Introduction to Signal Processing - egr.msu.edu€¦ · copyright 1997 by Alan V. Oppenheim and...
Transcript of Introduction to Signal Processing - egr.msu.edu€¦ · copyright 1997 by Alan V. Oppenheim and...
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1) Signals2) Systems3) For example ...
“Figures and images used in these lecture notes by permission,copyright 1997 by Alan V. Oppenheim and Alan S. Willsky”
Introduction to Signal Processing Summer 2007
Basics: Signals and SystemsKeyur Desai
(Slides: Courtesy of Prof. Alan S. Willsky)
16 May 2007
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SIGNALS
Signals are functions of independent variables that carry information. For example:
• Electrical signals --- voltages and currents in a circuit• Acoustic signals --- audio or speech signals (analog or
digital)
Spectrogram
Time-domainSpeech signal
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SIGNALS• Video signals --- intensity variations in an image (e.g. a
CAT scan)
• Biological signals --- sequence of bases in a gene DNA
Its signal representation
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THE INDEPENDENT VARIABLES• For electrical signal the value of voltage or current changes with
time, hence time is called independent variable and voltage or current is called dependent variable
• Independent variable can be continuous— Trajectory of a space shuttle— Mass density in a cross-section of a brain
• Independent variable can be discrete— DNA base sequence— Digital image pixels
• Independent variable can be 1-D, 2-D, ••• N-D
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THE INDEPENDENT VARIABLESWhat are the independent variables in these signals?(i) Speech (ii) CAT scan image (iii) DNA sequence(iii) Time (ii) Spatial Location (iii) Location on DNA molecule
For this course: Focus on a single (1-D) independent variable which we call “time”.
Continuous-Time (CT) signals: x(t), t — continuous valuesDiscrete-Time (DT) signals: x[n], n — integer values only
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CT Signals
• Most of the signals in the physical world are CT signals—E.g. voltage & current, pressure, temperature, velocity, etc.
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DT Signals
• Examples of DT signals in nature:— DNA base sequence— Population of the nth generation of certain species
• x[n], n — integer, time varies discretely
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Many human-made DT Signals
Ex.#1 Weekly Dow-Jonesindustrial average
Why DT? —Can be processed by modern digital computers
and digital signal processors (DSPs).
Ex.#2 digital image
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SYSTEMS
For the most part, our view of systems will be from an input-output perspective:
A system responds to applied input signals, and its response is described in terms of one or more output signals
x(t) y(t)CT System
DT Systemx[n] y[n]
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•An RLC circuit
•What is the input signal? •x(t) (the D.C. source)
•What is the output signal? •y(t) (the signal across capacitor)
•What is the system? •The whole RLC network
EXAMPLES OF SYSTEMS
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•Dynamics of an aircraft or space vehicle•An algorithm for analyzing financial and economic factors to predict bond prices•An algorithm for post-flight analysis of a space launch•An edge detection algorithm for medical images
What are the inputs and what are the outputs in above examples?
EXAMPLES OF SYSTEMS
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SYSTEM INTERCONNECTIONS•An important concept is that of interconnecting systems— To build more complex systems by interconnecting
simpler subsystems— To modify response of a system
•Signal flow (Block) diagram
Cascade
Feedback
Parallel +
+