Lecture 1 Introduction to signals meiling chen signals

Lecture #1 Introduction to signals meiling chen signals & systems 1

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 meiling chen signals & systems 2

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 “time” Continuous time x(t) , t– continuous values Discrete time x[k], k– Integer values only meiling chen signals & systems 3

Continuous time (CT) signal Most of the signals in the physical world are CT signals— E. g. voltage & current, pressure, temperature, velocity, etc. meiling chen signals & systems 4

Discrete time (DT) signal Examples of DT signals in nature: • DNA base sequence • Population of the nth generation of certain species meiling chen signals & systems 5

Continuous-time analog signal Sampling Discrete-time analog signal Quantizing & encoding Discrete-time digital signal 0001 meiling chen signals & systems 6

Classification of signals • • Continuous-time and discrete-time signals Even and odd signals Periodic and nonperiodic signals Deterministic and random signals Periodic signals meiling chen signals & systems 7

Even signal odd signal meiling chen signals & systems 8

Elementary signals • • Exponential signals Sinusoidal signals Step function Rectangular pulse Impulse function Derivatives of the impulse Ramp function meiling chen signals & systems 9

Exponential signals meiling chen signals & systems 10

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Step function Shift a meiling chen signals & systems 12

Rectangular pulse meiling chen signals & systems 13

Impulse function Amplitude width meiling chen signals & systems 14

Derivatives of the impulse meiling chen signals & systems 15

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Ramp function meiling chen signals & systems 17

simple operation meiling chen signals & systems 18

Basic operations on signals • Operations performed on dependent variables – Amplitude scaling, Addition, Multiplication, differentiation • Operations performed on independent variables – Time scaling – Reflection – Time shifting meiling chen signals & systems 19

Time scaling meiling chen signals & systems 20

Reflection meiling chen signals & systems 21

Time shifting meiling chen signals & systems 22

Precedence rule for time shifting and time scaling Example 1. 5 find y(t)=x(2 t+3) meiling chen signals & systems 23

Precedence rule for discrete-time signal meiling chen signals & systems 24