# Device for picking up useful signal against background of noise with minimisation of end effects through piecewise multiplication of estimations

FIELD: information technology.

SUBSTANCE: proposed invention relates to information measuring devices and can be used in computer engineering, in signal control and processing systems. The devices has a register for storing measurement results (1), delay unit (2), approximation unit (3), register for storing estimations (4), averaging unit (5), control unit (6), clock generator (7), and a comparator unit (8).

EFFECT: pickup of useful signal against a background of noise with minimisation of end effects, in conditions of insufficient prior information on statistical characteristics of adaptive noise and useful signal function given a single realisation of the measuring process.

4 dwg

The present invention relates to the field of computer engineering and can be used in control systems and signal processing.

Input the implementation of the results of measurements represents only a discrete sequence of y_{1}, y_{2}, ..., y_{n}where y_{k}=y(t_{k}),.

A mathematical model of the measurement results can be presented in the form:

where S_{k}- a useful component; u_{k}additive noise component.

Relative to the random noise component is assumed that Mi_{k}=0,

Du_{k}=σ^{2}and its value at different points in time are uncorrelated (i.e. cov(u_{k}u_{s})=0, k≠s).

The main task - the selection of the useful signal against the background noise to minimize end effects, in conditions of insufficient a priori information about the statistical characteristics of the additive noise and the function of the useful signal in the presence of a single realization of the measured process. To be known a priori that the source is a useful component smooth Anderson, i.e. on some intervals can be accurately approximated by a polynomial of not higher than the second degree. A similar problem can occur: 1) in the operation of transceiver devices gave the her or space communications;
2) in radio when evaluating noise immunity of schemes (algorithms) signal processing; 3) in meteorology when changing various characteristics of the atmosphere, etc. In cases where the useful part of S_{k},belongs to a known class of functions and is defined by a finite number of parameters are used parametric methods of assessment (this includes methods of regression analysis, that is based on the classical theory of least squares). In cases where no a priori information about the function useful component for the estimation used non-parametric methods, such as smoothing. It is known that the best way of smoothing averaging over the ensemble of realization of y_{i,k},the original process.

In practice, however, typically assumes that only one realization of the measured process. In this case, it is advisable to use methods of smoothing.

Known such method of selection of usable components, as averaging over the ensemble of implementation (Bendat J., Persol A. Applied analysis of random data. - M.: Mir, 1989. - 540 C.). For its realization it is necessary to have N initial process. Each implementation is a time seriesresults ISM is rhenium process y(t),
obtained at n equally spaced points in time t_{1}, t_{2}, ..., t_{n}. These observations can be represented in a matrix implementation:

where y_{j1}, y_{j2}, ..., y_{jn}- j-I implementation of the original process, which is a sum of functions of the useful signal S_{k}and noise component u_{k}.

Averaging over the ensemble implementation requires memorization of N input realization of y_{j1}, y_{j2}, ..., y_{jn}(j=1, 2,..., N), calculate the arithmetic mean value of these implementations in each moment of time, the replacement values of the initial realizations of the random process obtained average rating.

When applying this method calculates the arithmetic average matrix columns implementations (2), the result is a smoothed time series

Signs of a device similar to the matching characteristics of the proposed technical solution, the following: storing digital signal, finding the arithmetic mean, the replacement of the original time series smoothed.

The disadvantages of the known devices are:

for use of the device similar to the need to have multiple implementations.

Barriers to achieving the desired technical result are as follows:

- about what bennoti device similar is not allowed to handle only the implementation of the initial process, and not allow it to be applied to the already smoothed values (unlike ways, working with a single implementation);

the result of processing multiple implementations significantly depends on the number of implementations, the statistical characteristics of the noise component from the signal-to-noise.

The structural scheme of the device that implements the method, holds for N realizations of the N buffer units, the inputs of which are the device inputs and outputs are connected through switches to the inputs of the blocks storing the measurement results, the outputs of which are connected to the inputs of the arithmetic unit through a switch, whose output is connected to the input of the storage register of the trend, and the output register is an information output device.

