# Method of managing observation clustering when filtering frequency-modulated signals

FIELD: information technology.

SUBSTANCE: invention relates to radio engineering and can be used to filter information processes transmitted using frequency-modulated signals. The method involves prediction of the estimate of the modulating signals on the i-th (i=1, 2,…) extrapolation interval with duration h; determining on that interval the derivative of the reference radio signal dependant on said predicted estimate, synchronously with time sampling of said derivative and the input signal with frequency F>1/h, determining products of their readings; generating a signal on the i-th extrapolation interval which is proportional to the sum of these products; improving the predicted estimate of the modulating signal using said sum; frequency-modulation, using the predicted estimate of the modulating signal, of a pulsed signal which controls sampling of the input signal and the derivative of the reference radio signal.

EFFECT: high processing accuracy owing to adaptive clustering of observations when filtering frequency-modulated signals.

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The object of the invention is a method of controlling the grouping of observations in filtering the frequency-modulated signals. The proposed method relates to radio engineering, because the task of filtering the frequency-modulated signals is essential for a large class of radio systems receive and process messages.

Known way to control the grouping of observations [1]. Its disadvantage is the lack of coordination between sampling observations with the current frequency characteristics of the transmitted signal measured during filtering.

The absence of such coordination can significantly affect the quality of processing in the task of filtering the frequency-modulated signals, when the period of the received oscillations varies widely, and the sampling frequency remains unchanged.

There is also known a method of controlling the grouping of observations [2], which consists in predicting the evaluation of the modulating signal at the i-th (i=1, 2, ...) the extrapolation interval of duration h, the definition in this interval depend on the derivative of the reference signal, the synchronous sampling time of this derivative and the input signal with frequency F>^{1}/_{h}independent evaluation of the modulating signal, the determination of their works, the formation of the Institute for the i-th interval extrapolation of the signal,
proportional to the sum of those products, the refinement with its help, the predicted estimates of the modulating signal.

It also provides for coordination between the sampling rate and measured frequency characteristics of the signal.

The aim of the invention is to improve the accuracy of processing by the adaptive grouping of observations in the process of filtering the frequency-modulated signals.

The invention consists in predicting the evaluation of the modulating signal at the i-th (i=1, 2, ...) the extrapolation interval of duration h, the definition in this interval depend on the derivative of the reference signal, the synchronous sampling time of this derivative and the input signal with frequency F>^{1}/_{h}, the definition of their works, the formation of the i-th interval extrapolation of the signal proportional to the sum of those products, the refinement with its help, the predicted estimates of the modulating signal, the modulating frequency using the predicted estimate of the modulating signal is a pulse signal that controls the sampling process.

Comparative analysis of the proposed method and the described method of controlling the grouping of observations shows the following significant differences of the proposed method:

1. Enter the control discretization step, and hence the cha is the Thoth sampling observations independent evaluation of the modulating process;

2. Enter the control volume of the collected sample for grouping observations;

3. The method is characterized by the presence of additional actions on material objects:

for each interval extrapolation in accordance with the projected estimate of the frequency of the radio signal is frequency modulated pulse signal, the control mode sample rate of the observed process.

theoretical basis of the grouping of observations in filtering the frequency-modulated signals [3].

Under the grouping of observations in signal processing understand the Association in the interval prediction (extrapolation) information (modulating) process multiple samples of the observed signal. Such integration is possible due to the fact that the frequency of the received radio signal is much larger than the bandwidth occupied by the modulation signal. In other words, the information flow is much more slow than the observed signal, and for its presentation requires considerably smaller than the sampling frequency.

Denote by h the interval extrapolation, and through the Δ - sampling of the input process at a time, then the grouping of the observations will be characterized coeff what they grouping k=^{
h}/_{Δ}.

Typically, the step Δ sample rate of the input process at a time when the grouping of observations is chosen so as to ensure 6-10 times for one period of oscillation [4].

To further increase the number of samples with the availability of fluctuation errors almost does not increase the accuracy of signal representation.

The Figure 1 presents graphs of the

wherethe relative standard deviation due to the fluctuation error;

k_{T}- the number of samples in one period of oscillation; s(x,k_{T}- a linear approximation of the function sinx with a uniform distribution of samples in [0,2π], for different values of σ.

From the graphs it follows that when k_{T}>8 the precision of the signal varies slightly.

For task frequency modulation period of the oscillation signal varies. Therefore, known methods of control group observations suggest selecting step and the sampling frequency based on the carrier frequency signal ω_{0}

,

where.

