Formula-for-Signal-Noise-Ratio-Calculation

• Explain the formula for Signal to Noise Ration Calculation - Signal-to-noise ratio (often abbreviated SNR or S/N) is an electrical engineering measurement, also used in other fields (such as scientific measurements, biological cell signaling), defined as the ratio of a signal power to the noise power corrupting the signal.

In less technical terms, signal-to-noise ratio compares the level of a desired signal (such as music) to the level of background noise. The higher the ratio, the less obtrusive the background noise is.

In engineering, signal-to-noise ratio is a term for the power ratio between a signal (meaningful information) and the background noise:

where P is average power and A is root mean square (RMS) amplitude (for example, typically, RMS voltage). Both signal and noise power (or amplitude) must be measured at the same or equivalent points in a system, and within the same system bandwidth.

Because many signals have a very wide dynamic range, SNRs are usually expressed in terms of the logarithmic decibel scale. In decibels, the SNR is, by definition, 10 times the logarithm of the power ratio. If the signal and the noise is measured across the same impedance then the SNR can be obtained by calculating 20 times the base-10 logarithm of the amplitude ratio:

Maximum-Data-Rate-of-Channel

• Maximum Data Rate of a Channel - In 1924, H.Nyquist realized the existence of the fundamental limit and derived the equation expressing the maximum data for a finite bandwidth noiseless channel. In 1948, Claude Shannon carried Nyquist work further and extended it to the case of a channel subject to random noise.

In communications, it is not really the amount of noise that concerns us, but rather the amount of noise compared to the level of the desired signal. That is, it is the ratio of signal to noise power that is important, rather than the noise power alone. This Signal-to-Noise Ratio (SNR), usually expressed in decibel (db), is one of the most important specifications of any communication system. The decibel is the logarithmic unit used for comparisons of power levels or voltage levels. In order to understand the implication of db, it is important to know that a sound level of zero db corresponds to the threshold of hearing, which is the smallest sound that can be heard. A normal speech conversation would measure about 60 db.

If an arbitrary signal is passed through the Low pass filter of bandwidth H, the filtered signal can be completely reconstructed by making only 2H samples per second. Sampling the line faster than 2H per second is pointless. If the signal consists of V discrete levels, then Nyquist theorem states that, for a noiseless channel Maximum data rate= 2H.log2 (V) bits per second.

Band-Limited-Signals

Band Limited Signals - A bandlimited signal is a deterministic or stochastic signal whose Fourier transform or power spectral density is zero above a certain finite frequency. In other words, if the Fourier transform or power spectral density has finite support then the signal is said to be bandlimited.

A bandlimited signal can be fully reconstructed from its samples, provided that the sampling rate exceeds twice the maximum frequency in the bandlimited signal. This minimum sampling frequency is called the Nyquist rate. This result, usually attributed to Nyquist and Shannon, is known as the Nyquist–Shannon sampling theorem, or simply the sampling theorem.

An example of a simple deterministic bandlimited signal is a sinusoid of the form . If this signal is sampled at a rate so that we have the samples , for all integers n, we can recover completely from these samples. Similarly, sums of sinusoids with different frequencies and phases are also bandlimited.

The signal whose Fourier transform is shown in the figure is also bandlimited. Suppose is a signal whose Fourier transform is , the magnitude of which is shown in the figure. The highest frequency component in is . As a result, the Nyquist rate is

or twice the highest frequency component in the signal, as shown in the figure. According to the sampling theorem, it is possible to reconstruct completely and exactly using the samples

for integer and

as long as

The reconstruction of a signal from its samples can be accomplished using the Whittaker–Shannon interpolation formula.

A bandlimited signal cannot be also timelimited. More precisely, a function and its Fourier transform cannot both have finite support. This fact can be proved by using the sampling theorem.