In patent No. 2207622, IPC 7 G06F 17/18 was proposed method of reproduction estimates with a limited amount of a priori data and only the implementation of the initial process.

The considered device-similar involves: 1) memorizing the input realization of y_{1}, y_{2}, ..., y_{n}; 2) splitting the input implement at intervals of random numbers having a uniform distribution law; 3) the condition that the intervals include not less than L-values in the original implementation, if the condition is not met, then the newly generated random h the SLA break;
4) the presence on each interval of the input realization estimates of the coefficients of the approximating polynomial a+bt+ct^{2}using the method of least squares; 5) repeat the procedures in paragraphs 2-4, times; 6) finding a smoothing function as the arithmetic mean "piecewise quadratic" approximating functions in each moment of time.

Signs of a device similar to the matching characteristics of the proposed technical solution, the following: storing digital signal, finding the arithmetic mean, the replacement of the original time series smoothed.

The disadvantages of the known devices are:

- to handle the implementation, you need to remember the whole sample;

it is impossible to realize the processing of the original implementation in real-time;

growth allocation errors of the useful signal with a limited increase in the reproduction of the original implementation.

Barriers to achieving the desired technical result are as follows:

for processing of the initial realization you have to have the whole sample, the method of propagation estimates in real time is extremely limited;

the assumption that on each interval partitioning the original implementation of the useful signal can be described by a polynomial of the second degree, being the it growth allocation errors of the useful signal with a decrease in the length of interval splitting and increasing the variance of the additive noise component.

The structural scheme of the device that implements the method, contains a buffer unit, the inlet of which is an information input device and an output connected to information inputs of the storage units of measurement results to the control inputs of which through the switches connected to the outputs of the block partitioning of the original implementation, which contains the generator of random numbers distributed according to the uniform law, the output of which is connected to the input of the block address associated values, the output of which is connected to the input of block ranking, the output of which is connected to the register storing the sample of random numbers, whose output is an information output unit is split; the outputs of the storage units are connected to the inputs of blocks approximation, the outputs which is connected to the inputs of registers storing estimates of the baseline function, the outputs are connected to inputs of the arithmetic summing device, the output of which is connected to the input of the storage register of the trend, whose output is an information output device. Synchronous operation of the device is provided by a clock.

The known method exponential smoothing [Bendat J., Persol A. Applied analysis of random data. - M.: Mir, 1989. - 540]. Its peculiarity lies in the fact that in the process of finding useful assessment the component uses only the previous values of the input and results of measurements,
taken with a certain "weight", and the value of the weights decreases to the beginning of the implementation. To use this method, only one realization of y_{1}, y_{2}, ..., y_{n}the original process.

The method of exponential smoothing involves memorizing the original discrete implementation of the results of measurements y_{1}, y_{2}, ..., y_{n}random process, the choice of the smoothing parameter α (0<α<1), the values of Q_{0}the calculation estimates the useful component of the recurrent formula:

k=1, 2, ..., n

replace the original values of the measurement results y_{1},_{2}, ..., y_{n}smoothed values of Q_{1}, Q_{2}, ..., Q_{n}.

To use exponential smoothing of the measurement results is determined by the initial value of Q_{0}evaluation of the useful component and the smoothing parameter α. Wrong choice of initial conditions can have a significant impact on the result of processing the original discrete implementation of the measurement results. In practical recommendations on the use of exponential smoothing [Bendat J., Persol A. Applied analysis of random data. - M.: Mir, 1989. - 540 S.] proposed to choose as initial values of Q_{0}either the first value of the measurement results, or the arithmetic average of the first few clinorette measurements,
for example : Q_{0}=(y_{1}+y_{2}+y_{3})/3. On the other hand, the influence of the initial conditions decreases with increasing number of measurements and becomes insignificant when a large number of measurements.

Signs of a device similar to the matching characteristics of the proposed technical solution, the following: storing digital signal representation of the estimates of the useful component in the form of a polynomial from the discrete values of the initial implementation of the measurement results, the replacement values of the initial implementation of the measurement results of the smoothed values.

