Analysis of Discrete-time Linear-Invariant Systems

we shall demonstrate that such systems are characterized in the time domain simply by their response to a unit sample sequence.we shall also demonstrate that any arbitrary input signal can be decomposed and represented as a weighted sum of unit sample sequences.As a consequence of the linearity and time-in variance properties of the system,the response of the system to any arbitrary input signal can be expressed in terms of the unit sample response of the system.the general form of the expression that relates the unit sample response of the system and the arbitrary input signal to the output signal,called the convolution sum or the convolution formula,is also derived.Thus we are able to determine the output of any linear,time-invariant system to any arbitrary  input signal.
Techniques for the analysis of Linear Systems

There are two basic methods for analyzing the behavior or response of a linear system to a given input signal.One method is based on the direct solution of the input-output equation for the system,which,in general,has the form
y(n)=F[y(n-1),y(n-2),.......y(n-N),x(n),x(n-1),....,x(n-M)]
where F[.]denotes some function of the quantities in brackets.
Resolution of a Discrete-Time signal into Impulses
suppose we

Single Acting Cylinder in Pneumatic

With single-acting cylinders compressed air is applied on only one side of the piston face.The other side is open to atmosphere.The cylinder can produce work in only one direction.The return movement of the piston is effected by a build-in spring or by the application of an external force.The spring force of the build-in-spring is designed to return the piston to its start position with a reasonably high speed under no load conditions.
For single-acting cylinder with build-in spring,the stroke is limited by the natural length of the spring.Single-acting cylinder are therefore only available in stroke lengths of up to approximately 80mm.

Air Preparation

For the continuing performance of control systems and working elements it is necessary to guarantee that the air supply is:

• at the required pressure
• dry and
• clean

If these conditions are not fulfilled,then short to medium term degeneration of the system will be accelerated.The effect is downtime on the machinery in addition to increased costs for repair or replacement of parts.

The generation of compressed air starts off with compression.The compressed air flows through an entire series of components before reaching the consuming device.The type of compressor and its location to a lesser or greater degree affect the amount of dirt particles,oil and water which enter into a pneumatic system.The equipment to be considered in the generation and preparation of air include:

• Inlet filter
• Air compressor
• Air reservoir
• Air dryer
• Air filter with water separator
• pressure regulator
• Air lubricator as required
• Drainage points

poorly-prepared compressed air will inevitable lead to malfunctions and may manifest itself in the system as follows:

• Rapid wear of seals and moving parts in the cylinders and valves
• Oiled-up valves
• Contaminated silencers
• Corrosion in pipes,valves,cylinders and other components
• Flushing out of lubrication of moving components

In the case of leakage,escaping compressed air may impair the materials to be processed(e.g food)

Application of microprocessor

Microprocessors field wide applications in the fields of instrumentation,communication,data processing,industrial process instrumentation,commerce and consumer products.
A few exemplifying applications in each field are given below:
1. Instrumentation: Automatic test equipment,electronic instrument;and analytical,chemical,and medical equipment.
2. Communication: Remote terminals,programmable controller, switching systems,multiplexers,message handling and error detection.
3.Data processing: programmable calculators;peripheral processors,I/O controllers and communication interface.
4. Industrial: Data acquisition system,numerical control and environmental monitoring process control and instrumentation.
5.Commercial: Inventory control system,payroll,banking and financial system and auto-transaction system.
6.Consumer: Education systems,intelligent toys,games,automotive system and programmable appliances.
The electronic industry has been benefited by the introduction of microprocessors in the three broad areas of flexibility,reliability and cost.Mini or small business computer industry,the electronics industry and the large-scale data processing industry are the major beneficiary from introduction of microprocessor

Hard Disk

hard disks are on-line storage devices.The term on-line means that the device (hard disks) is permanently connected to the computer system.when computer is on,the device (hard disks) is available to store information or to give information.Hard disks are used as secondary memory for mass (bulk) storage of information permanently.They store program,data,operating system,compilers,assemblers,application programs,database,etc.

A hard disk is made of aluminum( or other metal or metal alloy) with a thin coating of magnetic material (iron oxide) over it,standard size of hard disks is 3.5 inch.The 2.5 inch disk are used in portable computers.Hard disks and read/write heads are kept in a sealed,air filtered enclosure.This technique is known as winchester technique.Hard disks together with read/write heads,access mechanism and driving motor constitute an unit called hard disk drive platter.It cannot be removed or inserted into a hard disk drive unit.Hard disk drive unit under discussion is of large capacity,and is used as secondary memory.Recently removable hard disks and external hard disks of smaller capacity for backup memory have also been developed.

To increase the storage capacity several hard disk(platters) are mounted on common drive to constitute a disk pack,as shown in fig.The set of all tracks at the same distance from the spindle on the record able surface of the disk pack will lie on the surface of an imaginary cylinder.All the tracks which lie on a cylinder have same number.for example,track-10 of each recordable surface of the pack will lie on the cylinder which is numbered as cylinder-10.The disks are addressed by drive number(because more than one drives are used in a computer),cylinder number (i.e. track number),surface number and sector number. 

Unions

Unions are a concept borrowed from structures and therefore follow the same syntax as structures.However,there is major distinction between them of storage.In structures,each member has its own storage location,whereas all the members of a union use the same location.This implies that,although a union may contain many members of different type,it can handle only one member at a time.

a union can be declared using the keyword union as follows:

union item

{

int m;

float x;

char c;

}

code;

The declares a variable code of type union item.The union contains three members,each with a different data type.However,we can use only one of them at a time.This is due to the fact that only one location is allocated for a union variable,irrespective of its size.

The compiler allocated a piece of storage i.e large enough to hold the largest variable type in the union.

Searching and Sorting

Searching and sorting are the two most frequent operations performed on arrays.Computer scientists have devised several data structures and searching and sorting techniques that facilitate rapid access to data stored in lists.
sorting is the process of arranging elements in the list according to their values,in ascending or descending order.A sorted list is called an ordered list.sorted lists are especially important in list searching because they facilitate rapid search operations.Many sorting techniques are available.The three simple and most important among them are:

• Bubble sort
• Selection sort
• Insertion sort

Other sorting techniques include shell sort,Merge sort and Quick sort.
Searching is the process of finding the location of the specified elements in a list.The specified elements is often called the search key.If the process of searching finds a match of the search key with a list elements value,the search said to be successful;otherwise,it is unsuccessful.The two most commonly used search techniques are:

• Sequential search
• Binary search