A discrete signal or discrete-time signal is a function of a continuous argument; however, it may have been obtained by sampling from a continuous-time signal, and then each value in the sequence is called a sample.By acquiring values of an analog signal at constant or variable rate. This process is called sampling

time axis is discrete whereas in continuous single time axis is continuous .

A continuous signal or a continuous-time signal is a varying quantity (a signal) whose domain, which is often time, is a continuum (e.g., a connected interval of the reals). That is, the function's domain is an uncountable set. The function itself need not be continuous. To contrast, a discrete time signal has a countable domain, like the natural numbers.

A digital signal is discrete-time signal for which not only the time but also the amplitude has been made discrete; in other words, its samples take on only values from a discrete set

Digital signal

A deterministic signal is a signal in which each value of the signal is fixed and can be determined by a mathematical expression, rule, or table.

A non-deterministic signal has a lot of uncertainty about its behavior. The future values of a random signal cannot be accurately predicted and can usually only be guessed based on the averages of sets of signals For a non-deterministic signal the physical phenomenon cannot be represented mathematically.

Periodic signals repeat with some period T, while aperiodic, or nonperiodic, signals do not . We can define a periodic function through the following mathematical expression, where t can be any number and T is a positive constant:

f (t) = f (T + t)

(1)

The fundamental period of our function, f(t), is the smallest value of T that the still allows Equation 1 to be true.

(a) A periodic signal with period T0

ENERGY SIGNAL

If the total energy of a signal is a finite non-zero value, then that signal is classified as an energy signal.Typically the signals which are not periodic turns out to be energy signals. For example, a single rectangular pulse and a decaying exponential signal are energy signals.

POWER SIGNAL

If power of a signal is a finite non-zero value and its energy is infinite, then that signal is classified as a power signal.

The unit step

The unit step function is equal to zero when its index is negative and equal to one for non-negative indexes

UNIT STEP:

u(n)={1 if n≥00 otherwise

a signal that satisfies the unit step function is called unit step function.

Ramp signal

The Step signal can be interpreted as a ramp of width zero, when the ramp is defined as follows

$\begin{displaymath} \mathrm{ramp}(x,w) = \left\{ \begin{array}{ll} 1 & \textrm... ...eq x < w$}\\ 0 & \textrm{if $x < 0$}\\ \end{array} \right. \end{displaymath}$

Signum signal

The signum function of a real number x is defined as follows:

$\sgn(x) = \begin{cases} -1 & \text{if } x < 0, \\ 0 & \text{if } x = 0, \\ 1 & \text{if } x > 0. \end{cases}$

If the dependent variable x is replaced with the time the signal obtained is called signum signal.

Rectangular pulse

A rapid, transient change in the amplitude of a signal from a baseline value to a higher or lower value, followed by a rapid return to the baseline value is known as pulse and if pulse is in rectangular form it is called rectangular pulse signal.

The impulse signal

The impulse function, also known as Dirac delta function or Dirac impulse, is defined by

$\begin{displaymath} \delta(\mathrm{x})= \left\{ \begin{array}{ll} \infty & \textrm{if $x=0$}\\ 0 & \textrm{else}\\ \end{array} \right. \end{displaymath}$

Linear system

A linear system is a mathematical model of a system based on the use of a linear operator. Linear systems typically exhibit features and properties that are much simpler than the general,nonlinear case. As a mathematical abstraction or idealization, linear systems find important applications in automatic control theory, signal processing, and telecommunications. For example, the propagation medium for wireless communication systems can often be modeled by linear systems.

A general deterministic system can be described by operator, $H$ , that maps an input, $x(t)$ , as a function of $t$ to an output, $y(t)$ , a type of black box description. Linear systems satisfy the properties of superposition and scaling or homogeneity. Given two valid inputs

$x_1(t) \,$

$x_2(t) \,$

as well as their respective outputs

$y_1(t) = H \left \{ x_1(t) \right \}$

$y_2(t) = H \left \{ x_2(t) \right \}$

then a linear system must satisfy

$\alpha y_1(t) + \beta y_2(t) = H \left \{ \alpha x_1(t) + \beta x_2(t) \right \}$

for any scalar values $\alpha \,$ and $\beta \,$ .

