Технические науки / 12.
Автоматизированные системы управления на производстве
Kulyk A.Y., Kulyk
Y.A.
Vinnitsia national
technical university
Using median filter
systems for transmitting information
In systems of information transfer one of the main problems is
clear informative signals from noise. It is fundamental and stems from the main
purpose of these systems, transmission of information.
In communications systems information is often transmitted by electrical
signals and them form can be significantly distorted by noise during
transmission, which is determined by the nature of environment and transmission
parameters of the channel. To clear a signal from noise are used different
filters. Information transmission system which
does not perform filtering of a signal from noise is ineffective, especially if
the signals carry information in digital rather than analog form. In
devices for transmitting information on the receiver side are frequently used
digital filters that clean the received signal from noise.
Devices
and algorithms for removing impulse noise can be divided into several groups.
The first group includes methods based on the use of limited signals and key
circuits. But they can be used only for certain
types of signals, to a certain extent change the shape and substantially reduce
the signal/noise ratio [1]. The second group includes adaptive
compensation algorithms. They are difficult, work for small levels of noise and
are considered only in theory [2]. The third group contains algorithms based on
nonparametric statistical methods [3] and is quite resistant to the effects of
interferences. However, they require training
samples of the ensemble noise whose elements should be independent. Use of
these algorithms in transmission of broadband signals causes difficulties,
primarily due to the large number of calculations.
First group used primarily in
information transmission systems, second group in image processing.
Purpose of this article is building device with
algorithm of quick filtering method.
Last time for removing impulse noise are often used median filters [4],
which are considered very promising and can be one-dimensional and
two-dimensional. Median filter is a sliding window that usually covers an odd
number of N counts of analog signal.
Initial value of filter 
is a count for which in the window there are 
counts less than or equal to him for the
value and the same amount greater than or equal to him for the value
. (1)
The idea of the classical median
filter is that, because the signal can only have determined amplitude, it is
possible, with sufficient probability to estimate the level of noise in the
received signal. Considering that that
the expected value of noise is approached to 0, and for an informative signal is determined by some
rationed defined value, and that noise exposed mathematical
models describing it as random process it is possible to estimate the level of noise. Considering
this, level of noise can be reduced by replacing the signal value averaged
value from a several neighboring points. Amount of this points are determined by width (aperture) of the window.
The
order of the filter N is determined
by the size of aperture (window), which is used for filtering. The easiest, by definition, is one-dimensional median
filter with three-count window [5]. For this filter are formulated the basic
principles of hardware implementation, but for higher order filters it is very
difficult. Program implementation to be substantially easier, since the bipolar
digital signals output value equals to the arithmetic sum
. (2)
As to diminishing of hindrance it is necessary to know
the not level of signal, but level of amplitude overfalls between nearby
points, then the algorithm of rapid processing is based on the construction of
difference matrices by the threshold function of satiation Fij = f (x i – x j ), in which
. (3)
For filter with the aperture N = 5 for the first five values the matrix F0
will look like (4).
, (4)
or in the generalized kind
. (5)
This matrix characterizes overfalls between nearby
counts. The significance of these overfalls can say whether this point contains
a random component, i.e. the hindrance. Shift one position along the row gives a
matrix of values F1, in which need to count only nine values,
which are located in the selected region
, (6)
Thus, for realization algorithm of rapid processing
of values by median filter it is necessary to carry out the row of actions:
·
to form the matrix F0 for first N registered values according to chosen aperture of filter;
·
to calculate the value F0.j for each columns of matrix F0;
·
to choose a necessary value from first N registered;
·
for the matrix Fn
to define the value F(n +
j)(n + N – 1) and F(n + N
– 1)(n + j) at 0 < j <
N;
·
from the preliminary calculated values Fn.j+1 to withdraw the value F(n – 1)( n + j) and F(n + j)( n – 1);
·
to the column F(n +
j) of matrix Fn add the value F(n + j)( n +
N – 1).
Actions proceed until all
values will not be processed.
. (7)
where TADC is
duration of cycle of transformation of ADC;
TWR is duration of programmatic cycle start of ADC by an interface circuit by the moment of presentation of signal
“Starting”;
TRD is duration of program cycle of read data from ADC from a moment
determination of signal “End of transformation” to the moment of writing down
data to the memory.
For information transmission can use the device, structure which
corresponds to classical microprocessor.
At the transmitting side perform routine operations: read the array of discrete information, which
should be transferred, in block of standard size from carrier of information,
convert it in serial format, submit the readout information to the channel via
a modem and transmit it via information channels in additional can make coding and encryption.
On receiving side information receive from the communication channel via
a modem and a signal demodulated in the modem; demodulated signal goes to the
analog-digital converter, which is controlled by parallel port, filtering of a
signal is performed by the central processor: difference matrix is formed after
each received from the analog-digital converter via parallel port signal
"end of transformation”, process it, and data stored on media.
For transmitter and receiver are used the same structural units. The
difference between the transmitter and receiver that the transmitter does not
use the ADC (and sends data directly to the modem) and have other structure of
software.
Fig. 1 – Circuit of the device
for transmitting information;
The device works like this: when you switch on the power of receiver the
CPU 9 outputs to monitor 12 request of the initial block size information and
forward the message entered from the keyboard 6. Then, CPU 9 performs read data
from storage medium 5 in a standard size block of data in RAM 10. The CPU 9
sends bytes of information in parallel port 8, which transmits it to the modem
2. Next carried out program poll of register flags until will not set flag “the
end of the transmission of the byte” which indicate that the byte of data is
transferred to the channel 1. Then the next byte can be transmitted. The process is
repeated for as long as all information contained on the media 5, will not be
processed and transferred to channel 1.
In receiving mode the signal coming from channel 1 to modem 2,
demodulated and comes to the analog-digital converter 3. After receiving the
signal "start" from the CPU 9 through the parallel port 8 and take a
first bit of data ADC 3 begins its work. After converting the first bit of
information CPU 9 through the parallel port 8 reads and places them in RAM 10.
The CPU 9 of the first N values obtained from the ADC, form difference matrix,
processing its median filter implemented in program. Then, CPU 9 after receiving a
signal the "end of conversion from ADC 3 reads the following value and for
its further processing forms the following matrix difference.
The process continues until all processed values. After processing
the information is written to the data carrier 5. At the same time it can be displayed on the monitor 12.
Using
the median filter increases the reliability of received information by smoothing form of a signal. Fast median filter has a higher performance compared to other digital
filters, and in most cases show better results. The best result median filter gives at impulse character of
the noise.
Increasing aperture able to greatly
increase performance, but require additional hardware and software costs.
This article presents an algorithm of fast median filtering systems used
in information exchange, determined for different basic parameters of its
components and the evaluation of its effectiveness.
References:
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