The disadvantages of the known devices are:

- the uncertainty of the choice of the smoothing parameter α, in some cases (unreasonably) to determine the value of α based on the volume of smooth implementation: α=2/(n+1);

- the uncertainty of the choice of the parameter Q_{0}that leads to the unreasonableness of the repeated re-application of the method of exponential smoothing for other values of α and Q_{0}.

Barriers to achieving the desired technical result are as follows: method of exponential smoothing is not "plug and play" fashion, as the choice of the parameters α and Q_{0}is subjective and depends on experience and practical skills of the researcher, the value is of α and Q_{
0}there are functions in the form of signal, noise, sample size.

The structural scheme of the device that implements the method, comprises a generator of such pulses, the switch control unit, a storage register, the adder block multiplication, the output storage register evaluation useful component.

The known method median smoothing [Calamai VA, Kalinin V.N. Probability theory and mathematical statistics. - M.: INFRA-M, 1997. - 302]. To use this method, only one discrete implementation of the results of measurements y_{1}, y_{2},..., y_{n}. The main advantage of median smoothing is resistant to outliers. The basis of the method is the calculation of the moving median.

The median smoothing method involves the memorization of the original discrete implementation of the results of measurements y_{1}, y_{2}, ..., y_{n}the definition of length m interval number of y_{1}, y_{2}, ..., Y_{n}(or the width of the "sliding window"), to calculate the median, i.e. the ranking of the selected interval of the input implement the results of measurements, the medianreplacement of the Central value of the interval y_{1}, y_{2},..., y_{m}medianshift "sliding window" on one value to the right (i.e. the choice instead of interval y_{k
, yk+1, ..., yk+m-1the implementation of the interval yk+1, yk+2,..., yk+m), the calculation of the median on the new interval input implementation of the measurement results, and so until then, until it reaches the right end of the original implementation of the measurement results.}

Signs of a device similar to the matching characteristics of the proposed technical solution, the following: memorizing the input of the implementation of the measurement results, the allocation of time segments, the preservation of the implementation of the smoothed values.

The disadvantages of the known devices are:

the first p and last p values of the measurement results are not anti-aliased;

- due to the nonlinearity of the processing method is not strictly distinguish between the effect of median filtering on the signal and the noise;

- median smoothing can only be viewed as an effective method of pre-processing the input and results of measurements in the case of impulse noise.

Barriers to achieving the desired technical result are as follows:

- if the width of the smoothing window is equal to 2P_{+1}the first p and last p values of the initial implementation of the measurement results is not treated;

- median filtering is a nonlinear method of treatment;

- the dependence of the efficiency of smoothing the results of the s measurements on the shape of the useful and noise component.

The structural scheme of the device that implements the method, comprises a generator of such pulses, the switch control unit, a register storing unit rank, the block selecting the middle value, the output register that stores initial discrete implementation of the measurement results.

Known methods of extraction of useful component closest to the technical nature of the claimed device is the method of selection trend by the method of reproduction of the moving estimates trend his only source implementation ("MOLE") and device for its implementation (patent 2257610, MPK7 G06F 17/18). Consider this device as a prototype. To apply this method, only one realization of y_{1}, y_{2},..., y_{n}the original process.

The way of the moving propagation estimates of the trend suggests: remembering the implementation of the results of the measurementwhere m<n/2 (width of the moving window"), which will be approximated by a polynomial of second degree least-squares, the replacement of a number ofthe values of the approximation function, resulting in a number ofshift "sliding window" on one value to the right (i.e. the choice instead of cut the number of the next segmentfromthe repetition of the procedures described above until it reaches the right end of the row, i.e. j=n-m.

