The implementation of the two -order linear microcompany

1. Classic Micro Division Y = (V (T) -V (T -T))/T. At the interval time T, it has an enlarged effect on noise, and it cannot be applied to the task.

2. Second -order linear micro -division

3. C program verification

#include <stdio.h> 
 #include <stdlib.h> 
 #include "math.h" 
 #include "stdlib.h" 

 #Define TS (double) (0.01) /*Sample steps* / 
 #Define Tn (double) (0.05) /*micro -divided steps* / 

 double erjie (double x1, double x2, double u) 
 {{ 
     Double Ret; 
     Double Deta; 

     DETA = 1.0 / (TN * TN); 
     RET = DETA * (X1 -U) + X2 * 2 / TN; 

     Return -RET; 
 } 

 int Main () 
 {{ 
     int i = 0; 
     double tim, dv, ds; 
     double u_1; 
     double x1, x1_1, x2, x2_1; 
     File*fp,*fnp,*fdp; 

     x1 = 0; 
     x1_1 = 0; 
     x2 = 0; 
     x2_1 = 0; 
     srand (2); 
     if ((fp = fst_yuan.txt "," w+") == null) 
     {{ 
         Printf ("FAIL to Open fst_yuan.txt \ n"); 
         exit (0); 
     } 

     if (FNP = FOPEN ("FST_NOW.txt", "W+") == NULL) 
     {{ 
         Printf ("government to open fst_now.txt \ n"); 
         exit (0); 
     } 
     if (fdp = fopen ("fst_dev.txt", "w+") == null) 
     {{ 
         Printf ("government to open fst_dev.txt \ n"); 
         exit (0); 
     } 

     for (i = 0; I <1000; I ++) 
     {{ 
         TIM = TS * (i+1); 
        
         ds = sin (tIM) + 0.05*(RAND ()/32768.0);/*Simulated noise*/ 
         dv = cos (tim); /*ideal differential differential curve* / 

         x1_1 = x1 + ts*x2; /*micro -tracking* / 
         x2_1 = x2 + TS * Erjie (X1, X2, DS); 

         fprintf (fp, " %. 10lf %.10lf \ n", ds, dv); /*Save to the file. Draw curve through Matlab*/ 
         fprintf (fnp, " %. 10lf %.10lf \ n", x1_1, x2_1); 
         fprintf (fdp, " %. 10lf %.10lf \ n", x1_1, (ds -u_1)/ts); 
         x1 = x1_1; 
         x2 = x2_1; 
         u_1 = ds; 
     } 
     fclose (fp); 
     fclose (FNP); 
     fclose (fdp); 
     Printf ("Hello World! \ N"); 
     Return 0; 
 }

4. Matlab drawing

Load ('C: \\ Users \ Terryc \ Documents \ CodeBlocks \ Micro Division \ fSt_yuan.txt'); 
 LOAD ('C: \\ Users \ Terryc \ Documents \ CodeBlocks \ FST_now.txt'); 
 LOAD ('C: \\ Users \ Terryc \ Documents \ CodeBlocks \ FST_DEV.TXT'); 
 subplot (3,1,1); 
 plot (fst_yuan); 
 grid on; 
 subplot (3,1,2) 
 plot (fst_now); 
 grid on; 
 subplot (3,1,3) 
 plot (fst_dev); 
 grid on;

5. Result

In the middle of red is the output of the second -order microcompany, and the first -order microcompany is output. The interference noise is significantly suppressed.