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# Lecture #1

Jan 05, 2016

## Documents

abiba

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

#### ct signalse

• 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

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