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Lecture #1

Jan 05, 2016

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Lecture #1. Introduction to signals. signals. Signals are functions of independent variables that carry information. Electrical signals Voltages and currents in a CKT Acoustic signals Audio or speech signals Video signals Intensity variations in an image. Independent variables. - PowerPoint PPT Presentation

  • Lecture #1Introduction to signals

    signals & systems

  • signalsElectrical signalsVoltages and currents in a CKTAcoustic signalsAudio or speech signalsVideo signalsIntensity variations in an image

    Signals are functions of independent variables that carry information.

    signals & systems

  • Independent variables Can be continuous

    Can be discrete

    Can be 1-dimension, 2-D, N-D

    For this course we focus on a signal 1-D independent variable which we called timeContinuous time x(t) , t continuous values Discrete time x[k], k Integer values only

    signals & systems

  • Continuous time (CT) signalMost of the signals in the physical world are CT signalsE.g. voltage & current, pressure, temperature, velocity, etc.

    signals & systems

  • Discrete time (DT) signalExamples of DT signals in nature: DNA base sequence Population of the nth generation of certain species

    signals & systems

  • SamplingQuantizing&encodingContinuous-time analog signalDiscrete-time analog signalDiscrete-time digital signal0001

    signals & systems

  • Classification of signalsContinuous-time and discrete-time signalsEven and odd signalsPeriodic and nonperiodic signalsDeterministic and random signals

    Periodic signals

    signals & systems

  • Even signal odd signal

    signals & systems

  • Elementary signalsExponential signalsSinusoidal signalsStep functionRectangular pulseImpulse function Derivatives of the impulseRamp function

    signals & systems

  • Exponential signals

    signals & systems

  • signals & systems

  • Step functionShift a

    signals & systems

  • Rectangular pulse

    signals & systems

  • Impulse function

    signals & systems

  • Derivatives of the impulse

    signals & systems

  • signals & systems

  • Ramp function

    signals & systems

  • simple operation

    signals & systems

  • Basic operations on signalsOperations performed on dependent variablesAmplitude scaling, Addition, Multiplication, differentiation Operations performed on independent variablesTime scalingReflectionTime shifting

    signals & systems

  • Time scaling

    signals & systems

  • Reflection

    signals & systems

  • Time shifting

    signals & systems

  • Precedence rule for time shifting and time scalingExample 1.5 find y(t)=x(2t+3)

    signals & systems

  • Precedence rule for discrete-time signal

    signals & systems