Patent Publication Number: US-7212577-B2

Title: Information transfer methods

Description:
This application is a 371 of PCT/RU02/00103. 
   FIELD OF THE INVENTION 
   This invention relates to information transmission and reception methods and could be used in communication and measurement systems etc. 
   BACKGROUND OF THE INVENTION 
   There is a problem of limiting transmission speed when transmitting a discrete information over communication lines. 
   The greatest possible transmission speed C in a communication line could be determined in accordance with the Shannon&#39;s formula: 
                   C   =       Π   ·     log   2       ⁢         P   C     +     P   Π         P   Π           ,           (   1   )               
where Π is a bandwidth of communication line, KHz; P C  is a power of signal being transmitted, dB; P Π  is a power of interference in the communication line, dB.
 
   For a telephone line having a bandwidth Π 3.1 KHz (300 Hz−3.4 KHz) and a ratio P C /P Π =10000 (which corresponds to 40 dB), a greatest theoretically possible speed of transmission (and reception) of discrete information is
 
 C= 3.1·10 3 ·log 2 10000=40 Kbit/s.
 
   Modem telephone modems of firms “Robotics” and “Motorola” ensure the information transmission and reception speed up to 33.6 Kbit/s at the ratio P C /P Π =10000 (corresponding to 40 dB), which is indicative of implementing the transmission speed close to the potentially possible in accordance with the Shannon&#39;s formula. 
   Known is the method of information transmission, including steps of: at the transmitting side, forming an analog signal by means of converting a sequence of discrete digital information samples to the analog signal using a predetermined sampling function, and transmitting the formed analog signal to a communication line; and at the receiving side, receiving the transmitted analog signal from the communication line, and restoring from it the original sequence of discrete digital information samples (JP 10-098497 A, Int. Cl. H 04 L 27/10, 14.04.1998). 
   The information transmission and reception speed in such a method for transmitting an information depends on a method for converting a sequence of discrete digital information samples to an analog signal at the transmitting side, and a method for restoring from the analog signal the original discrete digital information samples at the receiving side, and this speed is limited by the utmost capacity of pulse-code modulation (PCM) equipment existing in the communication line. 
   When transmitting over a single communication line simultaneously two analog signals of the same power P C     1   =P C     2    (i.e., in the case of decompression into two similar powers), the equation (1) could be rewritten as follows: 
   
     
       
         
           C 
           = 
           
             
               
                 Π 
                 · 
                 
                   log 
                   2 
                 
               
               ⁢ 
               
                 
                   
                     P 
                     
                       C 
                       1 
                     
                   
                   + 
                   
                     P 
                     Π 
                   
                 
                 
                   P 
                   Π 
                 
               
             
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                   2 
                 
               
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   Then it follows that at a fixed power 
           P   =         P     C   1       2     +         P     C   2       2     ⁢     (       i   .   e   .     ,       at   ⁢           ⁢     P     C   1         =     P     C   2           )               
the maximum information transmission and reception speed could be brought to C=3.1·10 3 ·log 2  5000+3.1·10 3 ·log 2  5000≈73 Kbit/s. Hence, in telephone lines, the decompression into two powers allows to increase the information transmission and reception speed and to realize the utmost capacity of existing pulse-code modulation (PCM) equipment, which is 64 Kbit/s.
 
   TASK OF THE INVENTION AND THE TECHNICAL RESULT 
   The task of the present invention is to develop the method of information transmission using the decomposition into two powers, which method increases the speed of a discrete information transmission, or—what is the same—allows to transmit more information at the same speed. 
   The technical result of the invention is in that it ensures a passing via an existing communication channel (without changing its parameters) at least two analog signals instead of one analog signal at the same time. 
   SUMMARY OF THE INVENTION 
   In order to solve the set task, in a method of information transmission, including steps of: at the transmitting side, forming an analog signal from a sequence of digital information samples using a predetermined sampling function, and transmitting the formed analog signal to a communication line; and at the receiving side, receiving the analog signal from the communication line, and restoring from the analog signal the sequence of digital information samples using the predetermined sampling function,—in accordance with the present invention, the method includes steps of: at the transmitting side: forming a first and second analog signals from a first and second sequences of digital information samples, the first analog signal being formed from a difference of values of digital information samples of the first sequence and values of digital information samples of the second sequence taken in points of digital information samples of the first sequence, and the second analog signal being formed from digital information samples of the second sequence taken in points of digital information samples of the second sequence, which are between points of digital information samples of the first sequence; summing the first and second analog signals, and transmitting the summary analog signal to the communication line; and at the receiving side, first restoring the first sequence of digital information samples by means of sampling the summary analog signal with a clock frequency, then converting the first sequence of digital information samples using the predetermined sampling function to the analog signal of the first sequence; subtracting said analog signal of the first sequence from the summary analog signal; and restoring the second sequence of digital information samples from the obtained difference analog signal. 
   An additional feature of the method according to the present invention is in that the first and second sequences of samples are formed using a preliminary sampling function, as which is employed a function of the form 
               sin   ⁢           ⁢     x   ⁡     (       cos   ⁢     x   n       -   1     )           2   ⁢   n   ⁢           ⁢   sin   ⁢     x   n         ,         
where x=2πF u , F u  is the upper frequency in the spectrum of signal being transmitted, n is a number of employed frequency components, and as the predetermined sampling function is employed a function of the form
 
               (       sin   ⁢           ⁢     x   ⁡     (       cos   ⁢     x   n       -   1     )           2   ⁢   n   ⁢           ⁢   sin   ⁢     x   n         )     2     ,         
or a function of the form
 
               sin   ⁢           ⁢     x   ⁡     (       cos   ⁢     x   n       -   1     )       ⁢       (     1   -     cos   ⁢     x   n         )     k         2   ⁢   n   ⁢           ⁢   sin   ⁢       x   n     ·     2   k           ,         
where x=2πF u , F u  is the upper frequency in the spectrum of signal being transmitted, n (an integer more than one) is a number of employed frequency components, k=1–20 characterizes the degree of truncation of the predetermined sampling function. Moreover, the sample points of the second sequence are formed in the middle between the sample points of the first sequence, and the first and second sequences of digital information samples are supplied from a single information source or from two different information sources.
 

