ece 330 signals and systems ii - dept of computer...
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ECE 330 Signals and Systems II
Course Information Lecture 1
The lectures are taken from the recommended textbooks (“SIGNALS and SYSTEMS A MATLAB® Integrate approach” by Oktay Alkin and “Signals and Systems” by A. V. Oppenheim, A. S. Willsky, and S. H. Nawab).
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Course Information
u Course #: ECE 330 u Course Name: Signals and Systems II u Course Instructor: Vida Vakilian
u Email: [email protected]
u Course Objective: To apply knowledge of mathematics (namely algebra and calculus, complex variables and series) and engineering (basic circuits) to make important insights on the signals (that is a stream of data) and the systems (that process signals).
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Course Information
Recommended Textbooks Ø A. V. Oppenheim, A. S. Willsky, and S. H. Nawab, “Signals and Systems,” 2nd edition, Prentice Hall, 1997.
Ø Oktay Alkin, “Signals and Systems: A MATLAB Integrated Approach”, 1st edition, CRC Press, 2014.
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ECE 330 At a Glance Introduction to Signals and Systems (Week 1)
v Mathematical Modeling of Signals v Continuous-Time (C-T) and Discrete-Time (D-T) Signals and Systems
Analyzing D-T Systems in the Time Domain (Weeks 2-3) v Introduction to D-T Linear Time Invariant (LTI) Systems v Impulse Response & Convolution-Sum Representation of LTI Systems v Causality and Stability in D-T Systems
Fourier Analysis for D-T Signals and Systems (Weeks 4-6) v Fourier Series Representation of D-T Periodic Signals v Properties of D-T Fourier Series (DTFS)
The D-T Fourier Transform (Weeks 7-8) v D-T Fourier Transform (DTFT) v DTFT for Periodic & Aperiodic Signals
Sampling (Weeks 9-10) v Sampling of C-T Signals and the Sampling Theorem v Sampling of D-T Signals and D-T Interpolation
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u Labs performed weekly. u A total of 6 labs.
u In our Labs, we use EMONA SIGEx board
Lab Information
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Homework
u Homework will be assigned on a weekly basis. u Homework is due at the beginning of class on
the date specified. u No late submissions accepted.
u You are encouraged to discuss the homework problems with one another.
u However, you must submit your own work. u Copying solutions is considered cheating.
u Homework is essential to the learning process!
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Exams
u One midterm exam during the quarter. u All exams are closed-book. u No make-up exams.
u In the case of an emergency, see me. u Notify me in advance (whenever possible) if a
conflict or problem exists.
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Grading
u The final grade will be calculated as follows:
u Homework 10% u Lab 15% u Midterm 30% u Final Exam 45%
Signals & Systems II
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Signals & Systems
u A “Signal” is a function representing a physical quantity or variable, and typically it contains information about the behavior or nature of the phenomenon.
u The job of the “System” is often to extract, modify, transform, or manipulate that carried information
u So…a big part of “Signals & Systems” is using math models to see what a system “does” to a signal
Input Signal x(t) Output Signal y(t) System
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u Signal could be discrete or continuous.
u A System has a transfer function to evaluate output system for each input system. The output signal can be governed by convolution of input signal and the transfer function.
Continuous-Time & Discrete-Time
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Continuous-Time & Discrete-Time
Modern systems generally… u get a continuous-time signal from a sensor u a continuous-time system modifies the signal u an “analog-to-digital converter”(ADC or A-to-D) sample the signal to create a discrete-time signal…a “stream of numbers” u A discrete-time system to do the processing –and then (if desired) convert back to analog
Analog Electronics ADC Digital
Electronics
C-T Signal
C-T Signal
D-T Signal
D-T Signal
D-T System
C-T System Sensor
Continuous-Time Signals
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Signal Operations (C-T Signals)
u A < 0 ? u A > 0 ?
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Signal Operations (C-T Signals)
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Signal Operations (C-T Signals)
u B < 1 ? u B > 1 ?
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Signal Operations (C-T Signals)
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Signal Operations (C-T Signals)
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Signal Operations (C-T Signals)
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Signal Operations (C-T Signals)
Example 1:
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Signal Operations (C-T Signals)
Example 1:
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Signal Operations (C-T Signals)
Example 2:
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Signal Operations (C-T Signals)
Example 2:
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Signal Operations (C-T Signals)
Example 2:
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Signal Operations (C-T Signals)
Example 2:
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Signal Operations (C-T Signals)
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Signal Operations (C-T Signals)
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Signal Operations (C-T Signals)
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Basic Building Blocks
u Unit-impulse function u Unit-step function u Unit-pulse function u Unit-ramp function u Unit-triangle function u Sinusoidal signals
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Unit-Impulse Function
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Obtaining Unit-Impulse Function From a Rectangular Pulse
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Sampling Property of the Unit-Impulse Function
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Unit-Step Function
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Using the Unit-Step Function to Turn a Signal ON
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Using the Unit-Step Function to Turn a Signal OFF
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Unit-Pulse Function
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Constructing a Unit-Pulse From Unit-Step Functions
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Unit-Ramp Function
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Unit-Triangle Function
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Constructing a Unit-Triangle Using Unit-Ramp Function
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Sinusoidal Signals