Correlation

Correlation is a measure of similarity between two signals. The general formula for correlation is

∫∞−∞x1(t)x2(t−τ)dt$${\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}{x}_1(t)x_2(t-\tau )dt$$

There are two types of correlation:

• Auto correlation
• Cros correlation

Auto Correlation Function

It is defined as correlation of a signal with itself. Auto correlation function is a measure of similarity between a signal & its time delayed version. It is represented with R(τ$\tau$).

Consider a signals x(t). The auto correlation function of x(t) with its time delayed version is given by

R11(τ)=R(τ)=∫∞−∞x(t)x(t−τ)dt[+ve shift]$$R_{11}(\tau )=R(\tau )={\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}x(t)x(t-\tau )dt\text{[+ve shift]}$$

=∫∞−∞x(t)x(t+τ)dt[-ve shift]$$={\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}x(t)x(t+\tau )dt\text{[-ve shift]}$$

Where τ$\tau$ = searching or scanning or delay parameter.

What is Noise Figure? Explain different methods of noise figure measurement .Also describe which method is best and why ?

Noise Figure :

Noise figure is a measure of the degradation in signal to noise ratio and it can be used in association with radio receiver sensitivity.

Noise figure is a number by which the noise performance of an amplifier or a radio receiver can be specified. The lower the value of the noise figure, the better the performance.

Essentially the noise figure defines the amount of noise an element adds to the overall system. It may be a pre-amplifier, mixer, or a complete receiver. Often the noise figure may be used to define the performance of a receiver and in this way it can be used instead of the signal to noise ratio.

• Noise factor:   The noise factor can be derived simply by taking the SNR at the input and dividing it by the SNR at the output. As the SNR at the output will always be worse, i.e. lower, this means that the noise factor is always greater than one. The noise factor is rarely seen in specifications.
• Noise figure:   Noise figure is the parameter that is seen widely in specifications and in use when defining radio receivers and the elements within the receiver systems. The noise figure uses a logarithmic scale and is simply the noise factor expressed in decibels.

Using the diagram above it is possible to determine the noise figure formula fromt he conditions described above.

N=10log10(Si/NiSo/No)

In the diagram S1 is the signal at the input, N1 is the noise at the input
and S2 is the signal at the output and N2 the noise at the output

As an example if the signal to noise ratio at the input was 4:1, and it was 3:1 at the output then this would give a noise factor of 4/3 and a noise figure of 10 log (4/3) or 1.25 dB. Alternatively if the signal to noise ratios are expressed in decibels then it is quite easy to calculate the noise figure simply by subtracting one from another because two numbers are divided by subtracting their logarithms. In other words if the signal to noise ratio was 13 dB at the input and only 11 dB at the output then the circuit would have a noise figure of 13 - 11 or 2 dB.

Comment on Totem pole .

Totem pole is series connection of BJT and a diode. It ensures that at one time only one of the two output transistors is ON thus, reducing power dissipation. Also since the transistors are connected in common collector mode thus output impedance is small resulting in fast charging times of capacitive loads. The disadvantage of totem pole is that it does not facilitate wired logic. So we have to use open collector modes.

What is gray code ?

The reflected binary code (RBC), also known as Gray code after Frank Gray, is a binary numeral system where two successive values differ in only one bit (binary digit). The reflected binary code was originally designed to prevent spurious output from electromechanical switches. Today, Gray codes are widely used to facilitate error correction in digital communications such as digital terrestrial television and some cable TV systems

What is a flip flop ?

A flip flop is a binary storage device. It can store binary bit either 0 or 1. It has two stable states HIGH and LOW i.e. 1 and 0. It has the property to remain in one state indefinitely until it is directed by an input signal to switch over to the other state. It is also called bistable multivibrator.

Types of Noise in a noisy channel.

Noise is any undesired signal in a communication circuit. Another definition calls noise unwanted disturbances superimposed on a useful signal, which tends to obscure its information content. There are many varieties of noise; however, the four most important to the telecommunication/data communication technologist are thermal noise, intermodulation noise, crosstalk and impulse noise.

Thermal noise occurs in all transmission media and communication equipment, including passive devices. It arises from random electron motion and is characterized by a uniform distribution of energy over the frequency spectrum with a Gaussian distribution of levels. Every equipment element and the transmission medium itself contribute thermal noise to a communication system if the temperature of that element or medium is above absolute zero. Whenever molecules heat above absolute zero, thermal noise will be present. The more heat generated or applied, the greater the level of thermal noise.

Intermodulation (IM) noise is the result of the presence of intermodulation products. If two signals of frequencies F1 and F2 are passed through a nonlinear device or medium, the result will contain IM products that are spurious frequency energy components. These components may be inside or outside the frequency band of interest for a particular device. IM products may be produced from harmonics of the desired signals in question, either as products between the harmonics or between a harmonic of one of the signals and the other basic signal or between both signals themselves. The products result when two (or more) signals beat together or "mix."

Crosstalk refers to unwanted coupling between signal paths. There are essentially three causes of crosstalk: (1) electrical coupling between transmission media, such as between wire pairs on a voice-frequency (VF) cable, (2) poor control of frequency response (i.e., defective filters or poor filter design) and (3) nonlinear performance in analog (FDM) multiplex systems. Excessive level may exacerbate crosstalk. Analog transmission is distorted by crosstalk and it will deteriorate the BER performance of a digital path.

Impulse noise is a noncontinuous series of irregular pulses or noise "spikes" of short duration, broad spectral density and of relatively high amplitude. In the language of the trade, these spikes are often called "hits." Impulse noise degrades telephony only marginally, if at all. However, it may seriously corrupt error performance of a data circuit.

Expain application of antenna polarization.

Applications of antenna polarization

Different types of polarization are used in different applications to enable their advantages to be used. Linear polarization is by far the most widely used for most radio communications applications. Vertical polarization is often used for mobile radio communications. This is because many vertically polarized antenna designs have an Omni-directional radiation pattern and it means that the antennas do not have to be re-orientated as positions as always happens for mobile radio communications as the vehicle moves. For other radio communications applications, the polarization is often determined by the RF antenna considerations. Some large multi-element antenna arrays can be mounted in a horizontal plane more easily than in the vertical plane. This is because the RF antenna elements are at right angles to the vertical tower of pole on which they are mounted and therefore by using an antenna with horizontal elements there is less physical and electrical interference between the two. This determines the standard polarization in many cases.

In some applications there are performance differences between horizontal and vertical polarization. For example, medium wave broadcast stations generally use vertical polarization because ground wave propagation over the earth is considerably better using vertical polarization, whereas horizontal polarization shows a marginal improvement for long distance communications using the ionosphere. Circular polarization is sometimes used for satellite radio communications as there are some advantages in terms of propagation and in overcoming the fading caused if the satellite is changing its orientation.