   
     BRIEF DESCRIPTION OF DRAWINGS 
       FIG. 1  is the block diagram of the first and second sequences of digital information samples at the transmitting side; 
       FIG. 2  is the block diagram of forming the summary analog signal at the transmitting side; 
       FIG. 3  is the block diagram of communication system at the receiving side; 
       FIG. 4  is the view of the sampling function 
     
       
         
           
             
               
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       FIG. 5  is the spectrum of the sampling function shown in  FIG. 4 ; 
       FIG. 6  is the block diagram of the generator of the predetermined sampling function of the form 
               sin   ⁢           ⁢     x   ⁡     (       cos   ⁢     x   n       -   1     )           2   ⁢   n   ⁢           ⁢   sin   ⁢     x   n             
at the transmitting side.
 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   The method of information transmission according to the present invention is realized in the communication system, the block diagrams of which transmitting and receiving sides are shown, respectively, in  FIGS. 1 ,  2  and  3 . 
   The block diagram of processing the first and second sequences of digital information samples at the transmitting side comprises (see  FIG. 1 ) a clock frequency generator  1 , a first  2  and second  3  digital-to-analog converters, a subtractor  4 , an envelope former  5 , an analog-to-digital (A/D) converter  6 . 
   The clock frequency generator  1  forms at its first output the even signals of the clock frequency, and at its second output the odd signals of the clock frequency. The first output of the clock frequency generator  1  is coupled with the input of the first digital-to-analog (D/A) converter  2 , and the second output of the generator  1  is coupled with the input of the second digital-to-analog (D/A) converter  3 . The indicated D/A converters  2  and  3  convert the original sequences of discrete digital information samples to a sequence of rectangular signals having amplitudes equal to amplitudes of respective discrete digital samples. 
   The input of the first D/A converter  2  receives the first sequence of discrete digital information samples A 1   i , where i is the index number of digital information sample, i=0, 1, . . . , n−1, which sequence is converted to the first sequence of rectangular digital samples A 1   0 , A 1   1 , . . . A 1   n−2 , A 1   n−1 , of information and outputs from the D/A converter  2  by signals corresponding the even signals of the clock frequency from the clock frequency generator  1 . The method implementation is shown for n=4. 
   The input of the second D/A converter  3  receives the second sequence of discrete digital information samples A 2   i , where i=0, 1, . . . , n−1, which sequence is converted to the second sequence of rectangular digital samples A 2   0 , A 2   1 , . . . A 2   n−2 , A 2   n−1  of information and outputs from the D/A converter  3  by signals corresponding the odd signals of the clock frequency (i.e., with the clock frequency) from the clock frequency generator  1 . 
   The first and second sequences of digital information samples could come both from two independent information sources and from a single information source. In the last case, the sequence of digital samples of original information is divided by known techniques into two its own projections and supplied to the independent informational inputs of the units  2  and  3  in  FIG. 1 . 
   The output of the first D/A converter  2  is coupled with an input of subtractor  4 . The output of the second D/A converter  3  is coupled with an input of the envelope former  5  (which is a multiplier), and also outputs the second sequence of rectangular digital samples A 2   0 , A 2   1 , . . . A 2   n−2 , A 2   n−1  of information to the summary analog signal forming unit. A second input of the envelope former  5  is fed with a sampling function from sampling function generator. This sampling function hereinafter referring to as the predetermined one, could have the form 
               sin   ⁢           ⁢   x     x     ,     or   ⁢           ⁢         sin   ⁢           ⁢     x   ⁡     (       cos   ⁢     x   n       -   1     )           2   ⁢   n   ⁢           ⁢   sin   ⁢     x   n         .             
The output of the envelope former  5  is coupled with a first input of the analog-to-digital (A/D) converter  6 . At the output of the envelope former  5  is formed an envelope of the second sequence of digital information samples, which is supplied to the first input of the A/D converter  6 , to which second input are supplied even clock frequency signals from the first output of the clock frequency generator  1 .
 
