Network Basic

Well it has been long since I have come across the word Network. It seems to be a simple word with a general definition “an interconnected system of things or people”. But has ever anyone thought what would be the end line definition of this word. Well till date I have also not come across such a definition, which would limit the meaning of this word.

I have tried a lot to find the exact meaning of the word network but in vain because the domain expands to each and every thing we can imagine be it computers, humans etc.

Here what I am trying to deal is the computer networking concepts, their solutions and security that haunt us the most.

A general definition of the computer network could be “a computer network is a system for communication between computers” or “a data communications system that interconnects computer systems at various different sites”. Now the question lies in the point that how this data communication started or what was the base for this kind of communication to begin and so is the answer. 

Theoretical Basis for Data Communication

Communication has been of prime importance in human life without which all of us cannot perform even our daily activities. As rightly said, “Necessity is the mother of all inventions” so was the idea that information can be transmitted on wires by varying some physical properties such as voltage or current. By representing the value of this voltage and current as a single valued function of time, f(t), we can model the behavior of signal and analyze it mathematically.

The Fourier Analysis provided the answer for the question and is said to be as base of networking concept.

Fourier Analysis:  

It says “reasonably behaved periodic function, g(t), with period T can be constructed as a sum of a (possibly infinite) number sines and cosines”.

See the image for equation

So this was the starting of the communication over the electronic media. Here is a brief idea of relation between Fourier Analysis and Computers.

 

Fourier Analysis with Computers

There have been several techniques (tried and tested) that enable a computer to calculate the Frequency Spectrum of a signal. The first step in all cases is to convert the signal to a set of numbers for the computer to use. This is done by sampling the signal at a regular interval so that a table of values is created. Each sample value is separated from the next by a fixed period of time.

The number of points obtained and the time between samples combine to determine the length of time we look at the signal. Following definitions we take into consideration:

fs = sample rate in Hz

dT = 1/fs = interval between samples

N = number of samples taken

T = N x dT = total time period

f1 = 1/T = frequency of the first harmonic in Hz

For example, if we are interested in the AC power line and suppose we choose a sample rate (fs) of 6000 Hz and collect 100 samples (n=100). It gives the result as   dT = 0.1167 msec and T = 16.667 msec. Then the first harmonic would be f1 = 60 Hz.

The traditional mathematical approach to Fourier analysis was based on approximating continuous waveforms but computer techniques can only deal with a set of samples. This does not change the basic idea of harmonic analysis but now we keep in mind the following:

1. The spectrums based on sampled waveforms can generate only N/2 harmonics.

2. If the original signal contains more than N/2 harmonics, the higher frequency harmonics will cause errors in the magnitude spectrum.

This type of error is referred to as Aliasing. Aliasing can be prevented by filtering the input signal before performing the Fourier analysis so that there are no frequency components above f1 and N/2.

The most popular computer algorithm for generating a frequency spectrum is the FFT or Fast Fourier Transform. As the name implies, the FFT is very efficient but it does have one quirk that affects the way it is used. The FFT can only process a sampled waveform where N (number of samples) is a power of 2. Acceptable values of N include 128, 256, 512 and 1024.

 Note: 

The FFT, like most computer algorithms, generates an Exponential Fourier Series, instead of a Trigonometric Fourier Series. The two series are identical except that the magnitude generated by the exponential series are half the value of the trigonometric series. Most application software automatically compensates for this and presents the magnitude spectrum as a Trigonometric series.