Introduction to ECE 366

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Introduction to ECE 366

• Selin Aviyente
• Associate Professor

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Overview

• Lectures M,W,F 800-850 a.m.,
• 1257 Anthony Hall
• Web Page
• http//www.egr.msu.edu/aviyente/ece366_09
• Textbook Linear Systems and Signals, Lathi , 2nd
  Edition, Oxford Press.
• Office Hours M,W 300-430 p.m., 2210
  Engineering Building
• Pre-requisites ECE 202, 280

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Course Requirements

• 2 Midterm Exams-40
• October 16th
• November 20th
• Weekly HW Assignments-10
• Assigned Friday due next Friday (except during
  exam weeks)
• Will include MATLAB assignments.
• Should be your own work.
• No late HWs will be accepted.
• Lowest HW grade is dropped.
• Final Project-15 (MATLAB based project)
• Final Exam-35, December 15th

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Policies

• Cheating in any form will not be tolerated. This
  includes copying HWs, cheating on exams.
• You are allowed to discuss the HW questions with
  your friends, and me.
• However, you have to write up the homework
  solutions on your own.
• Lowest HW grade will be dropped.

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Course Outline

• Part 1- Continuous Time Signals and Systems
• Basic Signals and Systems Concepts
• Time Domain Analysis of Linear Time Invariant
  (LTI) Systems
• Frequency Domain Analysis of Signals and Systems
• Fourier Series
• Fourier Transform
• Applications

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Course Outline

• Part 2- Discrete Time Signals and Systems
• Basic DT Signals and Systems Concepts
• Time Domain Analysis of DT Systems
• Frequency Domain Analysis of DT Signals and
  Systems
• Z-transforms
• DTFT

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Signals

• A signal is a function of one or more variables
  that conveys information about a physical
  phenomenon.
• Signals are functions of independent variables
  time (t) or space (x,y)
• A physical signal is modeled using mathematical
  functions.
• Examples
• Electrical signals Voltages/currents in a
  circuit v(t),i(t)
• Temperature (may vary with time/space)
• Acoustic signals audio/speech signals (varies
  with time)
• Video (varies with time and space)
• Biological signals Heartbeat, EEG

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Systems

• A system is an entity that manipulates one or
  more signals that accomplish a function, thereby
  yielding new signals.
• The input/output relationship of a system is
  modeled using mathematical equations.
• We want to study the response of systems to
  signals.
• A system may be made up of physical components
  (electrical, mechanical, hydraulic) or may be an
  algorithm that computes an output from an input
  signal.
• Examples
• Circuits (Input Voltage, Output Current)
• Simple resistor circuit
• Mass Spring System (Input Force, Output
  displacement)
• Automatic Speaker Recognition (Input Speech,
  Output Identity)

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Applications of Signals and Systems

• Acoustics Restore speech in a noisy environment
  such as cockpit
• Communications Transmission in mobile phones,
  GPS, radar and sonar
• Multimedia Compress signals to store data such
  as CDs, DVDs
• Biomedical Extract information from biological
  signals
• Electrocardiogram (ECG) electrical signals
  generated by the heart
• Electroencephalogram (EEG) electrical signals
  generated by the brain
• Medical Imaging
• Biometrics Fingerprint identification, speaker
  recognition, iris recognition

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Classification of Signals

• One-dimensional vs. Multi-dimensional The signal
  can be a function of a single variable or
  multiple variables.
• Examples
• Speech varies as a function of time?one-dimensiona
  l
• Image intensity varies as a function of (x,y)
  coordinates?multi-dimensional
• In this course, we focus on one-dimensional
  signals.

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• Continuous-time vs. discrete-time
• A signal is continuous time if it is defined for
  all time, x(t).
• A signal is discrete time if it is defined only
  at discrete instants of time, xn.
• A discrete time signal is derived from a
  continuous time signal through sampling, i.e.

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• Analog vs. Digital
• A signal whose amplitude can take on any value in
  a continuous range is an analog signal.
• A digital signal is one whose amplitude can take
  on only a finite number of values.
• Example Binary signals are digital signals.
• An analog signal can be converted into a digital
  signal through quantization.

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• Deterministic vs. Random
• A signal is deterministic if we can define its
  value at each time point as a mathematical
  function
• A signal is random if it cannot be described by a
  mathematical function (can only define
  statistics)
• Example
• Electrical noise generated in an amplifier of a
  radio/TV receiver.

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• Periodic vs. Aperiodic Signals
• A periodic signal x(t) is a function of time that
  satisfies
• The smallest T, that satisfies this relationship
  is called the fundamental period.
• is called the frequency of the signal
  (Hz).
• Angular frequency,
  (radians/sec).
• A signal is either periodic or aperiodic.
• A periodic signal must continue forever.
• Example The voltage at an AC power source is
  periodic.

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• Causal, Anticausal vs. Noncausal Signals
• A signal that does not start before t0 is a
  causal signal. x(t)0, tlt0
• A signal that starts before t0 is a noncausal
  signal.
• A signal that is zero for tgt0 is called an
  anticausal signal.

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• Even vs. Odd
• A signal is even if x(t)x(-t).
• A signal is odd if x(t)-x(-t)
• Examples
• Sin(t) is an odd signal.
• Cos(t) is an even signal.
• A signal can be even, odd or neither.
• Any signal can be written as a combination of an
  even and odd signal.

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Properties of Even and Odd Functions

• Even x Odd Odd
• Odd x Odd Even
• Even x Even Even
• Even Even Even
• Even Odd Neither
• Odd Odd Odd

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• Finite vs. Infinite Length
• X(t) is a finite length signal if it is nonzero
  over a finite interval alttltb
• X(t) is infinite length signal if it is nonzero
  over all real numbers.
• Periodic signals are infinite length.

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• Energy signals vs. power signals
• Consider a voltage v(t) developed across a
  resistor R, producing a current i(t).
• The instantaneous power p(t)v2(t)/RRi2(t)
• In signal analysis, the instantaneous power of a
  signal x(t) is equivalent to the instantaneous
  power over 1 resistor and is defined as x2(t).
• Total Energy
• Average Power

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• Energy vs. Power Signals
• A signal is an energy signal if its energy is
  finite, 0ltElt8.
• A signal is a power signal if its power is
  finite, 0ltPlt8.
• An energy signal has zero power, and a power
  signal has infinite energy.
• Periodic signals and random signals are usually
  power signals.
• Signals that are both deterministic and aperiodic
  are usually energy signals.
• Finite length and finite amplitude signals are
  energy signals.