Fourier-Analysis

• Fourier Analysis - In mathematics, Fourier analysis is a subject area which grew out of the study of Fourier series. The subject began with trying to understand when it was possible to represent general functions by sums of simpler trigonometric functions. The attempt to understand functions (or other objects) by breaking them into basic pieces that are easier to understand is one of the central themes in Fourier analysis. Fourier analysis is named after Joseph Fourier who showed that representing a function by a trigonometric series greatly simplified the study of heat propagation.

Today the subject of Fourier analysis encompasses a vast spectrum of mathematics with parts that, at first glance, may appear quite different. In the sciences and engineering the process of decomposing a function into simpler pieces is often called an analysis. The corresponding operation of rebuilding the function from these pieces is known as synthesis. In this context the term Fourier synthesis describes the act of rebuilding and the term Fourier analysisdescribes the process of breaking the function into a sum of simpler pieces. In mathematics, the term Fourier analysis often refers to the study of both operations.

In Fourier analysis, the term Fourier transform often refers to the process that decomposes a given function into the basic pieces. This process results in another function that describes how much of each basic piece are in the original function. It is common practice to also use the term Fourier transform to refer to this function. However, the transform is often given a more specific name depending upon the domain and other properties of the function being transformed, as elaborated below. Moreover, the original concept of Fourier analysis has been extended over time to apply to more and more abstract and general situations, and the general field is often known as harmonic analysis.

Each transform used for analysis has a corresponding inverse transform that can be used for synthesis.

Design-Issues-of-Layers

• Design Issues of Layers - There are some key design issues that are to be considered in computer networks. Every layer needs a mechanism for identifying senders and receivers. As many computers are normally connected in networks, few of which have multiple processors. A means for a process on one machine is needed to specify with whom it wants to communicate to. Thus some form of addressing scheme is to be devised.

Another design issue is data transmission modes. It concerns the rules for the data transfer. The systems can use serial or parallel transmission, synchronous or Asynchronous transmission, simplex or duplex transmission. The protocol also must determine how many logical channels the connection corresponds to and what their priorities are.

Another major design issue is Error Control techniques as physical circuits are not perfect. Some of the error detecting or correcting codes are to be used at both the ends of the connection. At the same time we need to consider Flow Control techniques is necessary to keep a fast sender from swamping a slow receiver. Some systems use some kind of feedback from receiver, which is useful to limit the transmission rate.

It is convenient or expensive to set up separate connection for each pair of communicating processes. Same connection can be used by multiple & unrelated conversation. Thus we need to focus on Multiplexing and de-multiplexing techniques as one of the design issue. Multiplexing is needed in the physical layer, where all the traffic for all connections has to be sent over at most a few physical circuits.

When there are multiple paths between the source and destination the complexity lies in finding the best, optimum and shortest path. Hence to find optimum path we need Routing schemes. Apart from these some the design issues can be related to security, compression techniques and so on.

Service-Primitives

• Service primitives - A service is formally specified by a set of primitives or operations available to the user to access the service. These primitives tell the service to perform some action or report an action taken by the peer entity. The primitives for the connection-oriented service are given in the table.

Primitive	Meaning
LISTEN	Block waiting for an incoming connection
CONNECT	Establish a connection with a waiting peer
RECEIVE	Block waiting for an incoming message
SEND	Send a message to the peer
DISCONNECT	Terminate a connection

Each protocol which communicates in a layered architecture communicates in a peer-to-peer manner with its remote protocol entity. Communications between adjacent protocol layers are managed by calling functions, called primitives, between the layers. A primitive initiates an action or advises the result of an action. Each primitive may contain parameters to convey the Protocol Control Information (PCI) needed to perform its functions.

Uses-of-Video-Conferencing

Uses of Video conferencing:

Video conferencing can be used in a host of different environments, which is one of the reasons the technology is so popular. General uses for video conferencing include business meetings, educational training or instruction and collaboration among health officials or other representatives. Thus far video conferencing has been used in the following fields:

• Telemedicine
• Telecommunication
• Education
• Surveillance
• Security
• Emergency Response