   The output of the A/D converter  6  is coupled with an input of the subtractor  4 . The A/D converter  6  performs the calculation (sampling) of values of samples of the second sequence of digital information samples in the points of samples of the first sequence, which are supplied to a second input of the subtractor  4  in the form of rectangular signal sequence ΔA 2   i : ΔA 2   0 , ΔA 2   1 , . . . , ΔA 2   n−2 , ΔA 2   n−1 . The subtractor  4  performs the subtraction from the first sequence of rectangular digital samples A 1   0 , A 1   1 , . . . , A 1   n−2 , A 1   n−1 , the corresponding values ΔA 2   0 , ΔA 2   1 , . . . , ΔA 2   n−2 , ΔA 2   n−1  sampled (calculated) in the A/D converter  6 . 
   A sequence of the difference of digital information samples A 1   0 , ΔA 2   0 , . . . , A 1   n−1 −ΔA 1   n−1 , as well as the second sequence of digital information samples A 2   0 , A 2   1 , . . . , A 2   n−2 , A 2   n−1 , converted to rectangular pulses are supplied to respective inputs of the summary analog signal forming unit at the transmission side (see  FIG. 2 ). 
   The sequences of digital information samples A 2   0 , A 2   1 , . . . , A 2   n−2 , A 2   n−1  and samples A 1   0 −ΔA 2   0 , . . . , A 1   n−1 −ΔA 2   n−1 , before they come to the summary analog signal forming unit (see  FIG. 2 ), are converted by known methods to a parallel code using a serial-to-parallel converter (not shown). 
   The block diagram of the summary analog signal forming unit at the transmission side comprises (see  FIG. 2 ) a predetermined sampling function former  7  which consists of a first (preliminary) sampling function generator  8 , second (predetermined) sampling function generator  9 , and predetermined sampling function multiplier  10  which inputs are connected to outputs of sampling function generators  8  and  9 , and an output is an output of the predetermined sampling function former  7 . 
   Further, the transmitting side includes two groups of multipliers  11 – 14  and  15 – 18 , each of which comprises n ( FIG. 2  shows an example for n=4) multipliers of the predetermined sampling function and a sequence of digital information samples, which sequence is supplied to information inputs of the multipliers. Reference inputs of the multipliers  11 – 14  and  15 – 18  are joint and connected to the output of the predetermined sampling function former  7 . 
   Information inputs of the multipliers  11 – 14  and  15 – 18  are fed, respectively, with the sequence of difference of digital information samples of the first sequence and digital samples in the points of the first sequence samples A 1   0 −ΔA 2   0 , . . . , A 1   n−1 −ΔA 2   n−1 , and the second sequence of digital information samples A 2   0 , A 2   1 , . . . , A 2   n−2 , A 2   n−1 . 
   An output of each of the multipliers  11 – 14  and  15 – 18  is coupled via a corresponding delay element  19 – 22  and  23 – 26  with a corresponding input of a first envelope former  27  and second envelope former  28 , respectively. Outputs of these envelope formers  27  and  28  are connected to inputs of a summer  29  which output is coupled, directly and via a quadrature phase-shifter  30  with information inputs of, respectively, first and second output multipliers  31  and  32 , to reference inputs of which are supplied quadrature reference waveforms of the carrier frequency f 0 , respectively cos ω 0 t and sin ω 0 t, where ω 0 =2πf 0 . Outputs of the multipliers  31  and  32  are connected to respective inputs of a summer  33  which output is connected to an input of communication channel (not shown), for example, wireless line. 
   In the diagram of  FIG. 2 , the delay elements  19 – 22  and  23 – 26  ensure: various time delay of analog signals coming to their inputs, phase shift of the predetermined sampling function from 0 to (n−1)π, respectively, and forming of envelope elements (fragments). The first delay element  19  of the first group delays an analog signal coming to its input for 0 sec. (not delays a signal), i.e., this element is depicted in the diagram of  FIG. 2  only for the uniformity. Each next one from delay elements  20 – 22  has the analog signal delay time differed from the delay time of the previous element for a value of repetition period of the sequence of digital information samples T c =1/F u , where F u  is the upper frequency in the spectrum of the analog signal being transmitted. The same rule is retained also for delay elements  23 – 26  of the second group, but the first delay element  23  has the delay time of T c /2. 
   The quadrature phase-shifter  30  ensures a phase change of analog signal coming to its input by the value π/2 (for the carrier f 0 ). 
   The receiving side of communication system comprises ( FIG. 3 ) a quadrature phase-shifter  34  which input is united with an information input of a first input multiplier  35  and connected to the output of the communication channel (not shown), and an output of the quadrature phase-shifter  34  is coupled with an information input of a second input multiplier  36 . Reference inputs of the first and second input multipliers  35  and  36  are fed with the same quadrature waveforms of the carrier frequency f 0 , respectively cos ω 0 t and sin ω 0 t, as at the transmission side. Outputs of the input multipliers  35  and  36  are connected to respective inputs of subtractor  37  which output is coupled with inputs of clock frequency extractor  38 , first analog-to-digital (A/D) converter  39 , and first input of subtractor  40 . An output of the first A/D converter  39  is coupled with a first input of envelope former  41  which second input is fed with a predetermined sampling function having the identical form with the predetermined sampling function at the transmitting side, and an output of said former  41  is connected to a second input of the subtractor  40 . Direct and inverting outputs of the clock frequency extractor  38  are connected to clock inputs of, respectively, the first A/D converter  39  and second A/D converter  42 , outputs of which converters being, respectively, an output  43  of first sequence of digital information samples and an output  44  of second sequence of digital information samples. 
   The quadrature phase-shifter  34  ensures a phase change of summary analog signal coming to its input by the value π/2 (for the carrier f 0 ). 
   The clock frequency extractor  38  could have any known embodiment ensuring the obtainment of the clock frequency signal from the summary analog signal coming to the input of the receiving side depending on how the clock signal is inserted into the summary analog signal being transmitted. In  FIG. 3  the inverting output of the clock frequency extractor  38  is marked out by a point. 
   As the first sampling function being formed by the preliminary sampling function generator  8 , could be used the known function of the type 
               sin   ⁢           ⁢   x     x     ,         
where x=2πF u , F u  is the upper frequency in the spectrum of the analog signal being transmitted. However, in order to decrease distortions when transmitting discrete information samples over real communication channels having a carrier, it is expedient to select as the first (preliminary) sampling function the function of the type:
 
                     sin   ⁢           ⁢     x   ⁡     (       cos   ⁢     x   n       -   1     )           2   ⁢   n   ⁢           ⁢   sin   ⁢     x   n         ,           (   2   )               
where x=2πF u , F u  is the upper frequency in the spectrum of the analog signal being transmitted, n is an integer more than one and equal to a number of used frequency components in the analog signal spectrum. The value n is defined in accordance with the formula n=T/T c , where T is the given processing interval (the period of the predetermined sampling function), in this case 10.66667 ms, and T c  is a repetition period of the sequence of digital information samples.
 