The number of samples per one period of the oscillation signal, thus changing in time the Yeni: k_{
T}(t), and the coefficient of group k observations, in contrast, remains unchanged.

To improve the processing accuracy for the given computational cost it is necessary that the number of samples per one period of oscillation with frequency ω(t) (frequency modulated signal), remained constant k_{T}=const. Thus the value of sampling time Δ=Δ(t) at the grouping of observations varies in such a way that remained invariant phase sampling

When filtering signals by grouping observations to prediction information of the process λ(t) used finite-difference scheme with step h, the value of which is determined by the upper boundary of the frequency range. Since frequency modulation, as a rule,

where η is the coefficient of deviation; λ_{max}- the maximum value of the modulating signal, then

Thus, within the intervals extrapolation duration h is the grouping of observations, sampling which is carried out in increments of Δ(t). Thus the factor grouping

where [·] means the integer part of the number that varies with time.

Given that for the i-th interval extrapolation of the AI can be predicted score frequency ω(t)=ω_{
0}+λ(t), which is approximately assumed constant for this intervalreceived

where k_{i}and Δ_{i}accordingly, the factor grouping observations

and the sampling rate for the i-th interval extrapolation;- predicted on

i-th interval extrapolation estimation of the modulating signal.

Note that for a well-known ways to control the grouping of observations coefficient grouping of observations k=const.

The structural scheme of the device that implements the grouping of observations in filtering the frequency-modulated signals presented on Figure 2. It used the following notation:

1 - the first key information 1_{1}and managing 1_{2}inputs;

2 - multiplier with inputs 2_{1}and 2_{2};

3 - accumulating adder with information 3_{1}and managing 3_{2}inputs;

4 - the third key information 4_{1}and managing 4_{2}inputs;

5 - unit assessment information 5_{1}, 5_{2}inputs;

6 is a generator of continuous assessment;

7 - the second key information 7_{1}and managing 7_{2}inputs;

8 the first delay line;

9 - the second delay line at time h;

10 - generator op is REGO signal;

11 - second pulse generator with a repetition period of the pulses h;

12 - frequency modulator with information 12_{1}and managing 12_{2}inputs;

13 - extrapolator;

14 - the first pulse generator.

The device presented in Figure 2, works as follows.

Input observation ξ(t) is supplied to the information input 1_{1}key 1. The counts of the input observations with its output fed to the input 2_{1}multiplier 2, 2_{2}which receives samples of the derivative of the reference signal output from the key 2. The results of the multiplication consistently served on the information input 3_{1}accumulating adder 3, in which the formation of the sum of k_{i}elements.

The results of the summation output unit 3 is fed to the input 4_{1}key 4, and further to the input 5_{1}unit assessment 5, where they are weighted summation with the predicted estimate of the modulating signal applied to the input 5_{2}from the output of extrapolator 13.

In addition, during interval extrapolation predicted score from the output unit 13 is fed to the input 12_{2}modulator 12 and to the input of the reference signal generator 10.

From the output of the block 10 the reference signal is fed to the input key 7 and further with the frequency depending on the predicted estimate of the modulating signal to the input b of the eye 2.

Control the sampling frequency of the input and reference signals is due to the frequency modulation of the pulses from generator 14 to the input 12_{1}modulator 12. The frequency-modulated pulses from the output of the modulator 12 serves to control inputs 1_{1}and 7_{2}accordingly keys 1 and 7.

The modulator 12 generates at its output a pulse signal frequencywhere ƒ_{0}- frequency signal; F_{0}=k_{T}ƒ_{0}- frequency pulse sequence generated by the generator 14.

The generator 11, the feeding pulses to the input 4_{2}key 4, ensures the delivery on the unit 5 the results of the summation block 3 with a frequency of^{1}/_{h}. These pulses passing through the delay line 8 and acting on input 3_{2}adder 3, reset to its zero state. The delay time h_{8}provided by line 8, should on the one hand to satisfy the condition of h_{8}<<h, and on the other to allow transfer of the sum to the input unit 5 at the end of each interval extrapolation.

The output signal of unit assessment 5, acting through the delay line 9 to the input unit 13, provides a prediction on the h estimation of the modulating signal. In addition, the output signal of unit assessment 5 in block 6 is restoring continuous signals the estimates.

