Abstract:
The signal processing-system using singularity is provided which is excellent in determination of the original signal against the degradation environment of an operating condition and robust to the signal degradation of noise, can generate the signal suitable to regeneration of the original signal, and has regeneration means to regenerate the original signal, wherein the system comprises: an original signal converter of the signal processing-system which converts the original signal contained in the inputted signal into the signal containing singular points by using the specific function, the converter outputting the signal containing singular points; an original signal regenerator which converts the incoming signals containing singular points into signals having singular points by the specific signal processing, the regenerator extracting the undesired-signal component from the signals having singular points; and a regenerator which regenerates the original signal by carrying out the operation of the generated undesired-signal and the above-mentioned signal-containing-singular-points, and outputs the regenerated signal.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a national phase application under 35 U.S.C. §371 of PCT Application No. PCT/JP2009/001520, filed Mar. 31, 2009, which claims the benefit of Japanese Patent Application No. 2008-095466, filed Apr. 1, 2008, and Japanese Patent Application No. 2008-100894, filed Apr. 8, 2008 and Japanese Patent Application No. 2008-100889, filed Apr. 8, 2008 and Japanese Patent Application No. 2008-186588, filed Jul. 17, 2008 and Japanese Patent Application No. 2009-080676, filed Mar. 27, 2009, the entire content of which are expressly incorporated herein by reference thereto. 
     BACKGROUND OF THE INVENTION 
     Field of the Invention 
     This invention relates to the signal processing-system using singularity and the associated information memory medium. The signal processing-system consists of the original signal converter and the original signal regenerator. The original signal converter consists of the signal conversion means, the undesired-signal extraction means, the input circuit, and the output circuit. The original signal regenerator consists of the conversion-processing means, the undesired-signal extraction means, the original signal regeneration means, the synchronization-signal extraction means, the input circuit, and the output circuit. 
     Especially, in the original signal converter, the inputted original signals are converted into the signals containing singular points for every synchronous cycle and the converted signals are outputted. In the original signal regenerator, the inputted signals containing singular points are converted into signals having singular points, the undesired wave component is regenerated by the signal processing for the singular points, and the original signals are regenerated by the operation using the signals having singular points. 
     This invention relates to the signal processing-system using singularity that can regenerate the original signals together with the advantage that is excellent in determination of the original signals against the degradation environment of the operating condition and robust to the signals degradation of noise etc. 
     Description of the Related Art Including Information Disclosed Under 37 CFR 1.97 and 1.98 
     Heretofore, the technology of extracting signals from the received wave buried in noise and/or undesired wave has been proposed. By such technology, the signals are estimated from the statistical character of the signal and noise or an undesired wave. For example, such statistical detection theory is described in the non-patenting reference 1. Moreover, there is WINNER filter that can minimize the second power average of the difference between the regenerated signals and the original signals. For example, these minimum-variance estimation methods are described in the non-patenting reference 2. 
     On the other hand, the interference elimination technology that can eliminate the interference such as echo interference that cannot be eliminated by receiving-filters although an out-band interference wave can be filtered by the receiving filter is also studied widely.
     Non-patenting reference 1: J. Hancock, P. Wintz “SIGNAL DETECTION THEORY” McGraw-Hill, New-York 1966   Non-patenting reference 2: Katayama “APPLICATION OF KALMAN FILTER, NEW EDITION”   Asakura Publishing Co., Ltd., Tokyo January 2000   Non-patenting reference 3: Ueno, Sunada, Arai “PLEASURE OF MATHEMATICS (THE WORLD OF SINGULAR POINT)   Nippon Hyoron-Sha. Tokyo November 2005   

     DISCLOSURE OF THE INVENTION 
     Brief Summary of the Invention 
     Problems to be Solved by the Invention 
     However, the following problems had arisen in the statistical detection. 
     Since generally the optimal value of signal regeneration would not be acquired if the statistical detection method were not applied to the statistically stable condition, correct signal regeneration was difficult when statistical characteristic of the fluctuating signal and the statistical characteristic of the interference wave are unstable. Moreover, when many disturbance factors existed, that are a delay wave, an interference noise, an interference wave, etc., the statistical detection method of signals had been complicated, and the detection result had remained in the realm of speculation. 
     On the other hand, in order to identify the statistical characteristic, statistical processing time had to be lengthened, it caused more delay of the processing operation time and it had the fault of making processing more complicated. 
     Moreover, since in the signal processing which treats digital signals higher reliability was required for the regenerated signals, the more powerful system that could overcome against many degradation factors under the operation environment, such as a delay wave, interference noise, distortion caused by means performance, was demanded. 
     Means for Solving the Problems 
     This invention was made in order to solve the above-mentioned problems. This invention provides the signal-processing system that converts the original signals into the signals containing singular points and analyzes the singularity area. This signal processing means has many advantages as follows: it is excellent in identifying of the original signals against the degradation of the operating environment, it is strong against the signal degradation by noise etc., and it is suitable for regeneration of the original signal. 
     This provided system consists of the original signal converter, which converts the original signals into the signals containing singular points by the signal processing, and followings: 
     The signal conversion means, the synchronization signal extraction means, the input circuit, the output circuit, the original signal regenerator, the conversion processing means, the undesired signal extraction means, the original signal regeneration means, the synchronization signal extraction means, the input circuit, and the output circuit. 
     Another system configuration consists of: 
     The original signal conversion feature, the signal conversion step, the synchronization-signal extraction step, the input means, the output means, the original signal regeneration feature, the conversion processing step, the undesired signal extraction step, the original-signal regeneration step, the synchronization-signal extraction step, the input means, and the output means. Furthermore, this invention provides the information memory medium that recorded the associated program to realize these systems. 
     Here, the following points or states are called the singular points: If the information of the original signals has the minimal points (including zero) on the original signals but the signals except the original signals have information of the signals, after predetermined signal processing was applied to the signals having the original signals. (The same applies hereinafter.) 
     On mathematics, it is defined as a place with the different feature from the circumference. For example, descriptions can be seen in the non-patenting reference 3. 
     The signal before being converted that can be converted into the signal having singular points by the specific signal processing is called the signal containing singular points. (The same applies hereinafter.) 
     To convert the signal containing singular points into signal having singular points by the specific signal processing is called the specific signal processing. (The same applies hereinafter.) 
     To convert the signals having singular points into signals containing singular points by the specific signal processing is called the specific inverse signal processing. (The same applies hereinafter.) 
     When there are many places to process singular points and they compose singular points overall, each signal of which singular point was processed is called as the signal containing quasi-singular points. (The same applies hereinafter.) 
     When an original signal and the singular point are orthogonal to each other, it is called as the orthogonal singular point. (The same applies hereinafter.) 
     However, when distinction is not necessary, singular points, quasi-singular points, and orthogonal singular points are simply called signals containing singular points. 
     In addition, when original signals are converted into the short signals by coding with the short period, it is called the short singular point, short quasi-singular point, and short orthogonal singular point respectively in order to distinguish from singular point, quasi-singular point, and orthogonal singular point. (The same applies hereinafter.) 
     However, when distinction is not necessary, short singular points, short quasi-singular points, and short orthogonal singular points are called signals containing singular points. (The same applies hereinafter.) 
     The transfer function of signals having singular points is called specific singularity-function. (The same applies hereinafter.) 
     The transfer function of the signals containing singular points is called the specific inverse singularity function. (The same applies hereinafter.) 
     The operation that converts an inverse singularity function into a singularity-function is called singularity operation. (The same applies hereinafter.) 
     Conversely, the operation that converts a singularity-function into an inverse singularity function is called inverse singularity operations. (The same applies hereinafter.) 
     Signals except original signals, such as thermal noise, an interference wave, and distortion noise, are called undesired-signal. (The same applies hereinafter.) 
     Technical Advantages of the Invention 
     This invention can provide the means that is excellent in identification of original signals against the degradation environment of an operating condition, robust to the signal degradation from noise and distortion, and enables the regeneration of the original signals, through the following two functions:
         The original signal converter converts the inputted original signals into the signals containing singular points for every synchronous cycle and outputs the signals having singular points.   The original signal regenerator converts the inputted signals containing singular points into the signals having singular points, regenerates the undesired wave component by signal processing at the singular points, and regenerates original signals through the operation of the signals having singular points.       