   The indicated preliminary sampling function has the form shown in  FIG. 4  (the function is shown for n=16), and spectrum shown in  FIG. 5 . 
   A block diagram of the generator of such preliminary sampling function is depicted in  FIG. 6 . This generator comprises eight separate conversion units  45 . 1  to  45 . 8  connected in series. Each conversion unit includes a first  46  and second  47  multipliers, quadrature phase-shifter  48 , and summer  49 . In  FIG. 6  each of eight used conversion units  45  is marked with the reference  45 .j, where j indicates the index number of this conversion unit  45 . Each element of the corresponding conversion unit  45  has a double reference as well, where the second digit indicates the number of that conversion unit  45  which comprises this element. In every conversion unit  45 , an output of the quadrature phase-shifter  48  is coupled with an information input of the second multiplier  47 , and outputs of both multipliers  46  and  47  are connected to respective inputs of the summer  49 . An output of the quadrature phase-shifter  48  is united with an information input of the first multiplier  46  and is an information input of this conversion unit  45 , and an output of the summer  49  is an output of this conversion unit  45 . 
   Reference inputs of the first multipliers  46 . 1  and  46 . 2  and reference inputs of the second multipliers  47 . 1  and  47 . 2  of the first and second conversion units  45 . 1  and  45 . 2  are respectively united and are inputs  50  and  51  of quadrature reference waveforms of doubled sampling frequency of the whole generator, i.e., the frequency that corresponds to the value 4x in expression (2). Reference inputs of the first multipliers  46 . 3  and  46 . 4  and reference inputs of the second multipliers  47 . 3  and  47 . 4  of the third and fourth conversion units  45 . 3  and  45 . 4  are respectively united and are inputs  52  and  53  of quadrature reference waveforms of the sampling frequency of the whole generator, i.e., the frequency that corresponds to the value 2x in the expression (2). At last, reference inputs of the first multipliers  46 . 5 ,  46 . 6 ,  46 . 7  and  46 . 8  and reference inputs of the second multipliers  47 . 5 ,  47 . 6 ,  47 . 7  and  47 . 8  of the fifth to eighth conversion units  45 . 5 ,  45 . 6 ,  45 . 7  and  45 . 8  are respectively united and are inputs  54  and  55  of quadrature reference waveforms of the half sampling frequency, i.e., the frequency that corresponds to the value x in the expression (2). An information input of the first conversion unit  45 . 1  is an information input  56  of the generator, and an output of the eighth conversion unit  45 . 8  is an output  57  of the preliminary sampling function generator. 
   The quadrature phase-shifter  48  in every conversion unit  45  ensures a change of phase of signal coming to its input by the value π/2 (for the upper frequency F u  in the spectrum of analog signal being transmitted). 
   In order to generate the preliminary sampling function, the input of the preliminary sampling function generator is fed with a rectangular pulses of unit amplitude with the frequency F u  (the upper frequency in the spectrum of analog signal being transmitted). Quadrature reference waveforms are fed to the respective inputs of the preliminary sampling function generator from an external pulse generator forming at its outputs quadrature reference waveforms of doubled, single and half sampling frequency. 
   The second (predetermined) sampling function being generated by the generator  9  in the predetermined sampling function former  7  could have various forms. Below, examples are given for implementing the method of the present invention for two different forms of the second sampling function at the output of the generator  9 : 
                          sin   ⁢           ⁢     x   ⁡     (       cos   ⁢     x   n       -   1     )           2   ⁢   n   ⁢           ⁢   sin   ⁢     x   n                      (   3   )                 and   ⁢           ⁢         (       cos   ⁢     x   n       -   1     )     k       2   k         ,           (   4   )               
where k=1–20 and characterizes a truncation degree of the predetermined sampling function. In the case, when the second sampling function generator  9  generates the first one from the above functions, defined by the expression (3), the subtractor  37  at the receiving side has at its output a digital filter with a pulse response characteristic of the type (3).
 
   The method of information transmission in accordance with the present invention is realized in a communication system of  FIGS. 1 ,  2  and  3  as follows. 
   Two (a first A 1   i  and a second A 2   i ) independent sequences of discrete digital information samples received either from the same information source, or from two information sources having the same repetition period T c =1/F u  of the sequence of digital information samples, where F u  is the upper frequency in the spectrum of an analog signal being transmitted, are fed simultaneously to the inputs of, respectively, the first (2) and second (3) D/A converters. After the D/A converters  2  and  3  the converted sequences of digital samples are directed: the first sequence of digital information samples A 1   0 , A 1   1 , . . . , A 1   n−2 , A 1   n−1  is fed to the input of the subtractor  4 , and the second sequence of digital information samples A 2   0 , A 2   1 , . . . , A 2   n−2 , A 2   n−1  is fed to the input of the envelope former  5  and, through a serial-to-parallel converter, each sample of the second sequence is fed to the corresponding information input of multipliers  15 – 18  of the summary analog signal forming unit ( FIG. 2 ). Since the first D/A converter  2  is fed from the clock frequency generator with even signals, and the second D/A converter  3  is fed with odd signals, then the digital information samples A 2   0 , A 2   1 , . . . , A 2   n−2 , A 2   n−1  of the second sequence after the D/A converter  3  will be taken in points of digital information samples of the second sequence, which are between points of digital information samples of the first sequence. 
   In the envelope former  5  the following steps take place: forming the second sequence of digital information samples in the points of digital samples of the second sequence using the predetermined sampling function, determining the digital sample values in the points of digital samples of the first sequence, and subsequent forming the second sequence of digital information samples taken in the points of digital samples of the first sequence: ΔA 2   0 , ΔA 2   1 , . . . , ΔA 2   n−2 , ΔA 2   n−1 . This sequence of digital information samples is fed to the subtractor  4 , where takes place the subtraction of values of digital information samples of the second sequence taken in the points of digital information samples of the first sequence ΔA 2   0 , ΔA 2   1 , . . . , ΔA 2   n−2 , ΔA 2   n−1 , from the values of digital information samples of the first sequence A 1   0 , A 1   1 , . . . , A 1   n−2 , A 1   n−1 , and the difference in the form of digital information samples A 1   0 −ΔA 2   0 , . . . , A 1   n−1 −ΔA 2   n−1  are fed through the serial-to-parallel converter to respective information inputs of the multipliers  11 – 14  of the summary analog signal forming unit. 
   The preliminary sampling function generator  8  ( FIG. 2 ) forms the first sampling function defined by the expression (2) at the time interval T c =10.66667 ms. The generator  9  generates the second, predetermined sampling function defined by the expression (3) or (4). In so doing, at the output of the multiplier  10  in the predetermined sampling function former  7 , in dependence on a specific type of the second sampling function, a signal is formed of a type 
                     sin   ⁢           ⁢     x   ⁡     (       cos   ⁢     x   n       -   1     )           2   ⁢   n   ⁢           ⁢   sin   ⁢     x   n         ·              sin   ⁢           ⁢     x   ⁡     (       cos   ⁢     x   n       -   1     )           2   ⁢   n   ⁢           ⁢   sin   ⁢     x   n                        (   5   )                 or   ⁢           ⁢       sin   ⁢           ⁢     x   ⁡     (       cos   ⁢     x   n       -   1     )       ⁢       (     1   -     cos   ⁢     x   n         )     k         2   ⁢   n   ⁢           ⁢   sin   ⁢       x   n     ·     2   k             ,           (   6   )               
where k characterizes the degree of truncation of the predetermined sampling function, e.g., k=16.
 
