Signals and Systems 1
Signals and Systems 1 EE 327
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This 13 page Class Notes was uploaded by Maudie Quitzon on Saturday September 12, 2015. The Class Notes belongs to EE 327 at West Virginia University taught by David Graham in Fall. Since its upload, it has received 52 views. For similar materials see /class/202853/ee-327-west-virginia-university in Electrical Engineering at West Virginia University.
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Date Created: 09/12/15
Introduction to Signals and Systems David W Graham EE 327 Definitions Signal Conveys information Function of time The way it evolves in time is what encodes the information Examples Voltage or current in an electronic circuit Speech and music Bioelectric signals eg ECG Two Types of Signals 1 Continuoustime signals 2 Discretetime signals 1 ContinuousTime Signals Signal that has a value for all points in time Function of time miten as xt because the signal x is a function of Commonly found in the physical world ex Human speech Displayed graphically as a line xt 2 DiscreteTime Signals Signal that has a value for only specific points in time Typically formed by sampling a continuoustime signal Taking the value of the original waveform at specific intervals in time Function of the sample value n Write as xn Often called a sequence Commonly found in the digital world ex wav file or mp3 Displayed graphically as individual values Called a stem plot Xn Sample number 12345678910quotn DiscreteTime 73 Digital Discretetime sequences are continuous in values but discrete only in time Digital signals are discrete in values and discrete in time they can only take on specific values Systems System A collection of items that together performs a function Modifies transforms an input to give an output Represented by System T xt gt ya Txt ex A squaring system xt t T input2 yt TXt X2t System Examples RealWorld Examples of Systems Circuits Car Inputs 9 Steering wheel force on accelerometer and brakes Outputs 9 Position of car velocity Chemical processes Electromechanical systems motors Economics stock market Biological processes heart Two Types of Systems Continuoustime systems Operate on continuoustime signals Commonly found in the physical world Represented mathematically using differential equations System parameters are defined on a continuum of time Discretetime systems Operate on discretetime signals ex Computer algorithms Represented mathematically by difference equations System parameters are defined only at discrete points in time Hybrid Systems Most real systems are hybrid systems Use both CT and DT systems ex Audio delay system b t c n d n e t ft CT ADC DT DAC CT System System System Ampli cation AnalogtoDigital ex Delay DigitaltoAnalog ex Smoothing filter converter converter Samper DT to CT to DT Audio Delay System Example at CT bt Cn DT dn et CT ft h ADC DAC System System System Ampli cation AnalogtoDigital eX Delay DigitaltoAnalog ex Smoothing filter converter converter Sampler DT to CT CT to DT S t t t et blttgt cm raiSEiSnZ r1223 3 o T T Ci 0 O O t t n OIn e 0 et Creating Useable Systems Purpose of system design To create an lO relationship that is predictable The system lO relationship must be the same every time the same today as it was yesterday and will be tomorrow Time Invariant Given any type of input the output follows a reasonable relationship Easiest is Linear Out Linear Out Nonlinear m ll 8 LTI System Most engineering systems are designed to be linear and time invariant LTI so that they are predictable The rest of this course focuses on LTI systems How to analyze How to use How to design
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