    
    
     
       BRIEF VIEWS OF THE SEVERAL VIEWS OF THE DRAWINGS 
         FIG. 1-A : Configuration diagram of the original signal converter that shows the 1 st  example of the signal processing-system of this invention. 
         FIG. 1-B : Configuration diagram of the original signal regenerator that shows the 1 st  example of the signal processing-system of this invention. 
         FIG. 2 : An example of the specific singularity-function. 
         FIG. 3 : An example of the specific inverse singularity-function. 
         FIG. 4 : An example of the singular point generation area of a specific inverse singularity function. 
         FIG. 5 : An example of block diagram of singular point conversion into signal domain. 
         FIG. 6-A : Configuration diagram of the original signal converter that shows the 2 nd  example of the signal processing-system of this invention. 
         FIG. 6-B : Configuration diagram of the original signal regenerator that shows the 2 nd  example of the signal processing-system of this invention. 
         FIG. 7 : Configuration diagram of the 3 rd  example of the signal processing-system of this invention. 
         FIG. 8 : Configuration diagram of the original signal converter that shows the 4 th  example of the signal processing-system of this invention. 
         FIG. 9-A : Configuration diagram of the original signal converter that shows the 5 th  example of the signal processing-system of this invention. 
         FIG. 9-B : Configuration diagram of the original signal regenerator that shows the 5 th  example of the signal processing-system of this invention. 
         FIG. 10 : An example of the signal that has polarity reverse between code-sequence. 
         FIG. 11-A : Configuration diagram of the original signal converter that shows the 6 th  example of the signal processing-system of this invention. 
         FIG. 11-B : Configuration diagram of the original signal regenerator that shows the 6 th  example of the signal processing-system of this invention. 
         FIG. 12 : An example of a short conversion signal. 
         FIG. 13 : An example of a short synchronization-signal of a short conversion signal. 
         FIG. 14 : An example of a short internal signal having singular points. 
         FIG. 15 : Configuration diagram of the original signal regenerator that shows the 8 th  example of the signal processing-system of this invention. 
         FIG. 16 : Configuration diagram of the original signal regenerator that shows the 9 th  example of the signal processing-system of this invention. 
         FIG. 17 : Configuration diagram of the original signal regenerator that shows the 10 th  example of the signal processing-system of this invention. 
         FIG. 18 : Configuration diagram of the original signal regenerator that shows the 11 th  example of the signal processing-system of this invention. 
         FIG. 19-A : Configuration diagram of the original signal conversion that shows the 12 th  example of the signal processing-system of this invention. 
         FIG. 19-B : Configuration diagram of the original signal regenerator that shows the 12 th  example of the signal processing-system of this invention. 
         FIG. 20 : Configuration diagram of the original signal conversion that shows the 13 th  example of the signal processing-system of this invention. 
         FIG. 21-A : Signal-processing step of the original signal converter that shows the 14 th  and 15 th  example of the signal-processing system of this invention. 
         FIG. 21-B : Signal-processing step of the original signal regenerator that shows the 14 th  and 15 th  example of the signal-processing system of this invention. 
         FIG. 22 : Signal-processing step that shows the 16 th  example of the signal processing-system of this invention. 
         FIG. 23-A : Signal-processing step of the original signal converter that shows the 17 th  example of the signal-processing system of this invention. 
         FIG. 23-B : Signal-processing step of the original signal regenerator that shows the 17 th  example of the signal-processing system of this invention. 
         FIG. 24-A : Signal-processing step of the original signal converter that shows the 18 th  example of the signal processing-system of this invention. 
         FIG. 24-B : Signal-processing step of the original signal regenerator that shows the 18 th  example of the signal processing-system of this invention. 
         FIG. 25-A : Signal-processing step of the original signal converter that shows the 19 th  example of the signal processing-system of this invention. 
         FIG. 25-B : Signal-processing step of the original signal regenerator that shows the 19 th  example of the signal processing-system of this invention. 
         FIG. 26 : Signal-processing step of the noise addition that that shows the 20 th  example of the signal processing-system of this invention. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Best Mode for Carrying Out the Invention 
     In order to realize the above mention, the best modes for carrying out this invention are explained based on a drawing, along the principle of this invention. In attached drawings, the same numeral codes are assigned to the drawings that have the same function. 
     The best mode explained below is thing for explanation, and does not restrict the range of this invention. Therefore, although a person skilled in the art can adopt the embodiment that replaced each of these elements or all elements by the thing equivalent to this, such embodiments are also included in the range of this invention. 
     Although the synchronization-signal extraction means is used in the best mode explained below, the synchronization-signal also can be supplied as follows based on this, and it is contained in the range of this invention. (This method is not drawn in the  FIG. 1 .) 
     When an external synchronization-signal is inputted, the concerned synchronization-signal extraction means is replaced to a synchronization-signal distribution means. When synchronization information is not included in an input signal, a synchronization-signal is generated in an internal synchronization-signal. 
     Although in the explanation below, continuous digital signals are imaged as the input original signals, this invention is applicable also to all signal forms such as a discrete digital signal, an analog signal, a composite signal (a synchronization-signal is included), a code, etc., and all of them are contained in the range of this invention. (They are not drawn in the  FIG. 1 .) 
     Although in the explanation below, the signal processing-system performs on the time axis, this invention is applicable also to a signal processing-system operating on the frequency axis, and it is contained in the range of this invention. (This method is not drawn in the  FIG. 1 .) 
     In addition to the signal processing-system itself, the information record medium that records the specific signal processing, the signals containing specific singular points, the function and the data of singular points, and the program of this invention can be distributed and sold independently. 
       FIG. 1-A  shows the configuration of the original signal converter  10  of the signal processing-system using singularity concerning to the 1 st  viewpoint of this invention. The original signal converter consists of the conversion means  14 , the 1 st  synchronization-signal extraction means  13 , the input circuit  12 , and the output circuit  15 . 
       FIG. 1-B  shows the configuration of the original signal regenerator  20  of the signal processing-system using singularity concerning to the 1 st  viewpoint of this invention. The original signal regenerator consists of the conversion-processing means  24 , the undesired-signal extraction means  25 , the original signal regeneration means  26 , the 2 nd  synchronization-signal extraction means  23 , the Input circuit  22 , and the output circuit  27 . 
     In the original signal converter  10 , the 1 st  synchronization-signal  16  of the original signal is extracted from the signal containing the original signal by the 1 st  synchronization-signal extraction means  13 . The 1 st  synchronization-signal  16  is sent to the input circuit  12 , the signal conversion means  14 , and output circuit  18 . 
     Based on the extracted 1 st  synchronization-signal  16 , the signal  11  is converted into the internal signal  17  by the input circuit  12 , and sent to the signal conversion means  14 . Applying signal processing with the specific inverse singularity operation, the signal conversion means  14  converts the internal signal  17  into the signal containing singular points, and sends it to the output circuit  15 . The output circuit  15  outputs the signals containing singular points  19 . 
     In the original signal regenerator  20 , the 2 nd  synchronization-signal  33  is extracted from the input signal  21  containing singular points by the 2 nd  synchronization-signal extraction means  23 . 
     The 2 nd  synchronization-signal  33  is sent to the input circuit  22 , the conversion-processing means  24 , the undesired-signal extraction means  25 , the original signal regeneration means  26 , and the output circuit  27 . 
     Based on the extracted synchronization-signal  33 , the signal  21  is converted into the internal signal  32  by the input circuit  22 , and sent to the conversion-processing means  24 . 
     Furthermore, based on the extracted 2 nd  synchronization-signal  33 , the conversion-processing means  24  converts the internal signal containing the singular points  32  from the input circuit  22  into the signal having singular points by the specific signal processing, and sends it to the undesired-signal extraction means  25 . 
     Undesired-signal extraction means  25  extracts an undesired-signal component from the signal having singular points and generates an undesired-signal by the specific inverse signal processing. Generated undesired-signal is sent to the original signal regeneration means  26 . Applying operation to the signals containing singular points and the undesired-signals, the original signal regeneration means  26  restores the signals containing singular points except the undesired-signals. Then, applying inverse operation of the inverse singularity function, the original signal regeneration means  26  regenerates the original signals. The output circuit outputs the regenerated signals  29 . 
       FIG. 2  shows an example of the singularity-function that has singular points on the time-axis. The singularity-function illustrated here has three singular points in the time duration of the one period. 
     The inverse singularity function that is related to the singularity-function by the inverse singularity operation (Here, double integration is applied) is shown in  FIG. 3 . 
       FIG. 4  shows the area where the internal signals are converted into the signals containing singular points by using the inverse singularity function, based on the 1 st  synchronization-signal extracted from the input signals  11 . 
     In this figure, shapes of an ellipse within the synchronous period show the area containing singular points. They are the area of the inverse-singular points that can be converted into the signals having singular points by the specific signal processing. An example of the operation up to converting into the signals containing singular points is explained using mathematical equations. 
     The following equation (1) expresses the internal signals  17  x(t) that is the output of the input circuit. 
     