   This predetermined sampling function is fed to the reference inputs of all multipliers  11 – 14  and  15 – 18  ( FIG. 2 ). 
   From the processing unit of the first and second sequences of digital information samples, respective digital information samples A 1   0 −ΔA 2   0 , . . . , A 1   n−1 −ΔA 2   n−1 , are fed to the information inputs of the first group of multipliers  11 – 14 , and respective digital information samples A 2   0 , A 2   1 , . . . , A 2   n−2 , A 2   n−1  are fed to the information inputs of the second group of multipliers  15 – 18  (preferably, sample points of the second sequence A 2   0 , A 2   1 , . . . , A 2   n−2 , A 2   n−1  are in the middle between sample points of the first sequence). 
   As a result, at an output of each multiplier  11 – 14  of the first group, depending on the type of the second, predetermined sampling function, is formed an analog signal of a type (where i is an index number of digital information sample, i=0, 1, . . . , n−1): 
   
     
       
         
           
             
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                             ⁢ 
                             
                               x 
                               n 
                             
                           
                         
                         ) 
                       
                       k 
                     
                   
                   
                     2 
                     ⁢ 
                     n 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     sin 
                     ⁢ 
                     
                       
                         x 
                         n 
                       
                       · 
                       
                         2 
                         k 
                       
                     
                   
                 
                 . 
               
             
           
         
       
     
   
   At an output of each delay element  19 – 22  following a multiplier  11 – 14  of the first group, an analog signal will be defined, taking into account a phase shift by 0 to (n−1)π, by the expression: 
   
     
       
         
           
             
               ( 
               
                 
                   A 
                   i 
                   1 
                 
                 - 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     A 
                     i 
                     2 
                   
                 
               
               ) 
             
             · 
             
               
                 sin 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   
                     ( 
                     
                       x 
                       - 
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         π 
                       
                     
                     ) 
                   
                   ⁡ 
                   
                     [ 
                     
                       cos 
                       ⁡ 
                       
                         ( 
                         
                           
                             
                               x 
                               - 
                               
                                 i 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 π 
                               
                             
                             n 
                           
                           - 
                           1 
                         
                         ) 
                       
                     
                     ] 
                   
                 
               
               
                 2 
                 ⁢ 
                 
                   n 
                   ⁢ 
                   
                       
                   
                   · 
                   sin 
                 
                 ⁢ 
                 
                   
                     x 
                     - 
                     
                       i 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       π 
                     
                   
                   n 
                 
               
             
             · 
             
                
               
                 
                   
                     
                       sin 
                       ( 
                       
                           
                       
                       ⁢ 
                       
                         x 
                         - 
                         
                           i 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           π 
                         
                       
                       ) 
                     
                     ⁡ 
                     
                       [ 
                       
                         cos 
                         ⁡ 
                         
                           ( 
                           
                             
                               
                                 x 
                                 - 
                                 
                                   i 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   π 
                                 
                               
                               n 
                             
                             - 
                             1 
                           
                           ) 
                         
                       
                       ] 
                     
                   
                   
                     2 
                     ⁢ 
                     
                       n 
                       · 
                       
                           
                       
                       ⁢ 
                       sin 
                     
                     ⁢ 
                     
                       
                         x 
                         - 
                         
                           i 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           π 
                         
                       
                       n 
                     
                   
                 
               
                
             
           
           , 
           
             
 
           
           ⁢ 
           
             or 
             ⁢ 
             
                 
             
             ⁢ 
             
               
                 ( 
                 
                   
                     A 
                     i 
                     1 
                   
                   - 
                   
                     Δ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       A 
                       i 
                       2 
                     
                   
                 
                 ) 
               
               · 
               
                 
                   
                     
                       
                         
                           sin 
                           ( 
                           
                               
                           
                           ⁢ 
                           
                             x 
                             - 
                             
                               i 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               π 
                             
                           
                           ) 
                         
                         ⁡ 
                         
                           [ 
                           
                             cos 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   
                                     x 
                                     - 
                                     
                                       i 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       π 
                                     
                                   
                                   n 
                                 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                           ] 
                         
                       
                       ⁡ 
                       
                         [ 
                         
                           1 
                           - 
                           
                             cos 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   x 
                                   - 
                                   
                                     i 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     π 
                                   
                                 
                                 n 
                               
                               ) 
                             
                           
                         
                         ] 
                       
                     
                     k 
                   
                   
                     2 
                     ⁢ 
                     
                       n 
                       · 
                       
                           
                       
                       ⁢ 
                       sin 
                     
                     ⁢ 
                     
                       
                         
                           x 
                           - 
                           
                             i 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             π 
                           
                         
                         n 
                       
                       · 
                       
                         2 
                         k 
                       
                     
                   
                 
                 . 
               
             
           
         
       
     
   
   At an output of each multiplier  15 – 18  of the second group, an analog signal is formed of the type: 
   
     
       
         
           
             
               A 
               i 
               2 
             
             · 
             
               
                 sin 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   x 
                   ⁡ 
                   
                     ( 
                     
                       
                         cos 
                         ⁢ 
                         
                           x 
                           n 
                         
                       
                       - 
                       1 
                     
                     ) 
                   
                 
               
               
                 2 
                 ⁢ 
                 n 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 sin 
                 ⁢ 
                 
                   x 
                   n 
                 
               
             
             · 
             
                
               
                 
                   
                     sin 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       x 
                       ⁡ 
                       
                         ( 
                         
                           
                             cos 
                             ⁢ 
                             
                               x 
                               n 
                             
                           
                           - 
                           1 
                         
                         ) 
                       
                     
                   
                   
                     2 
                     ⁢ 
                     n 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     sin 
                     ⁢ 
                     
                       x 
                       n 
                     
                   
                 
               
                
             
           
           , 
           
             
 
           
           ⁢ 
           
             or 
             ⁢ 
             
                 
             
             ⁢ 
             
               
                 A 
                 i 
                 2 
               
               · 
               
                 
                   
                     sin 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       x 
                       ⁡ 
                       
                         ( 
                         
                           
                             cos 
                             ⁢ 
                             
                               x 
                               n 
                             
                           
                           - 
                           1 
                         
                         ) 
                       
                     
                     ⁢ 
                     
                       
                         ( 
                         
                           1 
                           - 
                           
                             cos 
                             ⁢ 
                             
                               x 
                               n 
                             
                           
                         
                         ) 
                       
                       k 
                     
                   
                   
                     2 
                     ⁢ 
                     n 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     sin 
                     ⁢ 
                     
                       
                         x 
                         n 
                       
                       · 
                       
                         2 
                         k 
                       
                     
                   
                 
                 . 
               
