September 2, 2009ECE 366, Fall 2009 Introduction to ECE 366 Selin Aviyente Associate Professor

September 2, 2009ECE 366, Fall 2009 Overview Lectures: M,W,F 8:00-8:50 a.m., 1257 Anthony Hall Web Page: Textbook: Linear Systems and Signals, Lathi, 2nd Edition, Oxford Press. Office Hours: M,W 3:00-4:30 p.m., 2210 Engineering Building Pre-requisites: ECE 202, 280

September 2, 2009ECE 366, Fall 2009 Course Requirements 2 Midterm Exams-40% –October 16 th –November 20 th 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 15 th

September 2, 2009ECE 366, Fall 2009 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.

September 2, 2009ECE 366, Fall 2009 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

September 2, 2009ECE 366, Fall 2009 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

September 2, 2009ECE 366, Fall 2009 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

September 2, 2009ECE 366, Fall 2009 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)

September 2, 2009ECE 366, Fall 2009 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

September 2, 2009ECE 366, Fall 2009 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- dimensional Image intensity varies as a function of (x,y) coordinates  multi-dimensional –In this course, we focus on one-dimensional signals.

September 2, 2009ECE 366, Fall 2009 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, x[n]. –A discrete time signal is derived from a continuous time signal through sampling, i.e.:

September 2, 2009ECE 366, Fall 2009 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.

September 2, 2009ECE 366, Fall 2009 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.

September 2, 2009ECE 366, Fall 2009 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.

September 2, 2009ECE 366, Fall 2009 Causal, Anticausal vs. Noncausal Signals: –A signal that does not start before t=0 is a causal signal. x(t)=0, t<0 –A signal that starts before t=0 is a noncausal signal. –A signal that is zero for t>0 is called an anticausal signal.

September 2, 2009ECE 366, Fall 2009 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.

September 2, 2009ECE 366, Fall 2009 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

September 2, 2009ECE 366, Fall 2009 Finite vs. Infinite Length: –X(t) is a finite length signal if it is nonzero over a finite interval a<t<b –X(t) is infinite length signal if it is nonzero over all real numbers. –Periodic signals are infinite length.

September 2, 2009ECE 366, Fall 2009 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)=v 2 (t)/R=Ri 2 (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 x 2 (t). –Total Energy: –Average Power:

September 2, 2009ECE 366, Fall 2009 Energy vs. Power Signals: –A signal is an energy signal if its energy is finite, 0<E<∞. –A signal is a power signal if its power is finite, 0<P<∞. –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.