       
         
           
             
               
                 
                   
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             Here, ƒ(t) is the input signal including the original signals 
             h(t) is the impulse response of the input circuit  12   
           
         
       
    
     Express the singularity-function having specific singular points by g(t). 
     At this time, the following equation (2) can express the inverse singularity function s(t) related to this function by the inverse operation R(g).
 
 s ( t )= R{g ( t )}  (2)
 
       FIG. 3  shows the example of which the double integration was applied as the inverse operation, and the equation (2) is given by the following equation (3).
 
 s ( t )=∫∫ g ( t ) dt   (3)
 
     Consider equation (4) as an example of the singularity-function g(t) shown in  FIG. 2 .
 
 g ( t )=(−2α t   2 +3)×(−2α) 2   t×e   (−αt     2     ) ; α&gt;0  (4)
 
     By applying the inverse operation to the g(t) in the equation (4), the inverse singularity function s(t) becomes equation (5) and the wave form is shown in the  FIG. 3 .
 
 s ( t )=(−2α) t×e   (−αt     2     ) ; α&gt;0  (5)
 
     Applying the following operation to the digital signal x(t) given by the equation (1) and the inverse singularity function s(t), the signals containing singular points u(t) can be calculated as the following equation (6). 
     
       
         
           
             
               
                 
                   
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     Here, put T as the sampling length of the digital signal, and define t=nT and τ=mT. Substitute u(n) for u(t), x(n-m) for x(t-τ), and s(m) for s(τ) in discrete time domain. Then, the equation (6) can be expressed as the following equation (7) in discrete time domain. 
     
       
         
           
             
               
                 
                   
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       FIG. 5  shows an example of configuration of the digital circuit realized by equation (7). 
     Here, square □ shows the delay line of T sec. Triangle ∇ is weighting factor of the signal determined by the impulse response s(m). 
     Next, a method to find the inverse singularity-function s(t) by the operation processing on a frequency axis is shown. 
     Apply the Laplace transform to the signal function ƒ(t), h(t) and x(t) in the equation (1). 
     At this time, the equation (8) can express the digital signal X(s).
 
 X ( s )= H ( s ) F ( s )  (8)
 
     Here, the Laplace transforms of the function ƒ(t), h(t) and x(t) are F(s), H(s), and X(s), respectively. 
     Express the singularity-function g(t) and the inverse singularity-function s(t) in the equation (2) by G(s) and S(s), respectively and consider R(s) as the inverse operation processing. 
     Then, the equation 2 can be expressed by the following equation (9).
 
 S ( s )= R ( s ) G ( s )  (9)
 
     When R(s) is n th  order integration, R(s) is given by equation (10) and when R(s) is n th  order differential, R(s) is given by equation (11). 
     
       
         
           
             
               
                 
                   
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     Express the digital signal X(s) by the transfer function Q(s) that converts into the signal containing singular points, then, equation (12) can be got.
 
 S ( s )= Q ( s ) H ( s ) F ( s )  (12)
 
     Therefore, Q(s) is given by the following equation (13). 
     
       
         
           
             
               
                 