             
           
         
       
     
   
   At an output of delay element  23 – 26  following a multiplier  15 – 18  of the second group, an analog signal will be defined, taking into account a phase shift by 0 to (n−1)π, by the expression: 
   
     
       
         
           
             
               A 
               i 
               2 
             
             · 
             
               
                 sin 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   
                     ( 
                     
                       x 
                       - 
                       
                         π 
                         2 
                       
                       - 
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         π 
                       
                     
                     ) 
                   
                   [ 
                   
                     cos 
                     ( 
                     
                       
                         
                           x 
                           - 
                           
                             π 
                             2 
                           
                           - 
                           
                             i 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             π 
                           
                         
                         n 
                       
                       - 
                       1 
                     
                     ) 
                   
                   ] 
                 
               
               
                 2 
                 ⁢ 
                 
                   n 
                   ⁢ 
                   
                       
                   
                   · 
                   sin 
                 
                 ⁢ 
                 
                   
                     x 
                     - 
                     
                       π 
                       2 
                     
                     - 
                     
                       i 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       π 
                     
                   
                   n 
                 
               
             
             · 
             
                
               
                 
                   
                     sin 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         ( 
                         
                           x 
                           - 
                           
                             π 
                             2 
                           
                           - 
                           
                             i 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             π 
                           
                         
                         ) 
                       
                       [ 
                       
                         cos 
                         ( 
                         
                           
                             
                               x 
                               - 
                               
                                 π 
                                 2 
                               
                               - 
                               
                                 i 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 π 
                               
                             
                             n 
                           
                           - 
                           1 
                         
                         ) 
                       
                       ] 
                     
                   
                   
                     2 
                     ⁢ 
                     
                       n 
                       ⁢ 
                       
                           
                       
                       · 
                       sin 
                     
                     ⁢ 
                     
                       
                         x 
                         - 
                         
                           π 
                           2 
                         
                         - 
                         
                           i 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           π 
                         
                       
                       n 
                     
                   
                 
               
                
             
           
           , 
           
             
 
           
           ⁢ 
           
             or 
             ⁢ 
             
               
                   
               
               ⁢ 
               
                   
               
             
             ⁢ 
             
               
                 A 
                 i 
                 2 
               
               · 
               
                 
                   
                     sin 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         
                           
                             ( 
                             
                               x 
                               - 
                               
                                 π 
                                 2 
                               
                               - 
                               
                                 i 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 π 
                               
                             
                             ) 
                           
                           [ 
                           
                             cos 
                             ( 
                             
                               
                                 
                                   x 
                                   - 
                                   
                                     π 
                                     2 
                                   
                                   - 
                                   
                                     i 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     π 
                                   
                                 
                                 n 
                               
                               - 
                               1 
                             
                             ) 
                           
                           ] 
                         
                         [ 
                         
                           1 
                           - 
                           
                             cos 
                             ( 
                             
                               
                                 x 
                                 - 
                                 
                                   π 
                                   2 
                                 
                                 - 
                                 
                                   i 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   π 
                                 
                               
                               n 
                             
                             ) 
                           
                         
                         ] 
                       
                       k 
                     
                   
                   
                     2 
                     ⁢ 
                     
                       n 
                       ⁢ 
                       
                           
                       
                       · 
                       sin 
                     
                     ⁢ 
                     
                       
                         
                           x 
                           - 
                           
                             π 
                             2 
                           
                           - 
                           
                             i 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             π 
                           
                         
                         n 
                       
                       · 
                       
                         2 
                         k 
                       
                     
                   
                 
                 . 
               
             
           
         
       
     
   
   At the output of the former  27  the first envelope a 1 (x) is described by the following expression: 
   
     
       
         
           
             
               
                 a 
                 1 
               
               ⁡ 
               
                 ( 
                 x 
                 ) 
               
             
             = 
             
               
                 ∑ 
                 
                   i 
                   = 
                   0 
                 
                 
                   n 
                   - 
                   1 
                 
               
               ⁢ 
               
                   
               
               ⁢ 
               
                 
                   ( 
                   
                     
                       A 
                       i 
                       1 
                     
                     - 
                     
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         A 
                         i 
                         2 
                       
                     
                   
                   ) 
                 
                 · 
                 
                   
                     
                       sin 
                       ⁡ 
                       
                         ( 
                         
                           x 
                           - 
                           
                             i 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             π 
                           
                         
                         ) 
                       
                     
                     ⁡ 
                     
                       [ 
                       
                         cos 
                         ⁡ 
                         
                           ( 
                           
                             
                               
                                 x 
                                 - 
                                 
                                   i 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   π 
                                 
                               
                               n 
                             
                             - 
                             1 
                           
                           ) 
                         
                       
                       ] 
                     
                   
                   
                     2 
                     ⁢ 
                     
                       n 
                       · 
                       sin 
                     
                     ⁢ 
                     
                       
                         x 
                         - 
                         
                           i 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           π 
                         
                       
                       n 
                     
                   
                 
                 · 
                 
                    
                   
                     
                       
                         sin 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                             ( 
                             
                               x 
                               - 
                               
                                 i 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 π 
                               
                             
                             ) 
                           
                           ⁡ 
                           
                             [ 
                             
                               cos 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     
                                       x 
                                       - 
                                       
                                         i 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         π 
                                       
                                     
                                     n 
                                   
                                   - 
                                   1 
                                 
                                 ) 
                               
                             
                             ] 
                           
                         
                       
                       
                         2 
                         ⁢ 
                         
                           n 
                           ⁢ 
                           
                               
                           
                           · 
                           sin 
                         
                         ⁢ 
                         
                           
                             x 
                             - 
                             
                               i 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               π 
                             
                           
                           n 
                         
                       
                     
                   
                    
                 
               
             
           
           , 
           
             
 
           
           ⁢ 
           
             
               or 
               ⁢ 
               
                 
                     
                 
                 ⁢ 
                 
                     
                 
               
               ⁢ 
               
                 
                   a 
                   1 
                 
                 ⁡ 
                 
                   ( 
                   x 
                   ) 
                 
               
             
