Discrete Signal Processing

Transcription

1 1 Discrete Signal Processing C.M. Liu Perceptual Lab, College of Computer Science National Chiao-Tung University ( Office: EC538 (03) cmliu@cs.nctu.edu.tw

2 0. Preface 2 Engineer Modeling Discrete Signals & Systems Examples Definition Historical Perceptive Engineering Discovery Digital Environments Contents Discussed Topics & Textbooks Outline & Time Scheduling

3 0. Preface 3 Related Courses in NCTU Mathematics Signals & Systems Advanced Courses & Applications Requirements Presentation & Discussions Homework Score Decision

4 0.1 Modeling 4 Two distinct engineer modeling Physical systems are modeled by mathematical equations. Physical signals are modeled by mathematical functions. R i(t) C v(t 0 ) y(t) R C v(t 0 ) y zi (t) 1 t y ( t ) Ri ( t ) i ( ) d v ( t ) C 0 t 0 Problem formulation Physical system Solution translation Mathematical models of systems and signals Conceptual Aspects Mathematical Solutions of equations

5 5 0.2 Signals & Systems: Speech Example Speech Signals

6 6 0.2 Signals & Systems: Speech Example (c.1) Speech Modeling Applications Speech Synthesis Compression Systems Pitch period P Voiced DT Impulse Generation White-Noise Generation Unvoiced V U ADC voiced/unvoiced All-Pole Filter Gain estimate 0 ( z ) Parameter excitation Parameter excitation s( n) signal speech Output device Speech Recognition Systems Microphone Template memory

7 0.2 Signals & Systems: Audio Example 7 CD Record & Play Systems 0 t

8 0.2 Signals & Systems: Audio Example (c.1) 8 Psychoacoustic Modeling

9 Ear Functioning: Hearing

10 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 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 Page 193 (344)

11 Inner Ear: Vestibule, Canals, Cochlea

12 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.

13 Equal Loudness Curves (with labels) Source: - astr.gsu.edu/hbase/soun d/phon.html#c1 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"

14 0.2 Signals & Systems: Audio Example (c.2) 14 Psychoacoustic Modeling (c.1) Masking Just-noticeable Distortion Frequency (khz) 16

15 The Nature of Sound (P. 149) Sound as mechanical wave energy requires a medium such as air or water in which to move. 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)

16 Additive synthesis & Fourier analysis As in Fourier analysis of patterns of light, the same method can be used for representing and constructing complex sound wave phenomena. Figure 10.7, page 338 Here (d) is a composite of the fundamental (a) plus its second and third harmonics, (b) and (c).

17 0.2 Signals & Systems: Audio Example (c.3) 17 Spatial Information Applications Audio Compression 3D Sounds Music Synthesis L C R S L S R

18 0.2 Signals & Systems: Visual Example 18 Psychovisual Modeling Eye Structure Color Information Spectral Absorption of Three Types of Cones

19 The Human Eye

20 0.2 Signals & Systems: Visual Example 20 Image blurring Systems

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

22 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.

23 Copyright 2002 Wadsworth Group. Wadsworth is an imprint of the Wadsworth Group, a division of Thomson Learning at-man (man) Adapted from The Role of Frequency in Developing Perceptual Sets, by B. R. Bugelski and D. A. Alampay, 1961, Canadian Journal of Psychology, 15, Copyright 1961 by the Canadian Psychological Association. Reprinted with permission.

24 Copyright 2002 Wadsworth Group. Wadsworth is an imprint of the Wadsworth Group, a division of Thomson Learning Rat-Man (rat) Adapted from The Role of Frequency in Developing Perceptual Sets, by B. R. Bugelski and D. A. Alampay, 1961, Canadian Journal of Psychology, 15, Copyright 1961 by the Canadian Psychological Association. Reprinted with permission.

25 Copyright 2002 Wadsworth Group. Wadsworth is an imprint of the Wadsworth Group, a division of Thomson Learning Rat-Man (middle) Adapted from The Role of Frequency in Developing Perceptual Sets, by B. R. Bugelski and D. A. Alampay, 1961, Canadian Journal of Psychology, 15, Copyright 1961 by the Canadian Psychological Association. Reprinted with permission.

26 Copyright 2002 Wadsworth Group. Wadsworth is an imprint of the Wadsworth Group, a division of Thomson Learning at-man (man) Adapted from The Role of Frequency in Developing Perceptual Sets, by B. R. Bugelski and D. A. Alampay, 1961, Canadian Journal of Psychology, 15, Copyright 1961 by the Canadian Psychological Association. Reprinted with permission.

27 0.2 Signals & Systems: Definition 27 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

28 0.3 Historical Perspective 28 17th Century Invention of the Calculus (Newton, ) Model physical phenomena in terms of functions of continuous variables and differential equations. 18th Century Euler ( ) Bernoulli ( ) Lagrange ( ) 19th Century Gauss ( ) Fourier ( )

29 0.3 Historical Perspective (c.1) 29 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

30 0.4 Contents-- Topics & Textbooks 30 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, A.V. Oppenheim and R.W. Schafer, Discrete-Time Signal Processing, Pearson, 3 rd Edition, 2010.

31 Contents-- Outline & Time Scheduling (48 h) Introduction (1) 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

32 0.5 Related Courses in NCTU 32 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...

33 0.6 Requirements 33 Presentation (2h/week) Slices Discussion (1h/week) Homeworks Tests Reviewing Homeworks Problems Score Decision Homeworks (30%) 3 Examinations (70%) 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.