                   
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     In the conversion means, by converting the transfer function Q(s) given by the equation (13) into the angular frequency function and realizing it by the analog filter or the digital filter, the conversion means can be established. 
       FIG. 6-A  shows the configuration of the original signal converter  40  of the signal processing-system concerning to 2 nd  viewpoint of this invention. Its original signal converter consists of the signal conversion means  44 , the 1 st  synchronization-signal extraction means  13 , the input circuit  12 , and the output circuit  15 . 
     In the original signal converter  40 , the 1 st  synchronization-signal  16  of the original signal is extracted from the signals containing the original signals by the 1 st  synchronization-signal extraction means  13 . The 1 st  synchronization-signal  16  is sent to the input circuit  12 , the signal conversion means  44 , and the output circuit  45 . Based on the extracted 1 st  synchronization-signal  16 , the original signal  10  is converted into the internal signal  17  and sent to the signal conversion means  44 . Based on the extracted 1 st  synchronization-signal and using the inverse-quasi-singularity-function, the signal conversion means  44  converts the internal signal  17  into the signal containing quasi-singular points and sends it to the output circuit  45 . Here, the inverse-quasi-singularity-function is given by an inverse operation of the quasi-singularity-function, which is given by dividing the singularity-function having specific singular points. The output circuit  45  outputs the signals containing quasi-singular points received from the signal conversion means  44 . 
       FIG. 6-B  shows the configuration of the original signal regenerator  50  of the signal processing-system concerning to 2 nd  viewpoint of this invention. The original signal regenerator  50  consists of the conversion-processing means  54 , the undesired-signal extraction means  55 , the original signal regeneration means  56 , the 2 nd  synchronization-signal extraction means  23 , the input circuit  52 , and the output circuit  27 . 
     In the original signal regenerator  50 , the 2 nd  synchronization-signal extraction-means  23  extracts the 2 nd  synchronization-signal from the inputted signal that contains singular points  51 . The 2 nd  synchronization-signal is sent to the following circuits: The input circuit  52 , the conversion-processing means  54 , the undesired-signal extraction means  55 , the original signal regeneration means  56 , and the output circuit  27 . 
     Based on the extracted 2 nd  synchronization-signal  57 , the input circuit  12  converts the input signals  51  into the internal signals  57  and sends them to the conversion-processing means  54 . Then, based on the extracted 2 nd  synchronization-signal, the conversion-processing means  54  converts the signals containing quasi-singular points  57 , that come from the input circuit  52 , into the signals having singular points by the specific signal processing, and sends them to the undesired-signal extraction means  55 . The undesired-signal extraction means  55  extracts undesired-signal component from signals having singular points and generates undesired-signals by the specific inverse signal processing. The generated undesired-signals are sent to the original signal regeneration means  56 . Applying operation to the signals containing singular points and the undesired-signals, the original signal regeneration means restores the signals containing quasi-singular points except the undesired-signals. Then, applying inverse operation processing of inverse singularity function, the original signal regeneration means regenerates the original signals. The output circuit outputs the regenerated signals  29 . 
     Explanation of the operation of the signal processing containing singular points is deleted here, since it is the same as the 1 st  viewpoint of this invention. Here, by using quasi-singularity-function that is the divided singularity-function, an example of the conversion operation to the inverse-quasi-singularity signal by applying the inverse operation of the quasi-singularity-function is explained using mathematical expression as following. Express the singularity-function having specific singular points by g(t), express the Laplace transform of this function by G(s)=G 1 (s)G 2 (s), and separate G(s) into G 1 (s) and G 2 (s). Express the inverse Laplace transforms of G 1 (s) and G 2 (s) by g 1 (t) and g 2 (t), respectively. Here, g 1 (t) and g 2 (t) are called the quasi-singularity-function. (The same applies hereinafter.) Applying inverse operation R(g), the inverse quasi-singularity-function s 1 (t) is given by equation (14).
 
 s   1 ( t )= R{g   1 ( t )}  (14)
 
     Applying following operation to digital signal x(t) and singularity-function s 1 (t), the following equation (15) can express the signal containing singular points u 1 (t). 
     
       
         
           
             
               
                 
                   
                     
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     Here, put T as the sampling length of the digital signal, and define t=nT and τ=mT. Substitute u 1 (n) for u 1 (t), x(n-m) for x(t-τ), and for s 1 (τ) in discrete time domain. Then, the equation (15) can be expressed as the following equation (16) in the discrete domain. 
     
       
         
           
             
               
                 
                   
                     
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                       ( 
                       n 
                       ) 
                     
                   
                   = 
                   
                     
                       ∑ 
                       
                         - 
                         M 
                       
                       M 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       { 
                       
                         
                           x 
                           ⁡ 
                           
                             ( 
                             
                               n 
                               - 
                               m 
                             
                             ) 
                           
                         
                         ⁢ 
                         
                           
                             s 
                             1 
                           
                           ⁡ 
                           
                             ( 
                             m 
                             ) 
                           
                         
                       
                       } 
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
     The digital circuit ( FIG. 5 ) concerning the 1 st  viewpoint of this invention can be realized by using the equation 16. 
       FIG. 7  shows the configuration of the original signal converter  60  and the original signal regenerator  70 , that are the signal processing-system concerning to 3 rd  viewpoint of this invention. From the original signal converter  60 , the signals containing singular points and the synchronization-signal are sent to the original signal regenerator  70  directly. It is also possible to unify the signal conversion means  64  of the original signal converter  60  and the conversion-processing means  71  of the original signal regenerator  70  and to process a singular point. 
       FIG. 8  shows the configuration of the original signal converter  80  of the signal processing-system concerning to 4 th  viewpoint of this invention. The original signal converter consists of the signal conversion means  14 , the 1 st  synchronization-signal extraction means  13 , the inverse singularity-function generation means  81 , the error detection means  82 , the correction means  83 , the input circuit  12 , and the input circuit  15 . 
     Explanation of the operation to convert into the signals containing singular points is deleted here, since it is the same as the 1 st  viewpoint of this invention. 
     Here, an example of operation of the singularity-function generation means  81 , the error detection means  82 , and the correction means  83  is explained using mathematical expression as following. 
     In the original signal converter  80  concerning to 4 th  viewpoint of this invention, the error detection means  82  detects the difference between the singularity signal u(t) and singularity-function g(t) having specific singular points and its result is output as the error signal  84 . Here, the singularity signal u(t) is given by a specific signal processing of the signals containing singular points that are converted by the signal conversion means  14 . And the singularity function g(t) having specific singular points is generated in the singularity-function generation means  81 . 
     Express the error signal by r(t) and apply the Laplace transform to u(t), g(t), and r(t). 
     Express the Laplace transform of u(t), g(t), and r(t) by U(s), G(s), and R(s), respectively. Then, the error signal R(s) is given by equation (17). 
     
       
         
           
             
               
                 
                   
                     R 
                     ⁡ 
                     
                       ( 
                       s 
                       ) 
                     
                   
                   = 
                   
                     
                       G 
                       ⁡ 
                       
                         ( 
                         s 
                         ) 
                       
                     
                     
                       U 
                       ⁡ 
                       
                         ( 
                         s 
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
     Error detection means  82  performs the inverse Laplace transform of this error function R(s), and obtains the error signal r(t). Applying inverse signal processing to this error signal, the error detection means  82  generates the correction error signal r′(t) and sends it to the correction means  83 . 
     Here, put T as the sampling length of the digital signal and define t=nT. Then, the corrected signal u(n) can be expressed as the following equation (18) in the discrete domain. 
     
       
         
           
             
               
                 
                   
                     u 
                     ⁡ 
                     
                       ( 
                       n 
                       ) 
                     
                   
                   = 
                   
                     
                       ∑ 
                       
                         - 
                         M 
                       
                       M 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       { 
                       
                         
                           u 
                           ⁡ 
                           
                             ( 
                             
                               n 
                               - 
                               m 
                             
                             ) 
                           
                         
                         ⁢ 
                         
                           r 
                           ⁡ 
                           
                             ( 
                             m 
                             ) 
                           
                         
                       
                       } 
                     
                   
                 
               
               
                 
                   ( 
                   18 
                   ) 
                 
               
             
           
         
       
     
     The digital circuit ( FIG. 5 ) concerning the 1 st  viewpoint of this invention can be realized by using the equation 18. 
     In the signal processing-system concerning the 3 rd  viewpoint of this invention, the error correction function is generated from the difference between the signals having the singular points obtained by the specific signal processing of the signals containing singular points and the singularity-function g(t) having specific singular point. However, in addition to this method, the error correction function can be generated from the difference between the signals u′(t) having specific singular points and the inverse singularity function g′(t) having specific singular points. In this case, the error detection means  82  operates as follows: 
     The difference between the singularity signal u(t) containing singular points converted by the signal conversion means and the specific inverse singularity function g′(t) containing singular points is defined as the error correction function r′(t), and apply the Laplace transform to u′(t), g′(t), and r′(t). Express the Laplace transform of u′(t), g′(t), and r′(t) by F′(s), G′(s), and R′(s), respectively. 
     Then, the error function R′(s) can be expressed as following equation 19. 
     
