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1、Introduction to Signals and SystemsDavid W. GrahamEE 3271DefinitionsSignalConveys informationFunction of timeThe way it evolves in time is what encodes the informationExamplesVoltage or current in an electronic circuitSpeech and musicBioelectric signals (e.g. ECG)2Two Types of Signals1.Continuous-ti
2、me signals2.Discrete-time signals31. Continuous-Time SignalsSignal that has a value for all points in timeFunction of timeWritten as x(t) because the signal “x” is a function of timeCommonly found in the physical worldex. Human speechDisplayed graphically as a line42. Discrete-Time SignalsSignal tha
3、t has a value for only specific points in timeTypically formed by “sampling” a continuous-time signalTaking the value of the original waveform at specific intervals in timeFunction of the sample value, nWrite as xnOften called a sequenceCommonly found in the digital worldex. wav file or mp3Displayed
4、 graphically as individual valuesCalled a “stem” plotSample number5Discrete-Time DigitalDiscrete-time sequences are continuous in values, but discrete only in timeDigital signals are discrete in values and discrete in time (they can only take on specific values)6SystemsSystemA collection of items th
5、at together performs a functionModifies / transforms an input to give an outputRepresented bySystemT x(t)y(t) = Tx(t)T = input2x(t)y(t) = Tx(t) = x2(t)ex. A squaring system7System ExamplesReal-World Examples of SystemsCircuitsCarInputs Steering wheel, force on accelerometer and brakesOutputs Positio
6、n of car, velocityChemical processesElectromechanical systems (motors)Economics, stock marketBiological processes (heart)8Two Types of SystemsContinuous-time systemsOperate on continuous-time signalsCommonly found in the physical worldRepresented mathematically using differential equationsSystem par
7、ameters are defined on a continuum of timeDiscrete-time systemsOperate on discrete-time signalsex. Computer algorithmsRepresented mathematically by difference equationsSystem parameters are defined only at discrete points in time9Hybrid SystemsMost real systems are hybrid systemsUse both CT and DT s
8、ystemsex. Audio delay systemCTSystemADCDTSystemDACCTSystema(t)b(t)cndne(t)f(t)AmplificationAnalog-to-Digital converter-Sampler-CT to DTex. DelayDigital-to-Analog converter-DT to CTex. Smoothing filter10Audio Delay System ExampleCTSystemADCDTSystemDACCTSystema(t)b(t)cndne(t)f(t)AmplificationAnalog-to
9、-Digital converter-Sampler-CT to DTex. DelayDigital-to-Analog converter-DT to CTex. Smoothing filterSample at a constant rate (time period)11Creating Useable SystemsPurpose of system designTo create an I/O relationship that is predictableThe system I/O relationship must be the same every time the sa
10、me today as it was yesterday and will be tomorrowTime InvariantGiven any type of input, the output follows a reasonable relationshipEasiest is LinearLinearNonlinear12LTI SystemMost engineering systems are designed to be linear and time invariant (LTI) so that they are predictableThe rest of this course focuses on LTI systemsHow to analyzeHow to useHow to design13
