This innovation assigns for a procedure of compression, more exactly a general method of compression that can be applied on various forms of data sequences.

With general assigns here that the procedure of compression has a universal form that make it able to be used as a compressor of randomly sequence of data.

In general, compression methods are divided into two families, the destroying-compression and non-destroying-compression.

The non-destroying compression methods work on translating the entire data sequence or parts of it, such a set of code words are obtained. The degree of compression depends here on how much of the pure data is translated into shorter code words. The main advantage here is that compression method does not destroy the data. The disadvantage is that the code words shall be known beforehand. Also the data sequence can't be pure randomly, because the number of the code words would increase to be so much as the sequence itself, then we don't achieve any compression.

The destroying compression methods are methods that seek the parts of the data sequence that can be destroyed without affecting the usage of the information. For example, the MP3 techniques, compress the sound by represent the sound as the audible version for the human ear, which means that the data sequence of the sound transfers to a shorter sequence that includes only the elements that gives rise for audible sound for the human ears.

Yet, nor of those compression families can be applied to compress a sequence of randomly created data. The randomly created data occur in many of the real applications such as communications. In other words, in a communications link, the data that transfers has no other nature except of randomly, because we can't assume that data is a sound data, an image data or nay other human related perception. So we can simply not cut any part of the data sequence because it is no necessary, nor can we translate the sequence into smaller number of code words.

One more important thing to keep in mind, none of the compression methods are really fast that can be function in real time, hi other words, the compression methods are not so fast that the sequence of data is compressed in relative short time.

The aim of the present innovation is to achieve a compression method that is able to compress general/randomly data in real time context. In other words, the method of this innovation shall be able to compress an arbitrary sequence of data in relative short time so the real-time aspect is fulfilled.

The main task of this innovation to attain is how to represent several elements of information with less number of elements. By this definition, the compression method of this innovation belongs to the non-destroying compressors. Yet, some error is affecting the data sequence while compressing processes. This means that the compression method also belongs to the destroying compressors. Exactly, this method is something between the non-destroying and the destroying method of compressor. Assuming that we have two information elements, x and y, who are completely orthogonal to each other, in other words there is no correlation between x and y. The question here is how to represent these two elements into one element? This innovation answers this question.

Due to the orthogonal property that x and y have, the elements can be represented in a Cartesian coordination system (simple xy-plan). Thus applying a mathematical function that covers the xy-plan, an arbitrary point made by the two elements x and y can be represented by the new variable of this covering function.

The main idea is to use a periodical function that has the ability of obtaining a point in a Cartesian coordination system that require at least two variables, with one variable. The function that is able to achieve this task is a periodical function, and this function shall be covering the whole xy-plan. The most satisfying function for this requirement is a spiral function. The spiral function has only one variable and it covers the xy-plan. So the idea is to choose the input variable for the spiral function (z) such the output is the point in the xy-plan made by the variables x and y.

As a simple example of the periodical function, let us assume an angle fl that is equal to 30 degrees and another angle f2 that is equal to 390 degrees. In numbers, £2 is bigger than fl, but if we put the both of fl and f2 in a sin function like Fl = sin(fl) and F2 = sin(f2), then the result will be the same since sin(30) = 0,5 and sin(390) = 0,5.

From this short example, we can see that using a periodical function, gives several solutions in comparison of using another type of mathematical functions.

This innovations, assigns using of the periodical function and particularly using the spiral function where the periodical property is defined in two dimensions.

To get a deeper understanding of the compression procedure of this innovation, the procedure can be graphically described by figure 1 and 2. From figure 1, we can see an arbitrary point in a Cartesian coordination system, in other words a point that represents two arbitrary values in the orthogonal coordination (x and y). In figure 2 we can see the spiral function that hits the point and is depending on one variable (the letter psi in Greek).

A simple example could be like:

Let us assume two variables, x = 1356 and y = 8947. In an orthogonal coordination system, those variables will give a radius and a phase. The radius and the phase are calculated as: radius ) . In numbers, the radius is given to 9049 and the phase is given to 81,4 degrees. If we round the radius into whole numbers of 360-degrees period, thus adding to it the calculated phase, then the new number includes almost the radius and the phase. The rounded radius into whole numbers of 360-degrees is calculated to 9000, adding to it the phase will give us 9081. This number, can thus be used both as a radius but also as a phase due to its performance that it consist of a phase part and a whole number of periods. In other words, we could obtain a single number that gives two numbers when we use it inside a periodical function since a periodical number has always two parts, namely the phase-part and the whole-number-periods-part.