       
         
           
             
               
                 
                   
                     
                       R 
                       ′ 
                     
                     ⁡ 
                     
                       ( 
                       s 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         G 
                         ′ 
                       
                       ⁡ 
                       
                         ( 
                         s 
                         ) 
                       
                     
                     
                       
                         F 
                         ′ 
                       
                       ⁡ 
                       
                         ( 
                         s 
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
           
         
       
     
     Error detection means  82  carries out the inverse Laplace transform of this correction function R′(s) and obtains correction signal r′(t), and sends it to the correction means  83 . 
     Here, put T as the sampling length of the digital signal and define t=nT. Then, the corrected signal u′(n) can be expressed as the equation (18) in the discrete domain. 
     This figure shows the configuration of the original signal conversion means  92  and the polarity reversing function  91 , that are a part of the original signal converter  90  of the signal processing-system concerning to 5 th  viewpoint of this invention consists. Furthermore, the polarity reversing function  91  consists of the code-sequence generation means  93 , the code synchronization-signal generation means  94 , and the 3 rd  synchronization-signal generation means  95 . 
     Internal signal  17  from input circuit and the 1 st  synchronization-signal  16  extracted by the 1 st  synchronization-signal extraction means are input to the polarity reversing function  91 . (Here, the 1 st  synchronization-signal extraction means is not shown in  FIG. 9-A .) 
     Based on the 1 st  synchronization-signal  16 , the code synchronization-signal generation means  94  generates code synchronization-signal corresponding to the code-sequence length. 
     Moreover, based on the 1 st  synchronization-signal  16  the 3 rd  synchronization-signal generation means  95  generates the 3 rd  synchronization-signal  96  accelerated at the predetermined rate. 
     Based on the code synchronization-signal and 3 rd  synchronization-signal, the code-sequence generation means  93  inserts the code that generates orthogonal singular points within the code or among the code-sequence. 
       FIG. 10  shows the signal (orthogonal singular point) generated in the code-sequence generation means  93  of which polarity between the code-sequence was reversed. The 3 rd  synchronization-signal  96  is supplied to the signal conversion means  92  that generates signals containing singular points. 
       FIG. 9-B  shows the configuration of the original signal regenerator  100  of the signal processing-system concerning to 5 th  viewpoint of this invention. It consists of the 2 nd  synchronization-signal generation means  103 , the 4 th  synchronization-signal generation means  105 , the code synchronization-signal generation means  104 , the conversion-processing means  106 , the undesired-signal extraction means  107 , the code-sequence signal regeneration means  108 , the input circuit  102 , and the output circuit  27 . 
     In the original signal regenerator  100 , the 4 th  synchronization-signal  115  is extracted from the input signal containing singular points  101  by the 4 th  synchronization-signal extraction means  105 . The 4 th  synchronization-signal  115  is supplied to the input circuit  102 , the conversion-processing means  106 , undesired-signal extraction means  107 , the code-sequence signal regeneration means  108 , the code synchronization-signal generation means  104 , the 2 nd  synchronization-signal generation means  103 , and the output circuit  27 . On the other hand, the input signal  101  containing singular points are converted into the internal signal  112  by the input circuit  102  based on the 4 th  extracted synchronization-signal  115  and it is sent to the conversion-processing means  106  and the code synchronization-signal generation means  104 . Based on the 4 th  extracted synchronization-signal  115 , the internal signal  112  containing singular points from the input circuit  102  is converted into the signals having singular points by the specific signal processing and it is sent to the undesired-signal extraction means  107 . 
     The undesired-signal extraction means  107  detects the singular points from the signals containing singular points that are sent from the conversion-processing means  106 , detects the orthogonal singular points based on the code synchronization-signal  114  received from the code synchronization-signal generation means  104 , extracts the undesired-signal component, and generates undesired-signal by the specific inverse signal processing. 
     The generated undesired-signal is sent to the code-sequence signal-regeneration means  108 . The code-sequence signal regeneration means restores the signals containing singular points except the undesired-signal by operation of the signals containing singular points and the undesired-signals, regenerates the short code signal by the inverse operation processing, and regenerates the original signals from the regenerated short code by using the 4 th  extracted synchronization-signal  115  and the 2 nd  synchronization-signal. 
     The output circuit  27  outputs the regenerated original signal. 
       FIG. 11-A  shows the configuration of the code processing function within the code  121  in the original signal converter of the signal processing-system concerning to 6 th  viewpoint of this invention. It consists of the short code conversion means  122 , the short signal conversion means  123 , and the short synchronization-signal generation means  124 . Based on the synchronization-signal  18  that inputted into the code processing function within code  121 , the short synchronization-signal generation means  124  generates the short synchronization-signal by predetermined rate corresponding to the code length in the code. This short synchronization-signal is supplied to the short code conversion means  122  and the short signal conversion means  123 . Based on the short synchronization-signal  125 , the short signal conversion means  123  generates specific short codes, and by applying the operation processing to the internal signal  17 , it generates the short internal signals of which the time length is shorter than the original signal. The generated short internal signals are sent to the short signal conversion means  123 . Based on the short synchronization-signal, the signal conversion means  123  converts the short internal signals into the signals having singular points  129 . 
       FIG. 11-B  shows the configuration of the original signal regenerator  130  of the signal processing-system concerning to 6 th  viewpoint of this invention. It consists of the 2 nd  synchronization-signal generation means  134 , the short synchronization-signal extraction means  133 , the short conversion-processing means  135 , the undesired-signal extraction means  136 , the short signal regeneration means  137 , the original signal regeneration means  138 , the input circuit  132 , and the output circuit  25 . The original signal regenerator  130  extracts the short synchronization-signal  143  that was extracted from the signals containing the singular points  131  received from the original signal regenerator by the short synchronization-signal extraction means  133 . The extracted signal is sent to the input circuit  132 , the short conversion-processing means  135 , the undesired-signal extraction means  136 , the short signal regeneration means  137 , the original signal regeneration means  138 , and the output circuit  25 . On the other hand, based on the extracted short synchronization-signal  143 , the signals containing singular points  131  are converted into the short internal signals  142  by the input circuit  132 , and are sent to the short conversion-processing means  135 . 
     Furthermore, based on the extracted short synchronization-signal  143 , the short conversion-processing means  135  carries out the specific signal processing for the short internal signals containing singular points from the input circuit  132  and converts it to the signals having singular points. The converted signal is sent to the undesired-signal extraction means  136 . 
     The undesired-signal extraction means  136  detects the singular points from the signals having singular points, extracts undesired-signal components, and generates undesired-signals by specific inverse signal processing. The generated undesired-signals are sent to the short signal regeneration means  137 . The short signal regeneration means restores the signals containing the singular points except the undesired-signals by the operation of the signals containing singular points and the undesired-signals, and regenerates the signals having singular points  129  by the inverse operation. Furthermore, by using 2 nd  synchronization-signal  144 , it regenerates the original signals from the regenerated signals having singular points. The output circuit  27  outputs this regenerated original signal  139 . 
       FIGS. 12 to 14  show above-mentioned signal processing. 
       FIG. 13  shows the waveform of the short synchronization-signal  125  generated in the short synchronization-signal generation means  124 .  FIG. 12  shows the short internal signal (that is the output signal of the short code conversion means) composed of the predetermined code-sequence synchronizing with the short synchronization-signal  125 .  FIG. 14  shows the signal containing short singular point  129  converted by the above-mentioned short signal conversion means  123 . This figure also shows an example of the singularity domain containing short singular points and the orthogonal singularity domain of the short conversion codes. In the multiple original signal regenerators, the 1 st  original signal regenerator  152 - 1  regenerates the original signal  156 - 1 , while its undesired-signal detection means sends the detected undesired-signal  153 - 1  to the following original signal regenerator  152 - 2 . The next original signal regenerator  152 - 2  regenerates the original signal  156 - 2 , while its undesired-signal detection means sends the detected undesired-signal  153 - 2  to the following original signal regenerator  152 - 3 . In this way, multiple original signal regenerators operate. 
     The system shown in this figure is a signal processing-system using singularity that can regenerate multiple original signals. 
       FIG. 16  shows the original signal regenerator of the signal processing-system concerning the 9 th  viewpoint of this invention. The undesired wave signal  161  of the undesired-signal detection means of the above-mentioned original signal regenerator is sent to 2 nd  output circuit  162  and outputs the undesired-signal  163 . The signal processing-system using singularity shown in  FIG. 16  shows the signal processing-system using singularity that has the above-mentioned feature. 
       FIG. 17  shows a signal processing-system concerning the 10 th  viewpoint of this invention. The input signal  171  sent to the multiple original signal regenerators are divided by the branching circuit  172  and sent to individual original signal regenerators. The first  172 - 3 - 1  outputs the first undesired-signal  174 - 1  and the second original signal regenerator  172 - 3 - 2  outputs the first undesired-signal  174 - 2 . Like this way, multiple original signal regenerators output each undesired wave signal. The system shown in this figure is the signal processing-system using singularity characterized by the capability of restoring and outputting at least one or more specific undesired wave signals. 
       FIG. 18  shows the signal processing-system concerning the 11 th  viewpoint of this invention. The input signal  181  sent to the multiple original signal regenerators is sent to the first original signal regenerator  182 - 1 . While the 1 st  original signal regenerator outputs the 1 st  undesired-signal  183 - 1 , it sends the undesired-signal  183 - 1  to the 2 nd  original signal regenerator  182 - 2 . In the same way, the 2 nd  original signal regenerator outputs the 2 nd  undesired-signal  183 - 2 , it sends the undesired-signal  183 - 2  to the 3 rd  original signal regenerator. The system shown in this figure is the signal processing-system using singularity characterized by restoring and outputting at least one or more specific undesired wave signals by outputting an undesired wave signal one by one. 
       FIG. 19-A  shows the configuration of the original signal converter  190  of the signal processing-system concerning the 12 th  viewpoint of this invention. In the original signal converter, the signal conversion means sends the specific singularity-function to the function coding means. The function coding means resolves the specific singularity-function into the composition elements and encodes them. The encoder output  192  sends out the output signal  194 . 
       FIG. 19-B  shows the configuration of the original signal regenerator  195  of the signal processing-system concerning the 12 th  viewpoint of this invention. The function-coding signal  196  that was inputted into the coding input circuit of the original signal regenerator  195  are converted into the internal coding signals that are suitable for internal coding processing and the internal coding signal is sent to the singularity-function generation means  198 . The singularity-function generation means generates the singularity-function from the function-coding signal sent from the coding input circuit and sends it to the original signal regeneration means  26 . The original signal regeneration means detects the signals except for the original signal using above-mentioned singularity-function, and regenerates the original signal. The system shown in this figure is the signal processing-system using singularity characterized by above-mentioned original signal regeneration method. 
       FIG. 20  shows the configuration of the noise generation means  201  and the noise combiner  202  equipped in the signal processing-system concerning the 13 th  viewpoint of this invention. The noise signal generating method is realizable with following means: Method of generating a quasi-random signal by using signal processing operation, method of using thermal noise generated from a resistive element, method of referring a preliminarily measured noise data, etc.  FIG. 21-A  shows the original signal conversion feature  210  of the signal processing-system concerning the 14 th  viewpoint of this invention, and realizes program execution by the step shown below.
     Step 1: The input step 212 that receives the signal from the input means  211 .   Step 2: The synchronization-signal extraction step 213 that extracts the synchronization-signal from the received signal from the input step 212.   Step 3: The inverse singularity function generation step 214 that generates the specific inverse singularity function based on the synchronization-signal.   Step 4: The signal conversion step 215 that converts the signal  222  from the input step into the specific signal containing singular points.   Step 5: Output step 216 that sends the signal containing singular points  226  to the output means  217 .   

