SYSTEMS

GUIDED BY:- PRESENTED BY:-Mr. SYED AKBAR S VASANTH KUMAR.R-ECB1496 HOD VENKATESH.S -ECB1498(DEPARTMENT OF ECE) VIGNESH.S -ECB14100 VIJAYASEELAN.M -ECB14101

ABSTRACT

INTRODUCTIONDEFINITIONTYPES OF SYSTEMSAPPLICATIONSPROBLEMSQUERIES

INTRODUCTION

DEFINITION

SYSTEM:- It is a physical device, which is used to process the signal (or) to extract the information.

i)Continuous time system.ii)Discrete time system.

Block Diagram Representation of a System

CONTINUOUS SYSTEM

A system is continuous-time when its input and output signals are continuous-time.

DISCRETE SYSTEM

A system is discrete -time when its input and output signals are discrete-time.

TYPES OF SYSTEM

Static & Dynamic systemCausal & Non Causal systemStable & Unstable systemLinear & Non-linear systemTime variant & Time invariant system

STATIC SYSTEM

Output depend only on present input.Also called as memory-less system.

Examplesy(n) = 9x(n)y(t) = x2(t) + 8x(t) + 17

RESISTORS

+

-

SPST

R V

+

-Bt

DYNAMIC SYSTEM

Output depends on present, past, future inputs.It is also called as memory system.

Examples y(n)=x(n-1) y(t)=x(t+1)

CAPACITORS

CAUSAL SYSTEM

A system is said to be causal system if its output depends on present and past inputs only and not on future inputs.It is also called as anticipative system.

Examplesy(n) = x(n) + x(n-2)y(t) = x(t-1) – x(t-3)

SIGNIFICANCE OF CAUSAL SYSTEM

Practically realizable.All real time systems are causal systems.

NON-CAUSAL SYSTEM

A system whose present response depends on future values of the inputs is called as a non-causal system.It is also called as non-anticipative system.

ExamplesY(n) = x(n) + x(n+1)Y(n) = 7x(n+2)

SIGNIFICANCE OF NON-CAUSAL SYSTEM

Practically not realizable.But can be predictable.

EXAMPLES

Population growthWeather forecasting Planning commission

STABLE SYSTEM

A stable system is BIBO stable if and only if every bounded input produces bounded output.

UNSTABLE SYSTEM

An initially system is said to be unstable if bounded input produces unbounded (infinite) output.

SIGNIFICANCE OF UNSTABLE SYSTEM

Unstable system shows erratic and extreme behavior.When unstable system is practically implemented then it causes overflow.

LINEAR & NON-LINEAR SYSTEM

If the system satisfies superposition principle then the system is called linear system.If the system does not satisfies superposition principle then the system is called non-linear system.Communication channels and filters are examples of linear systems.

SUPERPOSITION PRINCIPLE

The weighted sum of input is equal to the weighted sum of output

T[a x1(t) + b x2(t)] = a y1(t) + b y2(t) T[a x1(n) + b x2(n)] = a y1(n) + b y2(n)

1 2 1 2

1 2 1 2

1 2 2

1 2 1 2

( ) ( ) ( ( ) ( ))

( ) ( ) ( ( ) ( ))

( ), ( ) , ( ), ( )

( ), ( ) ( ), ( )

ay n by n T ax n bx n

ay t by t T ax t bx t

x n x n Input discrete signal y n y n output discrete signal

x t x t input continuos signal y t y t output continuos signal

1

I

TIME VARIANT SYSTEM

If the system does not satisfies the following condition

y(t-T)=T[x(t-T)]then the system is said to be time variant system The human vocal tract is a time variant system

TIME INVARIANT SYSTEM

If the system satisfies the following condition y(t-T)=T[x(t-T)]Then the system is said to be time invariant

system.

LTI SYSTEM EXAMPLES

SEISMOGRAPH NMR SPECTROSCOPY

PROBLEMS

I. y(n) = x(n) II. y(t) = x(t+2)III. y(n) = x(2n-1)IV. y(t) = x(t2)V. y(n) = nx(n)VI. y(t) =ex(t)

VII.y(n)=x(2n)VIII.y(t)=x(t)cosωοt

QUERIES?