Ch1 EE412 Introduction to DSP and .ppt

Digital Signal Processing (DSP)
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,…

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 DSP’s process signals
 Signal – a detectable physical
quantity or impulse (as a voltage,
current, or magnetic field strength)
by which messages or information
can be transmitted (Webster
Dictionary)

Introduction to DSP
 Signal Characteristics:
 Signals are Physical Quantities:
 Signals are Measurable
 Signals are Analog
 Signals Contain Information.
 Examples:
 Temperature [oC]
 Pressure [Newtons/m2] or [Pa]
 Mass [kg]
 Speed [m/s]
 Acceleration [m/s2]
 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
 …

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

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whose "phase" is now . It has been shifted by radians

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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

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Calculation between phase angle φ° in degrees (deg), the time delay Δ
t and the
frequency f is:
Phase angle (deg)
(Time shift) Time difference
Frequency
λ = c / f and c = 343 m/s at 20°C.
Calculation between phase angle φ in radians (rad),
the time shift or time delay Δ t,
and the frequency f is:
Phase angle (rad)
"Bogen" means "radians". (Time shift) Time difference
Frequency
Time = path length / speed of sound

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S(t) = A sin(ωot − ϕ)

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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

 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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 Signal : convert data/../ to volt/current
ready to be sent.
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Text
data
Binary
data
Digital signal
3 011
7 111

What is DSP?
0
0.22
0.44
0.64
0.82
0.98
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0.64
0.44
0.22
0
-0.22
-0.44
-0.64
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-0.98
-1.11
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-1.26
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-1.11
-0.98
-0.82
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-2
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-1
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Analog-to-Digital and Digital-to-Analog

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Digital Telephone Communication System Example:

Signal Types
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Conversions Between Signal
Types
Sampling
Quantizing
Encoding
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Message Encoded in ASCII
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Noisy Message Encoded in ASCII
Progressively
noisier
signals
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Bit Recovery in a Digital Signal
Using Filtering
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Assignment 1 (Matlab implementation) 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 Image Filtered X-Ray Image
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Discrete-Time Systems
In a discrete-time system events occur at points in time but not
between those 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 n is the number of discrete-time
intervals that have elapsed since some beginning time n = 0.
y n
[ ]=1.97y n -1
[ ]- y n - 2
[ ]
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The equation
y n
[ ]=1.97y n -1
[ ]- y n - 2
[ ]
says in words “The signal value at any time n is 1.97 times the signal
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.
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y n
[ ]=1.97y n -1
[ ]- y n - 2
[ ]
We could solve this equation by iteration using a computer.
yn = 1 ; yn1 = 0 ;
while 1,
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.)
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y n
[ ]=1.97y n -1
[ ]- y n - 2
[ ]
With the initial conditions y[1] = 1 and y[0] = 0 the response
is
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Feedback Systems
In a feedback system 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.
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Feedback Systems
Below is an example of a discrete-time feedback system. The
response y[n] is fed back through two delays and gains b and c
and combined with the excitation x[n]. Different values of a,
b and c can create dramatically different responses to the same
excitation.
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Feedback Systems
Responses to an excitation that changes from 0 to 1 at n = 0.
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Sound Recording System
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Recorded Sound as a Signal
Example
 “s” “i” “gn” “al”
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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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 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.
-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)

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ADC
x(t) Analog
Low-pass
Filter
Sample
and
Hold
fs
b) Amplitude Quantized Signal
xa(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)
ya(nT)
c) Continuous Low-pass filtered Signal
b) Analog Signal
a) Digital Output Signal

DSP Application Domains

FPGA: Field Programmable Gate Arrays

 FPGA

END

Ch1 EE412 Introduction to DSP and .ppt

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