Introduction to systems
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Introduction to Systems. What are signals and what are systems The system description Classification of systems Deriving the system model – Continuous systems Continuous systems: solution of the differential equation. What are signals and what are systems.

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Introduction to systems
Introduction to Systems

  • What are signals and what are systems

  • The system description

  • Classification of systems

  • Deriving the system model – Continuous systems

  • Continuous systems: solution of the differential equation

What are signals and what are systems
What are signals and what are systems

  • Example 1 Removal of noise from an audio signal

Systems working principle
Systems working principle

  • Taking the voltage from the cartridge playing the ‘78’ rpm record

  • Removing the ‘hiss’ noise by filter

  • Amplifying the information signal

  • Recording the signal to new format

Introduction to systems

The system description
The System Description

  • The system description is based on the equations relating the input and output quantities.

  • This way of description is an idealisation, it is a mathematical model which only approximates the true process.

  • This type of approach assumes the real system is hidden in a ‘black’ box and all that is available is a mathematical model relating output and input signals.

Classification of systems
Classification of Systems

  • The reason for classifying systems:

    • If one can derive properties that apply generally to a particular area of the classification then once it is established that a system belongs in this area then these properties can be used with further proof.

  • Continuous /discrete systems

Analog signals

Analog signals


A/D conversion

Digital Signal


D/A conversion

& Filtering

Liner non liner systems
Liner/ non-liner Systems

  • The basis of a linear system is that if inputs are superimposed then the responses to these individual inputs are also superimposed. That is:

    • If an arbitrary input x1(t) produce output y1(t) and an arbitrary input x2(t) produce output y2(t), then if the system is linear input x1(t)+x2(t) will produce output y1(t)+y2(t).

    • For a linear system an input (ax1(t)+bx2(t)) produce an output ay1(t)+by2(t)), where a, b are constants.

Time invariant time varying systems
Time invariant /time varying systems

  • The time invariance can be expressed mathematically as follows:

    • If an input signal x(t) causes a system output y(t) then an input signal x(t-T) causes a system output y(t-T) for all t and arbitrary T.

  • If a system is time invariant and linear it is known as a linear time invariant or LTI system.

Instantaneous non instantaneous systems
Instantaneous/non-instantaneous systems

  • For the system such as y(t)=2x(t), the output at any instant depends upon the input at that instant only, such a system is defined as an instantaneous system.

  • Non-instantaneous systems are said to have a ‘memory’. For the continuous system, the non-instantaneous system must be represent by a differential equation.

Deriving the system model
Deriving the System Model

  • The steps involved in the construction fo the model:

    • Identifying the components in the system and determine their individual describing equations relating the signals (variables) associated with them

    • Write down the connecting equations for the system which relate how the individual components relate to the other.

    • Eliminate all the variables except those of interest, usually these are input and output variables.

Zero input and zero state responses
Zero-input and Zero-state responses

  • The zero-state response. This the response to the applied input when all the initial conditions (the system state) is zero

  • The zero-input response. This is the system output due to the initial conditions only. The system input is taken as zero.

Continuous systems solution of the differential equation
Continuous Systems: solution of the differential equation

  • The linear continuous system can in general be described by a differential equation relating the system output y(t) to its input x(t). The nth order equation can be written as:

    dny/dtn+an-1dny/dtn+…+a0y =

    bm dmx/dtm+bm-1dm-1x/dtm-01+…+b0x

    It can also be written as:

    (Dn+an-1Dn-1+…+a0)y=(bmDm+ bm-1Dm-1+…+b0)x