Signals and some of their characteristics.

Signals and some of their characteristics.

A signal is a material medium in the broad sense of the word. The variety of signals is large - it is impossible to give a definition suitable for all occasions. Moreover, the same can be signals and cannot. The whole diversity of signals is divided into 2 groups: 1) deterministic - a signal, if its values ​​at any time moment are strictly defined. 2) random - if its value at any time is a random variable.

The signals of these groups can be continuous or discrete. A continuous signal is a signal that takes all possible values ​​from x _min to x _max over a given time interval t. A discrete signal is a signal that is quantized by time or level, or simultaneously.

Quantization by level.

q - quantization step (resolution of the converter)

ε - quantization error

q = (x _max - x _min ) / (2 ⁿ -1) is the number of digits in the converter.

Error ε is fundamental for level quantization. It can be reduced only by increasing the discharge length of the converter n. n is limited from above by the presence of interference, starting with ,,, and at a given interference power, the real power transfer does not occur, because n is comparable to the level ,,,

ε is considered random. For an error, as for a random variable, the stationarity hypothesis is accepted, then the expectation is M [ε] = 0, and the variance is D = q 2/12 = ε ² => ε = q / 2√3 . There are linear and non-linear quantization scales. If the value of q over the entire range of x is constant, then the scale is uniform. However, linear scales are not always beneficial. The purpose of the use of linear scales is to improve the accuracy in the range of change of the scale in which it carries information.

Quantization on time.

n = 0, 1, 2 ...

T ₀ - the quantization period

Δ - functions

x [nT ₀ ] is a lattice function generated by an undefined function x (t).

U [nT ₀ ] - a single sequence generated, which controls the key, closing it according to the law of Δ - function.

x = ∑ ^∞ _{n = 0} x [nT ₀ ].

To determine the value   T ₀ the Kotelnikov theorem is used: T ₀ ≤1 / 2 f _max ; f _max - the maximum frequency of the spectrum of the quantized signal.

E _selected / E _remains ≤1%.

The non-realizability of the Kotelnikov theorem arises from the fact that in order to restore a function from known samples, each count must be multiplied by the function y = sinx / x and these works should be added.

The impossibility is that the function has the form:

The sum of the products ∑ ^∞ _-∞ , this implies the general impossibility of the exact reproduction of the time-quantized signal. However, given that the main part of the signal energy consists in region 1 :

Conclusions on quantization:

1) the guideline for choosing the quantization period T ₀ is the Kotelnikov theorem.

2) for any value of T _0, there is a fundamental error in the measurement of a continuous signal by its counting.

3) the smaller T ₀ , the less ... information about the signal.

Quantization by level and by time.

The level change can occur only at the moment t = nT ₀ , n = 0,1,2 ...

Signs and signals are used to construct sequences called messages . The set of all signs and signals from which messages are built is called the alphabet. Most often, signs are used to store information, and signals for its transfer. Signs clearly correspond to the signal. Often, signals are represented as serial signals. The rules by which a message is put in correspondence with real objects and processes are called coding . The reverse process by which each message is mapped to a real object or process is called decoding .

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