Overview of Signals and SystemsOverview of Signals and Systems

Overview of OverviewOverview of Overview Administrative detailsAdministrative details

• Syllabus, attendance, report, notebookSyllabus, attendance, report, notebook SignalsSignals SystemsSystems Examples of signals and systemsExamples of signals and systems What we do with signals and systems in What we do with signals and systems in

electrical engineeringelectrical engineering

SignalsSignals Information or data that varies with time.Information or data that varies with time.

Time is the independent variable that we’ll deal with in Time is the independent variable that we’ll deal with in electrical engineering.electrical engineering.

Examples:Examples: TV signal, radio signal, mp3TV signal, radio signal, mp3 Electrical signals (voltages and currents)Electrical signals (voltages and currents) Acoustic signals (both analog and digital)Acoustic signals (both analog and digital) Video signalsVideo signals

• Variation in the intensity of a colorVariation in the intensity of a color Biological signalsBiological signals

• DNA sequenceDNA sequence Economic signals – stock prices, DJIAEconomic signals – stock prices, DJIA

The Independent VariablesThe Independent Variables Can be continuousCan be continuous

Trajectory of a space shuttleTrajectory of a space shuttle Mass density in a cross-section of a brainMass density in a cross-section of a brain

Can be discreteCan be discrete DNA base sequenceDNA base sequence Digital Image pixelsDigital Image pixels

However, we will focus on a single independent However, we will focus on a single independent variable called time.variable called time. Continuous (CT) signals: x(t), tContinuous (CT) signals: x(t), t Discrete (DT) signals: x[n], nDiscrete (DT) signals: x[n], n

CT signalsCT signals

Voltage, current, pressure, temperature, Voltage, current, pressure, temperature, velocity…velocity… Most of the signals in the physical world.Most of the signals in the physical world.

DT SignalsDT Signals

x[n], n – integer, time varies discretelyx[n], n – integer, time varies discretely Examples of discrete signals in nature:Examples of discrete signals in nature:

DNA base sequence.DNA base sequence. Population of the nPopulation of the nthth generation of a certain generation of a certain

speciesspecies

Human-made DT signalsHuman-made DT signals

Why do we like digital signals?Why do we like digital signals?

SystemsSystems

Process inputs and produce outputs.Process inputs and produce outputs. For the most part, we will take an input-For the most part, we will take an input-

output perspective.output perspective.

Examples of SystemsExamples of Systems An RLC circuitAn RLC circuit

An edge detection algorithm for medical An edge detection algorithm for medical images.images.

A DSP system in a cell phoneA DSP system in a cell phone How many systems are in a cell phone?How many systems are in a cell phone?

System InterconnectionsSystem Interconnections

Doing stuff to inputs to produce outputs.Doing stuff to inputs to produce outputs. Transformations, shifting, scaling, invertingTransformations, shifting, scaling, inverting

What We’ll Be DoingWhat We’ll Be Doing MathMath

Linear algebra, complex numbers, some Linear algebra, complex numbers, some differential equations, time shifting, unit step differential equations, time shifting, unit step function, linear systems, causal and function, linear systems, causal and noncausal systems.noncausal systems.

Time domain analysisTime domain analysis Power, size, singularity functions, convolution, Power, size, singularity functions, convolution,

easy continuous functions.easy continuous functions. Discrete versions of the above; difference Discrete versions of the above; difference

equations.equations.

What We’ll Be DoingWhat We’ll Be Doing Laplace Transform for Continuous SystemsLaplace Transform for Continuous Systems

Bode plots, filters, pole analysisBode plots, filters, pole analysis Z Transform for Discrete SystemsZ Transform for Discrete Systems

Only briefly; at the end of the semesterOnly briefly; at the end of the semester Fourier SeriesFourier Series Fourier TransformFourier Transform

Why We Are Doing ThisWhy We Are Doing This Will you ever have to do these by hand at your Will you ever have to do these by hand at your

job?job? Probably not.Probably not.

You will, however, need to know how to provide You will, however, need to know how to provide a computer proper inputs and be able to a computer proper inputs and be able to interpret the outputs.interpret the outputs. Garbage in, garbage out.Garbage in, garbage out.

To develop an appreciation and an To develop an appreciation and an understanding of how signal analysis works.understanding of how signal analysis works.

Examples of Signals that Need Examples of Signals that Need ProcessingProcessing

MotionMotion What’s the domain and range?What’s the domain and range? How do you see motion on a TV?How do you see motion on a TV?

SoundSound Associates a pressure value to every value of time Associates a pressure value to every value of time

and 3 space coordinates. A microphone converts and 3 space coordinates. A microphone converts sound pressure at just one place to just a function of sound pressure at just one place to just a function of time, using a voltage signal as an analog of the sound time, using a voltage signal as an analog of the sound signal.signal.

PicturesPictures Are these analog or digital?Are these analog or digital?

• What’s the domain and range?What’s the domain and range?