by Dr.
Robert Akl
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Sound Recording System
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Robert Akl
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Robert Akl
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Recorded Sound as a Signal
Example
“s”“i”“gn”“al”
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Robert Akl
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Example
“s”“i”“gn”“al”
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Robert Akl
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Robert Akl
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Robert Akl
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Robert Akl
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Robert Akl
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Robert Akl
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HW
1. given signal y(t) = 5 sin(2∏ft + Ф). Draw signal y(t)
for:
i..f = 2000 Hz, Ф =0, ∏ /4, ∏ /2, ∏.
Ii. use Matlab :
-display graphic representations of above signal.
-Display the sum of y(t) for Ф =0+ y(t) for Ф = ∏/4
-Display the sum of y(t) for Ф =0+ y(t) for Ф = ∏/4 +
- y(t) for Ф = ∏/2
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1. given signal y(t) = 5 sin(2∏ft + Ф). Draw signal y(t)
for:
i..f = 2000 Hz, Ф =0, ∏ /4, ∏ /2, ∏.
Ii. use Matlab :
-display graphic representations of above signal.
-Display the sum of y(t) for Ф =0+ y(t) for Ф = ∏/4
-Display the sum of y(t) for Ф =0+ y(t) for Ф = ∏/4 +
- y(t) for Ф = ∏/2
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2. given signal y(t):
Write equation representing y(t),
Write equation representing y(t-1),
Draw signal z(t) = 2y(t) + y(-t)
Use matlab and validate your answer.
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-3 -1 0 1 3 4
6
4
2
amplitude
time
Write equation representing y(t),
Write equation representing y(t-1),
Draw signal z(t) = 2y(t) + y(-t)
Use matlab and validate your answer.
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-3 -1 0 1 3 4
6
4
2
amplitude
time
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0 20 40 60 80 100
-10
0
10
t (ms)
0 10 20 30 40 50
-10
0
10
n (samples)
0 20 40 60 80 100
-10
0
10
t (ms)
0 10 20 30 40 50
-10
0
10
n (samples)
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ADC
x(t)
Analog
Low-pass
Filter
Sample
and
Hold
f
s
b) Amplitude Quantized Signal
x
a(nT)
x[n]
Quantizer DSP
c) Amplitude & Time Quantized –Digital Signal
a) Continuous Signal
ADC
x(t)
Analog
Low-pass
Filter
Sample
and
Hold
f
s
b) Amplitude Quantized Signal
x
a(nT)
x[n]
Quantizer DSP
c) Amplitude & Time Quantized –Digital Signal
a) Continuous Signal
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DAC
DSP
Digital to
Analog
Converter
Analog
Low-pass
Filter
y[n]
y(t)
y
a(nT)
c) Continuous Low-pass filtered Signalb) Analog Signala) Digital Output Signal
DAC
DSP
Digital to
Analog
Converter
Analog
Low-pass
Filter
y[n]
y(t)
y
a(nT)
c) Continuous Low-pass filtered Signalb) Analog Signala) Digital Output Signal
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DSP Application Domains
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20 May 2024 Veton Këpuska 92FPGA: Field Programmable Gate Arrays
FPGA
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END
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