     In case of the signal processing-system that has the original signal converter concerning the 15 th  viewpoint of this invention, although the above-mentioned step is the same, the singular point is read as a quasi-singular point. 
       FIG. 21-B  shows the original signal regeneration feature  230  of the signal processing-system concerning the 14 th  viewpoint of this invention, and realizes program execution by the step shown below.
     Step 1: The input step 232 that receives the signal from the input means  231 .   Step 2: The synchronization-signal extraction step 233 that extracts the synchronization-signal  243  from the received signal from the input step 232.   Step 3: The conversion processing step 234 that converts the signal having specific singular points based on the synchronization-signal  243 .   Step 4: The undesired-signal extraction step 235 that detects the undesired-signal component from the specific singular point and regenerates the undesired wave by the inverse singularity processing.   Step 5: The original signal regeneration step 236 that eliminates the undesired-signal component from the internal signal  242  from the input step 232 and regenerates the original signal.   Step 6: The output step 237 that sends the regenerated original signal to the output means  238 .   

     In case of the signal processing-system that has the original signal regenerator concerning the 15 th  viewpoint of this invention, although the above-mentioned step is the same, a singular point is read as a quasi-singular point. 
       FIG. 22  shows the original signal conversion feature  250  and the original signal regenerator  260  of the signal processing-system concerning the 16 th  viewpoint of this invention, and realizes program execution by the step shown below.
     Step 1: The input step 212 that receives the signal from the input means  211 .   Step 2: The synchronization-signal extraction step 213 that extracts the synchronization-signal  223  from the received signal from the input step 212.   Step 3 The inverse singularity function generation step 254 that generates the specific inverse singularity function based on the synchronization-signal  223 .   Step 4: The signal conversion step 255 that converts the signal  222  from the input step 212 into the specific signal containing singular points.   Step 5: The conversion-processing step 264 that converts into the specific signal having the singular points based on the synchronization-signal  223 .   Step 6: The undesired-signal extraction step 265 that detects the undesired-signal components from the specific singular point and regenerates the undesired wave by the inverse singularity processing.   Step 7: The original signal regeneration step 266 that eliminates the undesired-signal component from the signal  22  from the input step 212 and regenerates the original signal.   Step 8: The output step 237 that sends the regenerated original signal  247  to the output means  228 .   

