C.M. Liu

Perceptual Lab, College of Computer Science

National Chiao-Tung University

Discrete Signal Processing

Office: EC538

(03)5731877

cmliu@cs.nctu.edu.tw

(

http://www.cs.nctu.edu.tw/~cmliu/Courses/dsp/

1

0. Preface

Engineer Modeling

Discrete Signals & Systems

Examples

Definition

Historical Perceptive

Engineering Discovery

Digital Environments

Contents

Discussed Topics & Textbooks

Outline & Time Scheduling

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0. Preface

Related Courses in NCTU

Mathematics

Signals & Systems

Advanced Courses & Applications

Requirements

Presentation & Discussions

Homework

Score Decision

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0.1 Modeling

Two distinct engineer modeling

Physical systems are modeled by mathematical equations.

Physical signals are modeled by mathematical functions.

Physical

system

Mathematical

models of systems

and signals

Mathematical

Solutions of

equations

Conceptual Aspects

Problem formulation

Solution translation

Ry(t)Ci(t) v(t0)

Ryzi(t)C

v(t0)

y t Ri tC

i d v tt

t

( ) ( ) ( ) ( ) 1

00

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0.2 Signals & Systems:

Speech Example

Speech Signals

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0.2 Signals & Systems: Speech Example

(c.1)

Applications

Speech Synthesis

Compression Systems

Speech Recognition

Systems

0 ( ) z

s n( )

White-Noise

Generation

Pitch period PVoiced

Unvoiced

V

U

voiced/unvoiced

signal speech

Gain estimate

DT Impulse

GenerationAll-Pole

Filter

ADC

Microphone

Parameter

excitation

Parameter

excitation

Output

device

Template

memory

Speech Modeling

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0.2 Signals & Systems: Audio Example

CD Record & Play Systems

0t

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0.2 Signals & Systems: Audio Example (c.1)

Psychoacoustic Modeling

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Ear Functioning: Hearing

Page 193 (344)

Structures of the ear

The pinnae help collect the sound, but are also somewhat directionally sensitive (much more so in dogs, bats and other animals)

The ear canal actually amplifies frequencies of 2000-5000 Hz due to resonance.

The middle ear is filled with air through the Eustachian tubes which open in the throat.

The ossicles of the middle ear amplify the pressure waves through lever action and by concentration (the oval window is 15x smaller than the eardrum.

Tiny muscles on these bones reflex-ively contract in response to very high pressures, preventing cochlear damage

Inner Ear: Vestibule, Canals, Cochlea

Equal Loudness Curves

Two different 60 decibel sounds will not in general have the same

loudness

equal intensity is not the same thing as equal loudness.

Since the human hearing sensitivity varies with frequency, it is useful to plot equal loudness curves which show that variation for the average human ear.

Equal Loudness

Curves(with labels)

Qual loudness curves are the basis for the measurement of loudness in phons.

If a given sound is perceived to be as loud as a 60 dB sound at 1000 Hz, then it is said to have a loudness of 60 phons.

60 phons means "as loud as a 60 dB, 1000 Hz tone"

•Source: http://hyperphysics.phy-astr.gsu.edu/hbase/sound/phon.html#c1

0.2 Signals & Systems: Audio Example (c.2)

Psychoacoustic Modeling (c.1)

Masking

4 8 1216

Just-noticeable

Distortion

Frequency (kHz)

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The Nature of Sound (P.

149)

Sound: vibratory energy caused by movement of physical objects

Rate of vibration is called frequency

What we hear is pitch (high or low)

We hear 20-20,000 Hz (cycles/sec)

Size (intensity) of vibration is amplitude

What we experience is loudness

Measured in decibels (dB) (too loud too long = hearing loss)

Sound as mechanical wave energy requires a medium such as air or water in which to move.

Figure 10.7, page 338

Additive synthesis & Fourier analysisAs in Fourier analysis of patterns of light, the same method can be used for representing and constructing complex sound wave phenomena.

Here (d) is a composite of the fundamental (a) plus its second and third harmonics, (b) and (c).

0.2 Signals & Systems: Audio Example (c.3)

Spatial Information

Applications

Audio Compression

3D Sounds

Music Synthesis

L R

C

SL SR

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0.2 Signals & Systems: Visual Example

Psychovisual Modeling

Eye Structure

Color Information

Spectral Absorption of Three Types

of Cones

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The Human Eye

http://www.eyedesignbook.com/ch6/fig6-14bBG.jpg

0.2 Signals & Systems: Visual Example

Image blurring Systems

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Page 157 (38)A beam of light separated into its Wavelengths

The Electromagnetic Spectrum

Colour is a “secondary” quality, a relation between light entering eye and brain function,

a construct of the mind, not a quality in objects (not a “primary quality”)

Primary qualities are quantifiable, mathematical, external.

