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.