             = 
             
               
                 ∑ 
                 
                   i 
                   = 
                   0 
                 
                 
                   n 
                   - 
                   1 
                 
               
               ⁢ 
               
                   
               
               ⁢ 
               
                 
                   ( 
                   
                     
                       A 
                       i 
                       1 
                     
                     - 
                     
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         A 
                         i 
                         2 
                       
                     
                   
                   ) 
                 
                 · 
                 
                   
                     
                       sin 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           
                             
                               ( 
                               
                                 x 
                                 - 
                                 
                                   i 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   π 
                                 
                               
                               ) 
                             
                             ⁡ 
                             
                               [ 
                               
                                 cos 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     
                                       
                                         x 
                                         - 
                                         
                                           i 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           π 
                                         
                                       
                                       n 
                                     
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                               ] 
                             
                           
                           ⁡ 
                           
                             [ 
                             
                               1 
                               - 
                               
                                 cos 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     
                                       x 
                                       - 
                                       
                                         i 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         π 
                                       
                                     
                                     n 
                                   
                                   ) 
                                 
                               
                             
                             ] 
                           
                         
                         k 
                       
                     
                     
                       2 
                       ⁢ 
                       
                         n 
                         ⁢ 
                         
                             
                         
                         · 
                         sin 
                       
                       ⁢ 
                       
                         
                           
                             x 
                             - 
                             
                               i 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               π 
                             
                           
                           n 
                         
                         · 
                         
                           2 
                           k 
                         
                       
                     
                   
                   . 
                 
               
             
           
         
       
     
   
   At an output of the former  28  the second envelope a 2 (x) is described by the following expression: 
   
     
       
         
           
             
               
                 a 
                 2 
               
               ⁡ 
               
                 ( 
                 x 
                 ) 
               
             
             = 
             
               
                 ∑ 
                 
                   i 
                   = 
                   0 
                 
                 
                   n 
                   - 
                   1 
                 
               
               ⁢ 
               
                   
               
               ⁢ 
               
                 
                   A 
                   i 
                   2 
                 
                 · 
                 
                   
                     
                       sin 
                       ⁡ 
                       
                         ( 
                         
                           x 
                           - 
                           
                             π 
                             2 
                           
                           - 
                           
                             i 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             π 
                           
                         
                         ) 
                       
                     
                     [ 
                     
                       cos 
                       ( 
                       
                         
                           
                             x 
                             - 
                             
                               π 
                               2 
                             
                             - 
                             
                               i 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               π 
                             
                           
                           n 
                         
                         - 
                         1 
                       
                       ) 
                     
                     ] 
                   
                   
                     2 
                     ⁢ 
                     
                       n 
                       · 
                       sin 
                     
                     ⁢ 
                     
                       
                         x 
                         - 
                         
                           π 
                           2 
                         
                         - 
                         
                           i 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           π 
                         
                       
                       n 
                     
                   
                 
                 · 
                 
                    
                   
                     
                       
                         sin 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                             ( 
                             
                               x 
                               - 
                               
                                 π 
                                 2 
                               
                               - 
                               
                                 i 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 π 
                               
                             
                             ) 
                           
                           [ 
                           
                             cos 
                             ( 
                             
                               
                                 
                                   x 
                                   - 
                                   
                                     
                                       
                                           
                                       
                                       ⁢ 
                                       π 
                                     
                                     2 
                                   
                                   - 
                                   
                                     i 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     π 
                                   
                                 
                                 n 
                               
                               - 
                               1 
                             
                             ) 
                           
                           ] 
                         
                       
                       
                         2 
                         ⁢ 
                         
                           n 
                           ⁢ 
                           
                               
                           
                           · 
                           sin 
                         
                         ⁢ 
                         
                           
                             x 
                             - 
                             
                                 
                             
                             ⁢ 
                             
                               π 
                               2 
                             
                             - 
                             
                               i 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               π 
                             
                           
                           n 
                         
                       
                     
                   
                    
                 
               
             
           
           , 
           
               
           
           ⁢ 
           
             
 
           
           ⁢ 
           
             
               or 
               ⁢ 
               
                   
               
               ⁢ 
               
                 
                   a 
                   2 
                 
                 ⁡ 
                 
                   ( 
                   x 
                   ) 
                 
               
             
             = 
             
               
                 ∑ 
                 
                   i 
                   = 
                   0 
                 
                 
                   n 
                   - 
                   1 
                 
               
               ⁢ 
               
                   
               
               ⁢ 
               
                 
                   A 
                   i 
                   2 
                 
                 · 
                 
                   
                     
                       
                         
                           
                             sin 
                             ⁡ 
                             
                               ( 
                               
                                 x 
                                 - 
                                 
                                   π 
                                   2 
                                 
                                 - 
                                 
                                   i 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   π 
                                 
                               
                               ) 
                             
                           
                           [ 
                           
                             cos 
                             ( 
                             
                               
                                 
                                   x 
                                   - 
                                   
                                     π 
                                     2 
                                   
                                   - 
                                   
                                     i 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     π 
                                   
                                 
                                 n 
                               
                               - 
                               1 
                             
                             ) 
                           
                           ] 
                         
                         [ 
                         
                           1 
                           - 
                           
                             cos 
                             ( 
                             
                               
                                 x 
                                 - 
                                 
                                   π 
                                   2 
                                 
                                 - 
                                 
                                   i 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   π 
                                 
                               
                               n 
                             
                             ) 
                           
                         
                         ] 
                       
                       k 
                     
                     
                       2 
                       ⁢ 
                       
                         n 
                         · 
                         sin 
                       
                       ⁢ 
                       
                         
                           x 
                           - 
                           
                             π 
                             2 
                           
                           - 
                           
                             i 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             π 
                           
                         
                         n 
                       
                       ⁢ 
                       
                         2 
                         k 
                       
                     
                   
                   . 
                 
