3. Approbation of the received results

1. By carrying out of point 1 it is followed for chosen types of signals on the processing of experiment results altering sampling rate and applying fasten Fourier transform to control resulted curve on the Figure 1 - 7. To produce the quality analysis of curves, drawing attention to the dependence of their changing property for different meaning of sampling rate.

2. To install influence of signal types with quality degree on their practical wide of spectra for nose signals with uniform and gauss distribution

3. On carrying out of results of paragraph 3 it is necessary to change the parameters from par 1 and by statistics package to define effective wide of specters. And also by this package to figure out intervals of signal correlation and to build the graphs of their dependence on signal parameters.

To make conclusions.

4. Test questions

1. Spectral presentation of determined signals.

2. Fourier discrete transform.

3. Properties of Fourier transform.

4. Probabilistic features of random signals.

5. Correlation intervals.

6. Distribution solidity of random signals.

7. Normal and uniform distribution solidity of random size.

5. List of references

1. Абраменкова И.В., Дьяконов В.П., Круглов В.В. Matlab 5.3.1 с пакетами расширений. Под ред. проф. В.П. Дьяконова. – М.: Нолидж, 2001. – 880 с.

2. Дьяконов В. Matlab. Обработка сигналов и изображений. Специальный справочник. – СПб.: Питер, 2002. – 608 с.

3. Сергиенко А.Б. Цифровая обработка сигналов. – СПб.: Питер, 2003. – 608 с.

4. Баскаков С.И. Радиотехнические цепи и сигналы Учебник для вузов. - М. Высшая школа, 1988.

5. Thomas M. Cover J.O.Y A. Thomas. A Elements of Information Theory. Second Edition John Wiley &Sons, Inc., Publication, 2006, 774p.

Laboratory work 2 Spectral representation of periodic and acyclic signals

The purpose: phenomenon research spreading a spectrum of regular signals, influence of the form of a time window on results of the spectral analysis, experimental check of the basic parity between duration of a signal and resolution of a spectrum, consideration of influence of averaging on ensemble periodogram on statistical stability of a spectrum of noise signals.

1. Short theoretical data

Experimental installation represents the computer program created in the environment of programming LabView, which allows to model regular and noise radio signals and to build their spectra of capacity. The function chart is represented on Figure 1 In installation the generator of signals with the discrete time enters, allowing to generate two - tone harmonious with noise addition:

x (n) =A₁ cos (ω₁n) +A₂ cos (ω₂n) +A₃ ξ (n) (1.1)

Where A_1,2 - amplitudes of harmonious signals, ω_1,2 - them normed frequencies,

ξ (n) - discrete normal noise with intensity A₃. From expression (1. 1) it is visible that in work the mix of a two - tone signal with noise is used. The signal from the generator moves on the digital analyzer of the spectrum consisting of in cascade connected blocks: (a) a choice of function of the time window, allowing to choose one of three windows (rectangular, triangular, a window of Gauss); (b) the block of calculation FFT; the block of averaging of selective spectra of capacity. The number of points FFT and number of averaging’s gets out the user. The form of the received spectrum of capacity is displayed on an oscillograph. On other oscillograph the form of an analyzed signal is displayed.

On Figure 1 the forward panel of installation is resulted. On it settle down:

• a window of an oscillograph for visualization of the form of a signal (Signal Plot), scale

On time axis it is regulated by slider (Time scale);

Figure 1. View of the forward panel of installation for the analysis of spectra of discrete signals

• the window of the analyzer of a spectrum, scale on an axis of frequencies is regulated by roller (Frequency minimum) and (Frequency maximum), the scale on an axis of spectra is regulated roller (Spectrum scale), a choice of a scale of display of a spectrum is regulated by the switch (Linear scale - Logarithm scale);

• a window of a cursor position of the spectrum analyzer (X Y);

• a window of the discrete signals generator in which handles of management of amplitudes of harmonics (Amplitude1) and (Amplitude2), handles of management of frequencies of harmonics (Frequency1) and (Frequency2), the handle of management of intensity of noise (noise) settle down;

• a window of a choice of parameters of calculation of spectra in which the regulator setting number of points (N), a regulator setting number of averaging’s at calculation of a spectrum of capacity (Number of averaging’s) and the selector of a choice of a time window (Window choice settles down);

• needle indicator displaying the value of statistical stability of white noise spectrum capacity