A priori determined by the width of the moving window" m<n/2, which will be approximated by a polynomial of second degree least-squares. Determining a number m, remembered the first segment of the original series. From the condition of minimum of the sum of squared deviations:

,

determines coefficients,,approximating polynomial:

The evaluation of the approximation functionon the segment numberand it is memorization. Shifted by one sample "sliding window" and result in a new segment of the original series. Re is approximated by a polynomial of second degree least-squares, is evaluationand remembered. Thus, we get r=n-m+1 segments of the original series and r their assessments. The original seriesbroken into segments of length m, can be represented in the form of a matrix of size:

An approximate functionis determined by averaging over the side diagonals:

The features of device-prototype matching the characteristics of the proposed technical solution, the following: shift "sliding window" on one value to the right, replacing the original time series smoothed approximation polynomial of the second degree least-squares.

The disadvantages of this method are:

- on the interval [1, m] and [n-m, n], the useful component is not effective enough.

Barriers to achieving the desired technical result are as follows:

- for the first and last m values of the original implementation of multiple estimates contain a different number of elements.

The structural scheme of the device that implements the method, contains a register storing measurement results, the delay block, the block approximation register storing estimates, the power averaging, power management, clock.

The proposed device selection signal against the background noise to minimize end effects the way piecewise multiplication of estimates comes from having a single discrete implementation of the process under investigationwhere y_{k}=y(t_{k}), k=1, 2, ..., n, represent the work is the sum of the useful signal and noise,
i.e. y_{k}=S_{k}+u_{k}. A priori information about the process under study is that the selected interval m<^{n}/_{2}and m_{min}<m, the useful signal quite accurately described by a polynomial of the second degree S_{k}=a+bk+ck^{2}.

Consider the method involves the following sequence of steps: 1) memorizing implementation(j=1, 2, ..., m-m_{min}+1) of a random process, where m<n/2 (width of the moving window"), which will be approximated by a polynomial of second degree least-squares, m_{min}<m minimum width of the moving window"; (2) storing the values of the approximation function, resulting in a number of; 3) increasing the initial window width m_{min}per unit, resulting in a number of, storing the values of the approximation function; 4) repeat procedures 1-3 until the initial width of the window reaches the value m; 5) the shift of the "moving window" on one value to the right (i.e. the choice instead of cutthe number of the next segmentfrom; 6) the replacement of a number of(j=1, 2, ..., n-m) values of the approximation function
, resulting in a number of; 7) repeat procedures 5-6 until you reach the right end of the row, i.e. j=n-m; 8) reducing the width m of the "moving window" on the unit, i.e. the choice of the number of9) storing the values of the approximation function, resulting in a number of; 10) repeat the procedure for reducing the width of the window until it reaches the value m_{min}. The split procedure numberfigure 1 explains.

A priori determined by the initial m_{min}<m and the main m<n/2 the width of the window, which will be approximated by a polynomial of second degree least-squares. At the initial interval [1, m] the original implementation is divided into overlapping intervals with a fixed left border and the increasing length of the interval partitioning of m_{min}to m. On the interval [2, n] split the original implementation is made by the shift of the "moving window" on one value to the right. On the interval [n-m, n] split the original implementation is carried out with decreasing the length of the interval to the minimum value of m_{min}fixed right margin. Each of the resulting intervals is approximated by a polynomial of second degree least-squares.

Thus r=nm+2·m_{
min}segments of the original series and r their assessments. The original number can be represented in the matrix form:

An approximate function S(t) is determined by averaging over the side diagonals:

The device selection signal against the background noise to minimize end effects the way piecewise multiplication contains estimates (figure 2) register storing measurements 1, the inlet of which is an information input device and an output connected to the input of the delay unit 2, the output of which is connected to the input of the block approximation 3, the output of which is an information input of the register storing the estimated 4, the output of which is connected to the input of block averaging 5, the output of which is an information output device, for additional information inputs of blocks 2, 3, 4, 5, 8 connected to the output control unit 6. Additional input register storing measurement results connected to the input unit 8 comparison, the output of which is connected to the input of the delay unit 2 and the input of the register storing measurement results 1. Synchronous operation of the device is provided by a generator of clock pulses 7.

