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: vida.vakilian.ca@ieee.org

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