Galileo (1623) The book of Nature “is written in language of mathematics”

Newton (1721): “For the rays, to speak properly, are not colored.”

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Adapted from “The Role of Frequency in Developing Perceptual Sets,” by B. R. Bugelski and D. A.

Alampay, 1961, Canadian Journal of Psychology, 15, 205-211. Copyright © 1961 by the Canadian

Psychological Association. Reprinted with permission.

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Adapted from “The Role of Frequency in Developing Perceptual Sets,” by B. R. Bugelski and D. A.

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Adapted from “The Role of Frequency in Developing Perceptual Sets,” by B. R. Bugelski and D. A.

Alampay, 1961, Canadian Journal of Psychology, 15, 205-211. Copyright © 1961 by the Canadian

Psychological Association. Reprinted with permission.

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Adapted from “The Role of Frequency in Developing Perceptual Sets,” by B. R. Bugelski and D. A.

Alampay, 1961, Canadian Journal of Psychology, 15, 205-211. Copyright © 1961 by the Canadian

Psychological Association. Reprinted with permission.

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0.2 Signals & Systems: Definition

Signals

Functions of one or two variables.

Typically contain information about the behavior or nature of some

phenomenon.

Systems

Respond to particular signals by producing other signals.

Example 1: Electrical Circuits

Signals: Voltage and Currents as a function of time in a electrical circuit are

examples of signals.

Systems: The circuit is a system.

Example 2: Automobile Driver

Automobile Driver Depresses the Accelerator Pedal

Systems: The automobile

Input Signals: The pressure on the acceleration pedal.

Output Signals: Automobile speed

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0.3 Historical Perspective

17th Century

Invention of the Calculus (Newton, 1642-1727)

Model physical phenomena in terms of functions of continuous variables and differential equations.

18th Century

Euler (1707-1783)

Bernoulli (1700 - 1782)

Lagrange (1736-1813)

19th Century

Gauss (1777 - 1855)

Fourier (1772- 1837)

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0.3 Historical Perspective (c.1)

Digital Computer (1950s)

Analog Systems were used for real-time applications

The need for sophisticated signal processing

Oil prospecting.

Digital computers are used to simulate & approximate analog systems.

Microelectronics

Wafer-scale integration

DSP Processors

Flexibility and High Computing Speeds

High speed fixed point and floating point processor.

Personal Computers

Storage

Computing Power

Media Applications

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0.4 Contents-- Topics & Textbooks

Discussed Topics

The concepts of signals and systems arise in an extremely wide variety of fields.

Although the physical nature of the signals and systems may be drastically different, there are common tools for signal analysis and system design.

These common tools are the discussed topics in this course.

Objective of the Course

Provide the reader with the knowledge necessary for the wide scope of applications for digital signal processing.

A foundation for future developments.

Text Books

A.V. Oppenheim and R.W. Schafer, “Discrete-Time Signal Processing,” Prentice Hall, Inc., Englewood Cliffs, New Jersey, 2nd Edition, 1999.

A.V. Oppenheim and R.W. Schafer, “Discrete-Time Signal Processing,” Pearson, 3rd Edition, 2010.

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0.4 Contents-- Outline & Time Scheduling

(48 h)

Discrete-Time Signals and Systems (72 pages, 8 hours)

Sampling of Continuous-Time Signals (69 pages, 6 hours)

The z-Transform (53 pages, 4 hours)

Transform Analysis of Linear Time-Invariant Systems (88 pages, 5 hours)

Structures for Discrete-Time Systems (113 pages, 5 hours)

Filter Design Techniques (111 pages, 5 hours)

The Discrete Fourier Transform (67 pages, 4 hours)

Computation of the Discrete Fourier Transform (81 pages, 3 hours)

Fourier Analysis of Signals Using the Discrete Fourier Transform (73 pages, 3 hours)

Hilbert Transform

Discrete Cosine Transform

Introduction (1)

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0.5 Related Courses in NCTU

Course Links in Our Departments

Mathematics

Linear Algebra

Discrete Math.

Differential Equations

Probability

CS Courses

Electronics & Electrical Circuits

Computer Programming and Peripherals

Advanced Courses & Applications

Image Processing

Audio Processing

Speech Processing

Neural Network...................

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0.6 Requirements

Presentation (2h/week)

Slices

Discussion (1h/week)

Homeworks

Tests

Reviewing

Prospects

Thoroughly familiar with 80% of the

teaching and well acquainted with

another 20%.

Be able to tackle about the assigned

homeworks.

Have a reading time at least 5 hours

per week.

Homeworks

Problems

Score Decision

Homeworks (30%)

3 Examinations (70%)

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