Nonlinear system

nonlinear system is one that does not satisfy the superposition principle, or one whose output is not directly proportional to its input

Time-invariant system

A time-invariant (TIV) system is one whose output does not depend explicitly on time.

If the input signal $x(t)$ produces an output $y(t)$ then any time shifted input, $x(t + \delta)$ , results in a time-shifted output $y(t + \delta)$

To demonstrate how to determine if a system is time-invariant then consider the two systems:

System A: $y(t) = t\, x(t)$

System B: $\,\!b(t) = 10 x(t)$

Since system A explicitly depends on t outside of $x(t)$ and $y(t)$ then it is not time-invariant. System B, however, does not depend explicitly on t so it is time-invariant.

Time-variant system

A time-variant system is a system that is not time invariant (TIV). Roughly speaking, characteristics of its output depend explicitly upon time.

for better understanding of time variant system . Let:

x(t) be an excitation signal.

T(x(t), t) be the describe the input–output map of a system in relaxed state.

y(t) be the system's output response $y(t) = T(x(t), t)$ to the excitation signal.

Stable and unstable systems

The stability of control systems is an important property. Considering any bounded input signal

of a system, and if the output signal

of the system to such a signal is also bounded, then the system is called bounded-input-bounded-output stable. If the output signal does not show this property, the system is unstable. For illustration see Figure .

Types of Transmission Media

Transmission Media

The means through which data is transformed from one place to another is called transmission or communication media. There are two categories of transmission media used in computer communications.

1.GUIDED MEDIA/BOUNDED MEDIA
2.UNGUIDED /UNBOUNDED MEDIA

Bounded media are the physical links through which signals are confined to narrow path. These are also called guide media. Bounded media are made up o a external conductor (Usually Copper) bounded by jacket material. Bounded media are great for LABS because they offer high speed, good security and low cast. However, some time they cannot be used due distance communication. Three common types of bounded media are used of the data transmission. These are

Coaxial Cable

Twisted Pairs Cable

Fiber Optics Cable

1.COAXIAL CABLE:

Coaxial cable is very common & widely used commutation media. For example TV wire is usually coaxial.

Coaxial cable gets its name because it contains two conductors that are parallel to each other. The center conductor in the cable is usually copper. The copper can be either a solid wire or stranded martial.

Outside this central Conductor is a non-conductive material. It is usually white, plastic material used to separate the inner Conductor form the outer Conductor. The other Conductor is a fine mesh made from Copper. It is used to help shield the cable form EMI.

ADVANTAGES COAXIAL CABLE

Inexpensive
Easy to wire
Easy to expand
Moderate level of EMI immunity

DISADVANTAGE COAXIAL CABLE

Single cable failure can take down an entire network
Twisted Pair Cable
The most popular network cabling is Twisted pair. It is light weight, easy to install, inexpensive and support many different types of network. It also supports the speed of 100 mps.Twisted pair cabling is made of pairs of solid or stranded copper twisted along each other. The twists are done to reduce vulnerably to EMI and cross talk. The number of pairs in the cable depends on the type. The copper core is usually 22-AWG or 24-AWG, as measured on the American wire gauge standard. There are two types of twisted pairs cabling

1. Unshielded twisted pair (UTP)

2. Shielded twisted pair (STP)

Unshielded twisted pair (UTP)

UTP is more common. It can be either voice grade or data grade depending on the condition. UTP cable normally has an impedance of 100 ohm. UTP cost less than STP and easily available due to its many use.
- - Characteristics of UTP
- low cost
- easy to install
- High speed capacity
- High attenuation
- Effective to EMI
- 100 meter limit
Advantages of UTP
- Easy installation
- Capable of high speed for LAN
- Low cost
Disadvantages of UTP
- Short distance due to attenuation
Shielded twisted pair (STP)

It is similar to UTP but has a mesh shielding that’s protects it from EMI which allows for higher transmission rate.

Characteristics of STP
Advantages of STP:
Disadvantages of STP:

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Thursday, 17 May 2012

analog communication