       FIG. 23-A  shows the original signal conversion feature  270  of the signal processing-system concerning the 17 th  viewpoint of this invention, and realizes program execution by the step shown below.
     Step 1: The 2 nd  synchronization-signal generation step 271 that generates the 2 nd  synchronization-signal  276  by receiving the synchronization-signal  223  from the synchronization-signal extraction step 213.   Step 2: The code synchronization-signal generation step 272 that generates the code synchronization-signal based on the 2 nd  synchronization-signal  276  by receiving the signal  222  from the input step 212.   Step 3: The code-sequence generation step 273 that generates the specific code based on the 2 nd  synchronization-signal  276  and the code synchronization-signal.   Step 4: The signal conversion step 274 that converts the Input signal  222  into the signal containing the specific singular point.   Step 5: Output step 275 that sends the signal containing singular point  279  to the output means.   

       FIG. 23-B  shows the original signal regeneration feature  280  of the signal processing-system concerning the 17 th  viewpoint of this invention, and realizes program execution by the step shown below.
     Step 1: The Input step 282 that receives the signal from Input means  281 .   Step 2: The synchronization-signal extraction step 283 that extracts the 2 nd  synchronization-signal  293  from the received internal signal  292  from Input step 282.   Step 3: The code synchronization-signal step 288 that generates the code synchronization-signal  298  based on the 2 nd  synchronization-signal  293  and the internal signal  292 .   Step 4: The conversion-processing step 284 that converts the signal  292  received from the input step 282 based on the code synchronization-signal  298  and the 2 nd  synchronization-signal  293 .   Step 5: The undesired-signal extraction step 285 that detects the undesired-signal component from the specific singular point and regenerates the undesired wave by the inverse singularity processing.   Step 6: The code-sequence regeneration step 286 that eliminates the undesired-signal component from the internal signal  292  received from the input step 282 regenerates the code-sequence signal, and regenerates the original signal based on the synchronization-signal  299  received from the synchronization-signal regeneration step.   Step 7: The output step 238 that sends the regenerated original signal to the output means  287 .   

       FIG. 24-A  shows the original signal conversion feature  300  of the signal processing-system concerning the 18 th  viewpoint of this invention, and realizes program execution by the step shown below.
     Step 1: The short synchronization-signal generation step 302 that receives the synchronization-signal  223  from the synchronization-signal extraction step and generates the short synchronization-signal  307 .   Step 2: The short code conversion step 303 that receives the signal  218  from the input step 212 and converts to the short code based on the short synchronization-signal  307 .   Step 3: The short signal conversion step 304 that converts the short code  308  from the short code conversion step into the signals having the specific singular points based on the short synchronization-signal  307 .   Step 4: The out step 305 that sends the signal containing singular point  309  to the output means.   

       FIG. 24-B  shows the original signal regeneration feature  310  of the signal processing-system concerning the 18 th  viewpoint of this invention, and realizes program execution by the step shown below.
     Step 1: The Input step 312 that receives the signal from the input means  311 .   Step 2: The short synchronization-signal extraction step that extracts the short synchronization-signal  323  from the short synchronization-signal  323  received from the input step 312.   Step 3: The synchronization-signal extraction step 318 that extracts the synchronization-signal  328  from the short synchronization-signal  323 .   Step 4: The conversion-processing step 314 that converts the signal  322  from the input step 312 into the signal having the specific singular points based on the 2 nd  synchronization-signal  293 .   Step 5: The undesired-signal extraction step 315 that extracts the undesired-signal component from the specific singular points and regenerates the undesired wave by the inverse singularity processing.   Step 6: The original signal regeneration step 316 that eliminates the undesired-signal component from the signal  322  from the input step 312, and regenerates the original signal based on the synchronization-signal  328 .   Step 7: The output step that sends the regenerated original signal to the output means  228 .   

       FIG. 25-A  shows the original signal conversion feature  330  of the signal processing-system concerning the 19 th  viewpoint of this invention, and realizes program execution by the step shown below.
     Step 1: The Input step 212 that receives the signal from the input means  211 .   Step 2: The synchronization-signal extraction step 213 that extracts the synchronization-signal of the signal from the input step 212.   Step 3: The inverse singularity function generation step 274 that generates the specific inverse singularity function based on the synchronization-signal.   Step 4: The signal conversion step 215 that converts the signal  222  from the input step into the specific signals containing singular points.   Step 5: The output step 216 that sends the signals containing singular points to the 1 st  output means  335 .   Step 6: The 2 nd  output step 331 that sends the signal from the inverse singularity function generation step 274 to the 2 nd  output means  332 .   

       FIG. 25-B  shows the original signal regeneration feature  310  of the signal processing-system concerning the 18 th  viewpoint of this invention, and realizes program execution by the step shown below.
     Step 1: The 1 st  input step 232 that receives the signal from the 1 st  input means  231 .   Step 2: The synchronization-signal extraction step 233 that extracts the synchronization-signal  243  from of the signal from the 1 st  input step 232.   Step 3: The 2 nd  input step 343 that receives the code of the specific inverse singularity function from the 2 nd  input means  342 .   Step 4: The conversion-processing step that converts to the signal having the specific singular point by using the code  348  from the 2 nd  input step 343.   Step 5: The undesired-signal extraction step 235 that detects the undesired-signal component by using the specific singular point and regenerates the undesired wave by the inverse singularity processing.   Step 6: The original signal regeneration step 236 that deletes the undesired-signal component from the internal signal  229  received from the 1 st  input step 232.   Step 7: The output step 237 that sends the regenerated original signal to the output means  238 .   

       FIG. 26  shows the original signal conversion feature concerning the 20 th  viewpoint of this invention, and realizes program execution by the step shown below.
     Step 1: The noise generation step 351 that generates the noise  356  based on the synchronization-signal  223 .   Step 2: The combining step 352 that combines the signal from the input step 212 and the noise  356  from the noise generation step.   

     Moreover, in addition to the signal processing-systems that are claimed from the item 1 to the item 19 by this invention, by using program that is recorded on the information memory medium of this invention the following many applications may be realized: 
     Signal processing means, signal measurement means, information processing means (e.g. general-purpose computer), signal processing component, signal measurement component, and information processing component. 
     INDUSTRIAL APPLICABILITY 
     The signal processing-systems of this invention can realize using signal processing means, information processing means, and information memory medium. As the original signal, it is applicable even to an electric signal, an optical signal, and a sound signal. 
     Moreover, the signal processing-system of this invention can record the program of original-signal conversion method, the signal generated by the inverse singularity-function generator of this invention, and the digital signals containing singular points, on the information memory media, such as a compact disk, a floppy disk, a hard disk, and semiconductor memory. 
     EXPLANATIONS OF NUMERALS 
     
