17.10.2014
MEH329
DIGITAL SIGNAL PROCESSING
-1Discrete Time Signals
Instructor: Assoc.Prof.Dr. M. Kemal GÜLLÜ
Dept. Of Electronics & Telecomm. Eng.
Kocaeli University
http://akademikpersonel.kocaeli.edu.tr/kemalg/
Index
• Introduction
• Discrete Time Signals and Systems
• Frequency Domain Representation of Discrete
Time Signals and Systems
• Discrete Time Processing of Continuous Time
Signals and Systems
• Z-Transform Analysis of Signals and Systems
• Digital Filter Design
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References
• Sarp Ertürk, “Sayısal İşaret İşleme”, 2.Baskı, Birsen
Yayınevi, ISBN:9755113096, 2005 (Turkish).
• J.G. Proakis, D.G. Manolakis, “Digital Signal
Processing,
Principles,
Algorithms
and
Applications”,
4th
Edition,
Prentice-Hall
International, ISBN: 0131873741, 2006.
• A.V. Oppenheim, R.W Schafer, "Discrete-Time
Signal Processing", Second Edition, Prentice-Hall,
New Jersey, ISBN: 013083443-2, 1999.
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Lecture Objectives
Establishing a background in Digital Signal
Processing theory.
Understanding and applying:
•
•
•
•
Basics of discrete time signals and systems.
Differential equations and system functions.
Fourier transform and Z-transform.
Discrete Fourier transform and fast Fourier
transform.
• Sampling and reconstruction.
• Digital filter types and relationship between them.
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What is signal?
• It is a function that conveys information.
• Represented mathematically as functions of
one or more independent variables.
– Speech signal → function of time
– Image
→ function of two spatial variables
• A common convention is to refer to the
independent variable of the mathematical
representation of a signal as time.
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Examples
• Speech: 1-dimensional (1-D) signal that changes
with time s(t).
• Grayscale Image: 2-D signal that changes with
spatial coordinates i(x,y).
• Video: 3-D signal that changes with spatial
coordinates and time f(x,y,t).
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Signals
•
Analog input – analog output
•
Analog input – digital output
•
Digital input – analog output
•
Digital input – digital output
–
Digital recording of music
–
Touch tone phone dialing
–
Text to speech
–
Compression of a file on computer
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Well Known Physical Signals
• Electrical signals: voltage, current, magnetic
and electric fields…
• Mechanical signals: velocity, force,
displacement…
• Acoustic signals: sound, vibration…
• Other signals: pressure, temperature,
humidity…
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Signals
• Independent variable: continuous/discrete
– Continuous-time signals
– Discrete-time signals (discrete in time but
continuous in amplitude)
• Amplitude: continuous/discrete
– Analog signal: continuous in amplitude
– Digital signal: discrete in time and amplitude
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Signals
Quantized
amplitudes
signal
analog
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digital
discrete
time
Quantizer and
coder
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Discrete Time Signal
10
x(t)
0
-10
0
10
20
40
60
80
100
t (ms)
20
40
60
80
100
t (ms)
20
30
40
50 n (samples)
x(nTs) 0
-10
0
10
x[n]
0
-10
0
10
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Discrete Time Signal
• How about digital signal?
amplitude of x[n] quantized and coded to binary number format
0111
0000
1000
0
10
20
30
40
50 n (samples)
4-bit signed
binary number
format
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Periodicity
x(t)=x(t+T), for all t
10
x(t)
0
-10
0
20
40
60
t (ms)
80
100
40
50 n (samples)
x[n]=x[n+N], for all n
10
x[n]
0
-10
0
10
20
30
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Energy and Power Signals
• Signal’s energy is finite
→ Energy Signal
• Signal’s energy is infinite & power is finite (not
zero)
→ Power Signal
• If energy and power are infinite: neither
energy nor power signal
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Deterministic and Random Signals
• Deterministic signals: values are completely
specified for any given time.
– Thus, a deterministic signal can be modeled by a
known function of time (example: sin(ωt))
• Random signals: take random values at any
given time and must be characterized
statistically
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Signal Processing
Analog
Signal
Processing
Digital
Signal
Processing
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Mixed
Signal
Processing
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(Digital Signal Processing – DSP)
Analog Input
Signal
Sample &
Hold
A/D
Converter
Analog
Output Signal
Analog
LPF
D/A
Converter
Digital
Signal
Processing
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(Digital Signal Processing – DSP)
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Application Fields
• Speech Applications
– Compression, enhancement, special effects, synthesis,
recognition, echo cancellation…
– Cell Phones, MP3 Players, Movies, Dictation, Text-tospeech…
• Telecommunication
– Modulation, coding, detection, equalization, echo
cancellation…
– Cell Phones, dial-up modem, DSL modem, Satellite
Receiver…
• Automative
– ABS, GPS, Active Noise Cancellation, Cruise Control,
Parking Assistant…
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Application Fields
• Medicine
– Magnetic Resonance, Tomography, Electrocardiogram…
• Military
– Radar, Sonar, Space photographs, remote sensing, UAV,
AUV …
• Image and Video Applications
– DVD, JPEG compression, Movie special effects, video
conferencing…
• Mechanical
– Motor control, process control, oil and mineral
prospecting…
…
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Limitations of Analog Signal Processing
• Accuracy limitations due to
– Component tolerances, undesired nonlinearities
• Limited repeatability due to
– Tolerances
– Changes in environmental conditions
• Temperature, vibration,…
•
•
•
•
Sensitivity to electrical noise
Limited dynamic range for voltage and currents
Inflexibility to changes
Difficulty of implementing certain operations
– Nonlinear, time-varying operations
• Difficulty of storing information
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Pros of DSP - 1
– Accuracy can be controlled by choosing word
length.
– Repeatable (same results in a different time).
– Sensitivity to component tolerance and electrical
noise are minimal (robustness).
– Time multiplexing (different operations in same
time).
– Dynamic range can be controlled using floating
point numbers.
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Pros of DSP - 2
– Flexibility can be achieved with software
implementations (adaptive parameters).
– Non-linear and time-varying operations are easier
to implement .
– Digital storage is cheap.
– Digital information can be encrypted for security.
– Price/performance and reduced time-to-market.
– Provide very low frequency operations.
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Cons of DSP
– Sampling causes loss of information
– A/D and D/A requires mixed-signal hardware
(increased complexity)
– Limited speed of processors
– Quantization and round-off errors
– Frequency range (limited to sampling rate)
– Unsuitable for simple low power, applications
(high power dissipation of DSP)
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Example (Aliasing)
– A monochrome camera with 30 frames per second
capture rate (30fps)
– Rotating phasor with variable speed
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Example (mp3 recorder/player)
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Example (Telecommunication)
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Example (DSP Receiver)
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Example (AC Line Monitoring)
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Example (Cell Phone)
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Example (Driver Assistance)
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Quote:
• Optimist: “The glass is half full”
• Pessimist: “The glass is half empty”
• Engineer: “That glass is twice as large as it needs to be”
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