The idea of this innovation is how to make this process be applied for compression of data sequences. Theoretically, the compression occurs by a rounding-step inside a transformation step. The transformation here is a Cartesian-Polar-transformation and the rounding step affecting the transformed variables such a useful sum of the rounded variables in the Polar shape gives a useful variable in the Cartesian shape.

By this description, we can get a smaller value that can be used to achieve two values, and this is what a compression is.

Mathematically the compression process can be made according to the producer of this innovation like bellow steps:

1. Assume two data elements x and y of 16-bit size each.

2. The radius of the two elements is equal to radius =^x ² +y ² .

3. The phase φ between the two elements is equal to phase =tan ^" (— y ) x

4. The radius r is converted then to whole number of periods as r ^* =round( )* period , here we can choose the period into 360 degrees, which period makes the equation becomes as r ^* = roundi ) *360.

360

5. Here we can simply ad the phase and the rounded radius to obtain a number that gives two information when we soon use it within a periodical function, the sum (z) here is the compressed value of the originals value of x and y. In other words, z is calculated as z =r' + φ =round\ — * period + tan ^"1 — .

I period I \xj

6. Soon when we want to obtain the original values of x and y, we can simply get them by following calculation: x = z* cos(z) y= z * sin(z)

To put the method in the test, a simulation in Matlab was made. Matlab is a simple calculation programming language that is used by engineers and mathematicians. For more information, please check http://www.themathworks.com/matlab/.

1. a = round(randn(100,l).*16000);

2. a = intl6(a);

3. period = 180;

4. a = double(a);

5. a = a./1.42;

6. L = length(a);

7. xl = x(l ±12); x2 = x(L/2+l :end);

8. sig = xl+i*x2;

9. r = abs(sig); 10. f = angle(sig);

11. f= round(f.*(p/(2*pi)));

12. rr = r-mod(r,p);

13. yyy = rrff;

14. yy = round(yyy);

15. x = intl6(yy);

16. x = double(x);

17. r = x-mod(x,period);

18. r = r.*1.015;

19. f= mod(x,period);

20. f = f.*(2*pi/period);

21. yl = r.*cos(f)*0.995;

22. y2 = r.*sin(f)*0.995;

23. yyy = [yl;y2];

24. yy = yyy.*1.42;

25. b = intl6(yy);

26. T= l:length(b);

27. plot(T,a), hold, plot(T,b,'r')

28. T2 = l:length(x)

29. figure, plot(T2,x)

The program above is written such it testify the procedure of this innovation and follows the mathematically example identically. To understand the simulation in detail, please use the internet link to understand the syntaxes in the simulation above. The result of the simulation can be shown in figure 3-5. In figure 3 we can see the original sequence as a curve that includes the hundred data elements, hi figure 4, we can se the compressed sequence that includes fifty elements instead. Those fifty elements are the compressed data sequence of the hundred original elements. In figure 5 we can se the result of the uncompressed sequence, in other words, the fifty elements are unpacked into hundred elements. Both of the invariables are of 16-bit size and the compressed variable is also of 16-bit size.

The aim of the simulation is to show the performance of the compression procedure of the innovation. The figures show two curves that are almost identically to each other, but to be exactly, there are some differences between the original and the result. The difference here is the error in the compression method.

To define the quality of the compression method, we shall compare the original sequence with the result sequence. Here we can use the quality calculation that is used in signal theorem, which is defined by Claude Shannon theorem of Signal to Noise Ratio (SNR). The SNR gives how good the signal is in comparison to the noise, SNR is calculated as: the mean power of the signal and

A is the mean square amplitude (RMS).

Including this calculation in the simulation, the SNR was calculated to a mean value of 37,22 dB. This SNR was obtained when the same simulation was driven for a several times and for many data elements (1000 elements). The quality of the compression can be adjusted by design variables for a specific application. There are also some improvements steps that can be applied on the method like filtration and buffering, but these improvements do not belong here.