The device selection signal against the background noise to minimize end effects the way piecewise multiplication estimates is as follows. At the beginning of the flax interval [1,
m] in the buffer block is written, the first m_{min}the values of the initial implementation of the results of measurements (m_{min}- is the minimum width of the "moving window"), then in the buffer unit written m_{min}+1 values. As data is the approximation of the last received values of the least-squares polynomial of the second degree. The estimates obtained are recorded in the storage unit assessments for further averaging. When the width of the window reaches m, i.e. m_{min}+i=m, i=1...m-m_{min}the data in the block approximation served with a delay of one sample. The estimates obtained are recorded in the storage unit assessments. To achieve a "sliding window" end of the implementation is the reduction of its right border on one count until the value is reached [n-m, n]. According to the method of the arithmetic mean in each moment of time is determined by the final assessment of the useful component, which is supplied to the output device.

The device selection signal against the background noise to minimize end effects the way piecewise multiplication estimates is as follows. In the control unit sets the width of the moving window and m is the minimum window width m_{min}information that is supplied to the additional information input unit 8 comparison, the delay block 2, the block is and approximation 3,
the storage unit assessments 4 and block averaging 5. Unit 8 comparison signal from the register storing the results of measurements of the condition of m_{min}=m, if the condition is not met, then the size of the register storing the measurement results is incremented. If the condition m_{min}=m in unit 8 comparison is performed in the delay unit 2 is fed to the enable signal. The delay unit 2 holds the data stored in the register storing the measurement results in one clock cycle, if the auxiliary input signal resolution delay unit 8. In the event of termination of the receipt of the input data in block 1 (i.e. the "sliding window" has reached the end of the implementation), Comparer 8 stops the condition m_{min}+i=m, and the input sample is divided into intervals with decreasing per unit length to the minimum value of m_{min}fixed right margin. Data register storing measurement results 1 goes into the block approximation 3, where they are re-approximation of the least-squares polynomial of the second degree. Estimates in the block approximation 3, recorded in the register storage assessments 4 and enter the block averaging 5, which is the averaging of the grades obtained in the block approximation 3. The output of block averaging 5 is an information output device.

Technical the sky's the result - the selection of the useful signal against the background noise to minimize end effects in the conditions of insufficient a priori information about the statistical characteristics of the additive noise and the function of the useful signal in the presence of a single realization of the measured process.

Through simulation it was found that the device selection signal against the background noise to minimize end effects the way piecewise multiplication estimates has the following advantages:

The mean square error evaluating the function of the useful signal is much less of estimation errors when using other considered methods with limited a priori information about the process under study.

The proposed method enables to process the source data in real time.

Evaluation of the function of the useful signal regardless of the source function of the useful signal and the statistical characteristics of the additive noise adequately displays the basic regularities of changes in the useful signal.

Figure 3 presents an example of the multiplication of the estimated useful component (graph - 2), the original signal (graph - 1). Comparative analysis of the results presented in figure 2, shows that in the case of using the method of separation of useful signalosome reproduction estimates minimize end effects its value more close to the values of the original signal, than for the case of piecewise multiplication estimates without minimize end effects.

Figure 4 shows the dependences σ_{OST}=f(m) when processing a model of a harmonic signal of the form by the method of piecewise multiplication assessments and method piecewise multiplication estimates minimize end effects in the absence of the original implementation of the noise component (σ_{W}=0). Figure 4 the following notation: graph 1 corresponds to the case processing when p=1, the estimate of the error on the interval [0, n]; figure 2 correspond to the processing method piecewise multiplication estimates minimize end effects at p=1 (p - degree of approximating polynomial), with the estimate of the error on the interval [0, n], figure 3 is obtained when p=1, the estimate of the error on the interval [m, n-m] (excluding end effects). Charts 4-6 obtained under the same conditions as graphs 1-3, but for the case p=2. Analysis of the above graph shows that the use of the method of piecewise multiplication estimates to minimize end effects, when processing a model of harmonic forms allows, on average, 2 times to reduce the error in comparison with piecewise reproduction assessments without minimize end effects.

