MEH329 DIGITAL SIGNAL PROCESSING Instructor

19.09.2012

1

MEH329DIGITAL SIGNAL PROCESSING

Instructor: Assist.Prof.Dr. M. Kemal GÜLLÜDept. Of Electronics & Telecomm. Eng.

Kocaeli Universityhttp://http://akademikpersonel.kocaeli.edu.tr/kemalg/

-1-Discrete Time Signals

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

2MEH329 Digital Signal Processing

19.09.2012

2

References

• Sarp Ertürk, “Sayısal İşaret İşleme”, 2. Baskı,Birsen Yayınevi, ISBN:9755113096, 2005.

• J.G. Proakis, D.G. Manolakis, “Digital SignalProcessing, Principles, Algorithms andApplications”, 4th Edition, Prentice-HallInternational, ISBN: 0131873741, 2006.

• A.V. Oppenheim, R.W Schafer, "Discrete-TimeSignal Processing", Second Edition, Prentice-Hall,New Jersey, ISBN: 013083443-2, 1999.


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.


19.09.2012

3

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 mathematicalrepresentation of a signal as time.


Examples

• Speech: 1-dimensional (1-D) signal that changeswith time s(t).

• Grayscale Image: 2-D signal that changes withspatial coordinates i(x,y).

• Video: 3-D signal that changes with spatialcoordinates and time f(x,y,t).


19.09.2012

4

Signals

• Analog input – analog output – Digital recording of music

• Analog input – digital output– Touch tone phone dialing

• Digital input – analog output– Text to speech

• Digital input – digital output– Compression of a file on computer


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…


19.09.2012

5

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


Signalssignal

analog digital

discretetime

Quantizer andcoder

Quantizedamplitudes


19.09.2012

6

Discrete Time Signal

0 20 40 60 80 100-10

0

10

t (ms)

x(t)

0 10 20 30 40 50-10

0

10

n (samples)

x[n]

x(nTs)

0 20 40 60 80 100 t (ms)-10

0

10


Discrete Time Signal

0 10 20 30 40 501000

0000

0111

n (samples)

amplitude of x[n] quantized and coded to binary number format

• How about digital signal?

4-bit signedbinary number

format


19.09.2012

7

Periodicity

0 20 40 60 80 100-10

0

10

t (ms)

x(t)

x(t)=x(t+T), for all t

0 10 20 30 40 50-10

0

10

n (samples)

x[n]

x[n]=x[n+N], for all n


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: neitherenergy nor power signal


19.09.2012

8

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


Signal Processing

AnalogSignal

Processing

DigitalSignal

Processing

MixedSignal

Processing


19.09.2012

9

(Digital Signal Processing – DSP)

Analog InputSignal

Sample & Hold

A/DConverter

DigitalSignal

Processing

D/AConverter

AnalogLPF

AnalogOutput Signal


Application Fields• Speech Applications

– Compression, enhancement, special effects, synthesis, recognition, echo cancellation…

– Cell Phones, MP3 Players, Movies, Dictation, Text-to-speech…

• 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…


19.09.2012

10

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…

…


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


19.09.2012

11

Pros of DSP - 1

– Accuracy can be controlled by choosing word length.

– Repeatable (same operation 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.21MEH329 Digital Signal Processing

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.


19.09.2012

12

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)


Example (Aliasing)

– A monochrome camera with 30 frames per secondcapture rate (30fps)

– Rotating phasor with variable speed


19.09.2012

13

Example (Cell Phone)


Example (Driver Assistance)


19.09.2012

14

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”


MEH329 DIGITAL SIGNAL PROCESSING Instructor

Documents

Transcript of MEH329 DIGITAL SIGNAL PROCESSING Instructor