An algorythm for measuring the practical spectral width of unperiodical sygnals

An algorythm for measuring the practical spectral width of unperiodical sygnals

Todor I. Ivanov¹, Liliya A. Petrova²

¹Technical Colleg University “Prof. Dr. As. Zlatarov” Bourgas, Dept. of Electronics and Electrotechnics”, Aleksandrovska str. 101, 8010 Bourgas, Bulgaria, e-mail: todor_bg_2000@yahoo.com

²Technical Colleg University “Prof. Dr. As. Zlatarov” Bourgas, Dept. of Electronics and Electrotechnics”, Aleksandrovska str. 101, 8010 Bourgas, Bulgaria, e-mail: anest_bg@yahoo.com

Abstract: In the presented work analyzes a possibility for synthesising of algorithm, which will enable measurement of the practical width of used unpatriotically signal spectrum. (criteria – frequency and energy). 1. Formulation of the problem

For the theory, as well as the technical formulating and processing of the sygnal from importance is their analysis in relation to their spectrum and the energy distribution in it. A method for carrying out this problem is the harmonic analysis of unperiodical sygnals.

2. Mathematical correlation of the algorythm.

It is known, that Furie's direct and reverse transformation are the specral density [1,2]

and the accordingly presented sygnal

(2)
(t₁, t₂ - temporary interval of sygnal duration; in the common case when it is not strictly defined, it verges to -Ґ and +Ґ )
Correlation, that defines the relation between the energy of the sygnal (with resistance 1W ) and the absolute value of its spectral density, is know as the rule of Parseval [3].

(3) where S(w) - absolute value of the spectral density is defined by:

(4) where:

(5)

(6)

3. Algorythm of the measurement

The idea is, to define to following, in result of the realisation of the algorythm:
- what is the upper limit of the frequency interval w , for which the prevously set value of the energy W_g is reached;
- what is the value of the energy W, for which the compounds in the frequency interval is reached w _g;
For that purpose is proposed the algorythm, presented on fig. 1:

Names of teh connections:
20 - by verge frequency w _g;
21 - by prevously set value of the energy W_g;

4. Appliance - The preseneted algorythm can be applied for analysis of sygnals, where the conclusions made, can be taken for base of decesions concerning:
- the expediency in usage of such sygnal;
- frequency parameters of considered for usage chain;

Other options of the algorythm are:

- extending it with block (fig. 2) - with measuring the time for increase of the reaction through the chain [4] this important quantity of the sygnal can be analysed as well.

            3,8
    D t_N=--------
                     w

fig.2

- by modifying blocks 7, 11 can be defined the power D W, which relates to the sygnal in a given frequency interval with verges w₁ and w₂;
- when having possibility for preliminarily calculation of the result W_t, according to correlation 3, it is possible to extend with additional block (fig.3), which will input the as limitation the correlation:

W_g=a.W_t; (a=0 ё 1);

fig.3

5. Realisation of the algorythm

For resolving a particular problem are applied some numeral methods [5], but effective and expedient for engineer and scientific calculations applience has MATLAB (one of its last versions, widely used for calculation of many problems is reviewed in [6]).

References:

Алън Опенхайм, Алън Уилски, Ян Йънг; “Сигнали и системи”; Издателство “Техника”, София, 1993г.
Ервин Фердинандов ; “Сигнали и системи”; Издателска къща “Сиела”, София, 1999г.
И.С. Гоноровский; “Радиотехнические цепи и сигналы”; Советское радио, Москва, 1977г.
Н.В. Зернов, В.Г. Карпов; “Теория радиотехнических цепей”; Издателство “Енергия”, Ленинград, 1972г
Б. Сендов, В. Попов; “Числени методи – част І, ІІ”; Издателство “Наука и изкуство”, София, 1976 (1978) г.
В.Г. Потемкин; “Система инженерных и научных расчетов” – MATLAB 5.X (1 и 2 том); Акционерное общество “Диалог – МИФИ”, Москва, 1999г.