Figure 5 shows the dependences σ_{OST}=f(m), when processing the implementation of the model harmonic signal + noise (σ_{W}=0.1).

Take the s previously refer to figure 3 remain unchanged for 4.
Use of the method of piecewise multiplication estimates minimize end effects can reduce the total error estimate signal (figure 5, figures 2, 5), on average, 5 to 30%, and at large m - up to 50% compared with the method of piecewise multiplication estimates without minimize end effects. The nonlinear character of the dependence of σ_{OST}=f(m) with estimates of the error processing (graphics 3) due to the fact that at some values of m in the interval [0, m] and [n-m, n] are parts of the signal, where the error estimate reaches their maximum values.

The device selection signal against the background noise to minimize end effects the way piecewise multiplication estimates that contains the register storing the measurement results, the entrance of which is an information input device, the output of which is connected to the input of the delay unit, the output of the delay block is connected to the input of the block approximation, the output of which is connected to the input of the register storing the estimated output of the storage register evaluations connected to the input of block averaging, the output of which is an information output device, to the control inputs of the delay block, the block approximation register storage estimates, block averaging, connected to the output of the control unit, wherein the control input register storage of the measurement results you connected the od unit comparison the inlet of which is connected to the output of the control unit, for allowing the input of the delay block is connected to the output of the comparison and synchronization of operation of the device is provided with clock pulses.

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2 cl, 3 dwg

FIELD: information technologies.

SUBSTANCE: processing unit contains input implementation storage unit (1), switches (2.K), splitter (3), approximation units (3.K), evaluation storage unit (4.K), arithmetic adder (5), useful component evaluation storage unit (6), subtracter (7), storage unit (8), maximum absolute value estimator (9), subtracter (10), storage unit (11), comparator (12), threshold value unit (13), storage unit (14), random-number generator (15), related value eliminator (16), rating unit (17), random-number sample storage register (18), clock generator (19).

EFFECT: processing of black-and-white images with sudden brightness jump from white level to black level using estimate propagation method at insufficient a priori information on additive noise term statistics.

5 dwg

FIELD: education.

SUBSTANCE: method consists in the following: placing on the monitor of a control question and versions of the answer to the given question, a choice of one, preferable trained, a version of the answer by means of moving of the manipulator cursor to the location of its indicator and the subsequent definition of correctness of the answer on a final cursor position; after placing of indicators of versions of answers in the range from the moment of the cursor movement beginning till the moment of fixing of its final position form a file trajectory parametres of its movement on the monitor, determine autocorrelation function of the obtained array of trajectory parametres and determine level of confidence of the trained person in the obtained knowledge by position of a maximum of function at which arrangement within the set error of decision-making in the beginning of co-ordinates gives the conclusion about the confident or uncertain motivation of the answer.

EFFECT: increase of reliability and accuracy of the control of obtained knowledge level.

5 dwg

FIELD: computer engineering.

SUBSTANCE: controls (ACS) of technical systems (TS) which cannot be physically measured to evaluate control efficiency. The device contains group of sensors for ACS TS parameters, group of information parameter converters, ACS TS modeler, group of parameter counters for ACS TS model, group of converters for ACS TS model information parameters, storing device (SD) for model information, multiplexer, workstation for data input, terminal server with SD for control effectiveness evaluation program, imported information and converted imported information, database server with SD for converted information, knowledge workstation with SD for experts enquiry data, workstation for control effectiveness evaluation, database memory with SD for ACS TS structural elements, parameters, standards and weight coefficients, printer.

EFFECT: method and device functionality enhancement by means of modeling the values of automated systems parameters.

2 cl, 1 dwg

FIELD: computer engineering.

SUBSTANCE: invention relates to digital computer engineering and can be used in digital signal processing systems for optimum nonlinear filtering. The device contains six units for generating matrix functions, three correctors, three units for generating difference, three units for generating sum, three delay lines, unit for generating and outputting prior data, and two units for calculating regularisation parametre.

EFFECT: increased accuracy of evaluating information process parametres in measuring systems.

8 dwg