               
             
           
         
       
     
   
   In two last expressions, regardless of specific type of the used predetermined sampling function, the envelope a 2 (x) in the sample points x=iπ has the following values: a 2 (x)=ΔA 2   0  for i=0, a 2 (x)=ΔA 2   1  for i=1, . . . , a 2 (x)=ΔA 2   n−1  for i=n−1. 
   At an output of the summer  29  an analog signal a 1 (x)+a 2 (x) is provided, which takes the values of the first envelope in the sample points of the first analog signal, and is fed to units  30 – 33  for implementing a one-sideband modulation in order to transfer the summary analog signal a 1 (x)+a 2 (x) to a carrier frequency f 0 . To this end, the summary analog signal a 1 (x)+a 2 (x) is fed directly to the first output multiplier  31 , and through the quadrature phase-shifter  30  to the second output multiplier  32 . The multipliers  31  and  32  perform the multiplication of the direct and phase shifted summary analog signals a 1 (x)+a 2 (x) by the quadrature waveforms of the carrier frequency, after which the results of this multiplication are summed by the output summer  27 , and the thus formed summary analog signal is fed to the communication line. 
   The summary analog signal received at the receiving side ( FIG. 3 ) passes the units  34 – 39  which perform the conversion inverse to the performed in the units  30 – 33  at the transmitting side. I.e., the received summary analog signal passes directly and through the quadrature phase-shifter  34 , respectively, to the first and second input multipliers  35  and  36  which reference inputs are fed with the same quadrature reference waveforms of the carrier frequency f 0  as the multipliers  31  and  32  at the transmitting side. 
   As a result, at outputs of the first and second input multipliers  35  and  36  are formed quadrature components of the received summary analog signal. 
   These quadrature components are subtracted in the subtractor  37 , at which output is connected a digital filter having a pulse response characteristic of the type (3), if the second, predetermined sampling function generator  9  generates the function of the type (3). In this case, at an output of the subtractor with the digital filter is formed an analog signal a 1   r (x)+a 2   r (x), which components are described by the expressions: 
   
     
       
         
           
             
               
                 a 
                 r 
                 1 
               
               ⁡ 
               
                 ( 
                 x 
                 ) 
               
             
             = 
             
               
                 ∑ 
                 
                   i 
                   = 
                   0 
                 
                 
                   n 
                   - 
                   1 
                 
               
               ⁢ 
               
                   
               
               ⁢ 
               
                 
                   ( 
                   
                     
                       A 
                       i 
                       1 
                     
                     - 
                     
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         A 
                         i 
                         2 
                       
                     
                   
                   ) 
                 
                 · 
                 
                   
                     ( 
                     
                       
                         
                           sin 
                           ⁡ 
                           
                             ( 
                             
                               x 
                               - 
                               
                                 i 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 π 
                               
                             
                             ) 
                           
                         
                         · 
                         
                           ( 
                           
                             
                               cos 
                               ⁢ 
                               
                                 
                                   x 
                                   - 
                                   
                                     i 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     π 
                                   
                                 
                                 n 
                               
                             
                             - 
                             1 
                           
                           ) 
                         
                       
                       
                         2 
                         ⁢ 
                         
                           n 
                           · 
                           sin 
                         
                         ⁢ 
                         
                           
                             x 
                             - 
                             
                               i 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               π 
                             
                           
                           n 
                         
                       
                     
                     ) 
                   
                   2 
                 
               
             
           
           , 
           
             
 
           
           ⁢ 
           
             
               
                 a 
                 r 
                 2 
               
               ⁡ 
               
                 ( 
                 x 
                 ) 
               
             
             = 
             
               
                 ∑ 
                 
                   i 
                   = 
                   0 
                 
                 
                   n 
                   - 
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   In the case, when the second, predetermined sampling function generator  9  forms the predetermined sampling function of the type (4), the filter at the output of the subtractor  37  is not necessary. At the output of the subtractor  37  is then formed the signal a 1   r (x)+a 2   r (x), which quadrature components are described by the same expressions as the components a 1 (x)+a 2 (x) at the output of the summer  29  at the transmitting side ( FIG. 2 ). 
   The clock frequency extractor  38  extracts the signal with the clock frequency (sampling frequency at the transmitting side) from this summary analog signal, which clock frequency signal is employed for clocking the first  39  and second  42  A/D converters, the clocking of both these A/D converters being performed in antiphase. Values of analog signal a 1   r (x) comes from the output of the first A/D converter  39  in the moment of clocking digital information samples of the first sequence, i.e., in those very moments that correspond the sample points of digital information samples of the first sequence at the transmitting side. These digital information samples come to the output  43  in the form of the original first sequence of digital information samples A 1   i  which are restored by sampling the summary analog signal with the clocking frequency. 
   The indicated restored first sequence of digital information samples is fed to the input of the envelope former  41  which implements its conversion, using the predetermined sampling function, to the analog signal a 1   r (x) of the first sequence, which is then fed to the second input of the subtractor  40  which first input is fed with the summary analog signal a 1   r (x)+a 2   r (x) from the output of the summer  37 . The subtractor  40  subtracts the analog signal a 1   r (x) of the first sequence from the summary analog signal a 1   r (x)+a 2   r (x) with the result that an analog signal is formed at the output of the subtractor  40 , which analog signal being the analog signal a 2   r (x) that has the following values in the sample points x=iπ: a 2   r (x)=ΔA 2   0  for i=0, a 2   r (x)=ΔA 2   1  for i=1, . . . , a 2   r (x)=ΔA 2   n−1  for i=n−1. This analog signal is fed to the input of the second A/D converter  42  which is clocked with the inverted clock frequency (i.e., having the phase shift by π relative to the signal at the clock input of the first A/D converter  39 ). At the output of the second A/D converter  36 , after restoring from the received difference analog signal a 2   r (x), is provided the second sequence of digital information samples A 2   i  which come to the output  44 . Thus, at the outputs  43  and  44  of the receiving side there are restored first and second sequences of digital information samples transmitted over the communication line without changing its parameters, i.e., a decompression is performed. 
   Hence, the proposed method of information transmission ensures the transmission of at least two analog signals instead of one during the same time over the existing communication line, i.e., increases the information transmission rate, or information capacity of transmission and reception line. 
   INDUSTRIAL APPLICABILITY 
   This invention could be used in the communication technique, measurements, and any other applications where it is necessary to transmit or convert an information. In so doing, the proposed method ensures an increase of information transmission rate, or information capability of communication channel. 
   Although the present invention is described with reference to its specific example of embodiment, this example by no means restricts the scope of invention, which is defined by the enclosed claims taking into account possible equivalents.