         
           10  Original signal converter 
           11  Input signal containing the original signal 
           12  Input circuit 
           13  1 st  synchronization-signal extraction means 
           14  Signal conversion means 
           15  Output circuit 
           16  1 st  synchronization-signal 
           17  Internal signal 
           18  Signal containing singular point 
           19  Output signals of the signal containing singular points 
           20  Original signal regenerator 
           21  Input signals of the signal containing singular points 
           22  Input circuit 
           23  2 nd  synchronization-signal extraction means 
           24  Conversion-processing means 
           25  Undesired-signal extraction means 
           26  Original signal regeneration means 
           27  Output circuit 
           29  Output signals of the regenerated original signals 
           32  Internal signal of the signals containing singular point 
           33  2 nd  synchronization-signal 
           35  Regenerated undesired-signal 
           36  Regenerated original signal 
           40  Original signal converter 
           44  Signal conversion means 
           45  Output circuit 
           48  Signals containing quasi-singular points 
           49  Output signals of the signal containing quasi-singular points 
           50  Original signal regenerator 
           51  Input signals of the signal containing quasi-singular points 
           52  Input circuit 
           54  Conversion-processing means 
           55  Undesired-signal extraction means 
           56  Original signal regeneration means 
           57  Internal signals of the signal containing quasi-singular points 
           58  2 nd  synchronization-signal 
           60  Original signal converter 
           61  Input signals containing the original signals 
           62  Input circuit 
           63  Synchronization-signal extraction means 
           64  Signal conversion means 
           66  Synchronization-signal 
           69  Signals containing singular points 
           70  Original signal regenerator 
           71  Conversion-processing means 
           72  Undesired-signal extraction means 
           73  Original signal regeneration means 
           74  Output circuit 
           76  Signals having singular point 
           77  Undesired-signal 
           78  Regenerated original signal 
           79  Output signals of the regenerated original signal 
           80  Original signal converter 
           81  Singularity-function generation means 
           82  Error detection means 
           83  Correction means 
           84  Error signal 
           89  Signals containing singular point 
           90  Original signal converter 
           91  Polarity reversing function 
           92  Signal conversion means 
           93  Code-sequence generation means 
           94  Code synchronization-signal generation means 
           95  3 rd  synchronization-signal generation means 
           96  3 rd  synchronization-signal 
           99  Signals containing singular points and having orthogonal singular points 
           100  Original signal regenerator 
           101  Input signals of the signal containing singular points and having orthogonal singular points 
           102  Input circuit 
           103  2 nd  synchronization signal generation means 
           104  Short synchronization-signal generation means 
           105  4 th  synchronization-signal extraction means 
           106  Conversion-processing means 
           107  Undesired-signal extraction means 
           108  Code-sequence signal regeneration means 
           112  Internal signal 
           113  2 nd  synchronization-signal 
           114  Code synchronization-signal 
           115  4 th  synchronization-signal 
           121  Code processing function within the code 
           122  Short code conversion means 
           123  Short signal conversion means 
           124  Short synchronization-signal generation means 
           125  Short synchronization-signal 
           129  Short signal containing singular point 
           131  Input signals of the short signals containing singular points 
           132  Input circuit 
           133  Short synchronization-signal extraction means 
           134  2 nd  synchronization-signal generation means 
           135  Short conversion-processing means 
           136  Undesired-signal extraction means 
           137  Short signal regeneration means 
           138  Original signal regeneration means 
           139  Output signals of the regenerated original signals 
           142  Short internal signals 
           143  Short synchronization-signals 
           144  2 nd  synchronization signal 
           145  Signals having singular points 
           150  Multiple original signal regeneration means 
           151  Signals containing singular points 
           152 - 1  1 st  original signal regenerator 
           152 - 2  2 nd  original signal regenerator 
           152 -N N th  original signal regenerator 
           153 - 1  1 st  undesired wave signals 
           153 - 2  2 nd  undesired wave signals 
           156 - 1  Output signals of the 1 st  original signals 
           156 - 2  Output signals of the 2 nd  original signals 
           156 -N Output signals of the N th  original signals 
           161  Undesired wave signals 
           162  2 nd  output 
           163  Output signals of the undesired wave signals 
           170  Multiple original signal regenerator 
           171  Input signals of the signal containing singular points 
           172  Branching circuit 
           173 - 1  1 st  original signal regenerator 
           173 - 2  2 nd  original signal regenerator 
           173 -N N th  original signal regenerator 
           174 - 1  Output signals of the 1 st  undesired wave signals 
           174 - 2  Output signals of the 2 nd  undesired wave signals 
           174 -N Output signals of the N th  undesired wave signals 
           180  Multiple original signal regenerator 
           181  Input signals of the signal containing singular points 
           182 - 1  1 st  original signal regenerator 
           182 - 2  2 nd  original signal regenerator 
           182 -N N th  original signal regenerator 
           183 - 1  Output signals of the 1 st  undesired wave signals 
           183 - 2  Output signals of the 2 nd  undesired wave signals 
           183 -N Output signals of the N th  undesired wave signals 
           190  Original signal converter 
           191  Function coding means 
           192  Encoder output 
           194  Output signals of the encoded signals 
           195  Original signal regenerator 
           196  Input signals of the encoder 
           197  Encoder input 
           198  Singularity-function generation means 
           201  Noise generation means 
           202  Combining means 
           203  Output of the combined signal 
           210  Original signal converter 
           211  Input means 
           212  Input step 
           213  Synchronization-signal extraction step 
           214  Inverse singularity function generation step 
           215  Signal conversion step 
           216  Output step 
           217  Output means 
           222  Output signals of the input step 
           223  Synchronization-signal 
           226  Output signals of the output step 
           230  Original signal regenerator 
           231  Input means 
           232  Input step 
           233  Synchronization-signal extraction step 
           234  Conversion-processing step 
           235  Undesired-signal extraction step 
           236  Original signal regeneration step 
           237  Output step 
           238  Output means 
           242  Output signals of the input step 
           243  Synchronization-signal 
           247  Output signals of the output step 
           250  Original signal converter 
           254  Inverse singularity function generation step 
           255  Signal conversion step 
           260  Original signal regenerator 
           264  Conversion-processing step 
           265  Undesired-signal extraction step 
           266  Original signal regeneration step 
           270  Original signal converter 
           271  2 nd  synchronization signal extraction step 
           272  Code synchronization-signal generation step 
           273  Code-sequence generation step 
           274  Signal conversion step 
           275  Output step 
           276  2 nd  synchronization-signal 
           277  Code synchronization-signal 
           280  Original signal regenerator 
           281  Input means 
           282  Input step 
           283  2 nd  synchronization-signal extraction step 
           284  Conversion-processing step 
           285  Undesired-signal extraction step 
           286  Original signal regeneration step 
           287  Output step 
           288  Code synchronization-signal generation step 
           289  Synchronization-signal generation step 
           292  Output signals of the input step 
           293  2 nd  synchronization signal 
           298  Code synchronization-signal 
           299  Synchronization-signal 
           300  Original signal converter 
           302  Short synchronization-signal generation step 
           303  Short code conversion step 
           304  Short signal conversion step 
           305  Output step 
           307  Short synchronization-signal 
           308  Short code signals 
           309  Short signals 
           310  Original signal regenerator 
           311  Input means 
           312  Input step 
           313  Short synchronization-signal generation step 
           314  Conversion-processing step 
           315  Undesired-signal extraction step 
           316  Original signal regeneration step 
           317  Output step 
           318  Synchronization-signal generation step 
           322  Output signals of the input step 
           323  Short synchronization-signal 
           328  Synchronization-signal 
           330  Original signal converter 
           331  Output step 
           332  2 nd  output means 
           333  Code of the singularity-function 
           335  1 st  output means 
           340  Original signal regenerator 
           341  Input of the singularity-function code 
           342  2 nd  input means 
           343  2 nd  input step 
           348  Output signals of the 2 nd  input step 
           351  Noise generation step 
           352  Combining step 
           355  Output signals of the combining step 
           356  Output signals of the noise generation step