Introduction-Signals and Systems-Lecture 01 Slides-Electrical and Computer Engineering, Slides of Signals and Systems Theory

Download Introduction-Signals and Systems-Lecture 01 Slides-Electrical and Computer Engineering and more Slides Signals and Systems Theory in PDF only on Docsity! ECE 8443 – Pattern RecognitionECE 3163 – Signals and Systems • Objectives: Examples of Signals Functional Forms Continuous vs. Discrete Symmetry and Periodicity Basic Characteristics • Resources: MIT 6.003: Lecture 1 Wiki: Continuous Signals Wiki: Discrete Signals JF: MATLAB Resources ISIP: Signal Processing Demonstrations JHU: Java Applets LECTURE 01: CONTINUOUS AND DISCRETE-TIME SIGNALS Audio:URL: ECE 3163: Lecture 01, Slide 1 • Signals and Systems is a cornerstone of an electrical or computer engineering education and relevant to most engineering disciplines. • The concepts described in this class (e.g., Fourier analysis) have roots in applied mathematics, and have impacted virtually all engineering disciplines. In fact, many non-engineering disciplines, such as business and finance, exploit these concepts today. • Popular software tools such as Excel and Photoshop now include extensive signal processing capabilities. • Virtually all engineers will use some aspect of this course in their work, since even hardware design begins with computer modeling. • This course is actually an introduction to the design, simulation, and testing of systems. One often overlooked benefit of this course is to help you better appreciate some of that free software you download from the Internet. • We will focus on basic mathematical concepts, such as linearity, and common transformations (e.g., Laplace). More advanced courses deal with how you can combine such concepts into algorithms, and how to implement these concepts efficiently in hardware. • Though the analog portion of this course focuses on linear systems, digital systems are most often nonlinear in nature due to the ease with which the linearity assumption can be violated in software. Introduction ECE 3163: Lecture 01, Slide 4 Independent Variables • Time is often the independent variable for a signal. x(t) will be used to represent a signal that is a function of time, t. • A temporal signal is defined by the relationship of its amplitude (the dependent variable) to time (the independent variable). • An independent variable can be 1D (time), 2D (space), 3D (space) or even something more complicated. • The signal is described as a function of this variable. • There are many types of functions that can be used to describe signals (continuous, discrete, random are just a few of the concepts we will encounter this semester). ECE 3163: Lecture 01, Slide 5 Continuous Time (CT) Signals • Most of the signals in the physical world are CT signals, since the time scale is infinitesimally fine (e.g., voltage, pressure, temperature, velocity). • Often, the only way we can view these signals is through a transducer, a device that converts a CT signal to an electrical signal. • Common transducers are the ears, the eyes, the nose… but these are a little complicated. • Simpler transducers are voltmeters, microphones, and pressure sensors. ECE 3163: Lecture 01, Slide 6 Discrete-Time (DT) Signals • We can write a collection of numbers (1, -3, 7, 9) representing a signal as a function of a discrete variable, n. x[n] represents the amplitude, or value of the signal as a function of n, which takes on integer values. • Many human-generated signals are discrete (e.g., MIDI codes, stock market prices, digital images). • In this course, we will show that most of the properties that apply to CT signals apply in a similar manner to DT signals. ECE 3163: Lecture 01, Slide 9 Properties of Even/Odd Signals • Any signals can be expressed as a sum of even and odd signals. That is: • This is demonstrated to the right for a signal referred to as a unit step. 2/)]()([)( 2/)]()([)( : )()()( txtxtx txtxtx where txtxtx odd even oddeven ECE 3163: Lecture 01, Slide 10 Other Types Of Symmetry • A right-sided signal is zero for t < T and a left-sided signal is zero for t > T, where T can be positive or negative. • A signal can be bounded or unbounded depending on the stability of the system. ECE 3163: Lecture 01, Slide 11 Real and Complex Signals • Complex signals are an important abstraction in many disciplines such as communications and multidimensional signal processing. • In general, x is a complex quantity and has:  a real and imaginary part, or equivalently  a magnitude and a phase angle. • A very important class of signals is complex exponentials:  CT signals of the form x(t) = est  DT signals of the form x[n] = zn where z and s are complex numbers. • For example, suppose s = j t/8 and z = e j /8, the exponentials are purely imaginary, then the real parts are: )8/cos()( )8/cos()( 8/ 8/ neznx teetx njn tjst