The results of a computational experiment [3]

The model of the modulating signal:

where the first component λ_{1}has the sense of a verbal message [4];

α=1300; β=35000; n_{λ}- form noise, which M[n_{λ}(t)]=0;

M[n_{λ}(t)n_{λ}(t-τ)]*=*N_{λ}δ(τ); N_{λ}*=*6·10^{-5};

n_{ψ}- forming the noise that determines the instability of the phase signal;

M[n_{ψ}(t)]=0; M_{ψ}(t)n_{ψ}(t-τ)]=H_{ψ}δ(τ); N_{ψ}=3·10^{-2}; γ=60;

η=V·2π·10^{5};

η is the coefficient of deviation (values V in the process of numerical experiment will rely equal to 0.5, 1, 1.5).

Hereinafter, the parameters are given in dimensionless units. Frequency range λ_{1}(t) 0.5 is [200, 6000].

Model radio:

where n(t) - noise observations, which

M[n(M)]=0, M[n(t)n(t-τ)]=N_{0}δ(τ);

a=1, ω_{0}=2π·10^{-6}N_{0}=10^{-8}.

The model of the discrete filter frequency-modulated signal, is constructed on the basis of the proposed method.

The prediction of the modulating signal at the i-th interval extrapolation [t_{i-1}, t_{i-1}+h]:

where,,- predicted estimates.

the distribution parameters to control the grouping of observations:

,

where- predict the frequency of the signal.

The formation of the sum of k_{i}works counts of the input observations and the derived reference signal within the i-th interval extrapolation:

The formation of the a posteriori estimation of the modulating signal by weighted summation of the predicted estimate and the amount of r_{i}:

where

K_{1}, K_{2}, K_{3}- the weighting factor determined from the solution of the Riccati equation; in these circumstances To_{1}=0.03, K_{2}=0.037, K_{3}=0.037.

A computational experiment was carried out in MathCAD.

Modeling (11), (12) was carried out according to the Euler scheme with step 2·10^{-8}. To set noise processes transducers normally distributed random numbers. I assumed that

t∈[0,4·10^{-3}]; h=2·10^{-7}; k_{T}=10, 11, ..., 40; V=0.5, 1, 15.

Type of fragment based components λ_{1}modulating signal and assessmentfrom the time when k_{T}=10, V=1 are presented in Figure 3.

The results of the modeling were estimated average is the value of sampling

where M=2·10^{5}.

The resulting value was used when filtering the same implementations of the modulating signal (11), (12), but using a filter constructed based on the known method of controlling the grouping of observations for which in contrast to (15), (16)

Condition (20) corresponds to the condition of equality of the amount of computational effort when implementing both filtering procedures.

For both cases was calculated sample variance of estimates

where D_{1}- match filtering on the basis of the proposed method of control the grouping of observations;

D_{2}- match filtering on the basis of the known method.

Graphics dependencies

for different k_{T}and V are presented in Figure 4.

The gain in precision processing takes place for the entire range of variation of k_{T}and V.

Conclusion: the filter frequency-modulated signals, based on the proposed method of control the grouping of observations at comparable computational cost, provides a gain in precision (in terms of computational experiment to 24%) compared with the same filter, use the known SP is a way to control the grouping of observations.

Sources of information

1. Kharisov, VN, Efendiev R.N. Algorithms for nonlinear filtering with the grouping of observations. - Ed. higher education institutions. Electronics, 1989, 32, No. 8 p.29-33.

2. Tikhonov, V.I., Kharisov NR. Statistical analysis and synthesis of radio engineering devices and systems. M.: Radio and communication. 1991.

3. Hutori CENTURIES, Hasanov A.I. Phase stabilization of the mode of sampling observations in the problem of the digital filter frequency-modulated signals. - Radiotekhnika, No. 6, 2010.

4. Tikhonov, V.I., Coleman NICHOLAS Nonlinear filtering and quasicoherent reception of signals. M: Owls. radio, 1975.

The method of controlling the grouping of observations in filtering the frequency-modulated radio signals, which consists in predicting the evaluation of the modulating signal at the i-th (i=1, 2, ...) the extrapolation interval of duration h, the definition in this interval is dependent on the predicted estimate of the derivative of the reference signal, the synchronous sampling time of this derivative and the input signal with frequency F>^{1}/_{h}the definition of the works of their samples, the formation of the i-th interval extrapolation of the signal proportional to the sum of those products, the refinement with its help the predicted estimate of the modulating signal, characterized in that predicted for the i-th interval extrapolation estimation of the modulating signal modulates an hour and the h pulse signal,
managing discretization of the input signal and the derivative of the reference signal.

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