🚀 go-pugleaf

In <2421@radio.oakhill.UUCP> charlie@oakhill.UUCP (Charlie Thompson) writes:
>I am looking for C source code for sine wave curve fitting algorithms.  Such an algorithm can be
>used to compute THD/Noise in a digitized sine wave.

For simplicity a Taylor series would be ok.   However, here  is a fourth
order Chebyshev series  that is much faster for  the accuracy.  It finds
sin(y) for y from  0 to  Pi/2 with a  max  error of 0.000124.   This was
obtained with Maple.

                                                  2                3
c2 := .00011389456 + .9962889583 y + .0195161068 y  - .2031187635 y 

                   4
   + .02856566868 y 

If I plot both sin(y)  and c2 you can't tell  any difference, so here is
the error plotted:

> plot(sin(y)-c2,y=0..Pi/2);

+ 0.000124                                                                     
|     AAA                                                                      
|     A  AA                                     AAAAAAA                       A
|    A     A                                   A       A                      A
|   A      A                                 AA        A                      A
+ 0.0000624 A                               A           AA                    A
|  A         A                             A              A                  A 
|  A         A                            A               A                  A 
| A           A                          A                 A                 A 
| A            A                        A                   A                A 
| A            A                       A                     A              A y
+-0-------------*---+-----------------*+-------------------+--*-------------*-+
0 A             A .393               .785                1.18 A            1.57
| A              A                   A                         A            A  
|A                A                 A                          A            A  
|A                 A               A                            A          A   
+A-0.0000624        A             A                              A         A   
|A                   A           A                                A       A    
*                    A          A                                  A     A     
*                     AA      AA                                    A   A      
*                       A   AA                                       AAA       
*                        AAA                                                   
+ -0.000125                                                                    
>

You can   work out  how many  Taylor  terms  it would  take  to get that
accuracy.  Editorial: Taylor series are for wimps.

If the angle is outside [0,1.57] use the obvious reduction formulae.

If you want the formula in degrees, or a different accuracy, tell me and
I'll work it out.

Historical  note: IBM in Fortran finds  sin(x)  by reducing the angle to
[0,1.57],  then using a half  angle formula to reduce   x further to [0,
22.5 degrees in radians], then uses a 2 term Chebyshev.  This gives full
single (maybe double) precision accuracy.

Note on Chebyshev   series: They give  the  best maximum  error over  an
interval, for  polynonials of  a   given   degree.  However,  the  error
increases very fast outside  the interval, so  don't try to  enlarge the
interval   w/o recalculating  the series.    Also,   if you want reduced
accuracy and increased speed, it  is not sufficient to  just drop a high
order term or 2.  You have to go back to the Chebyshev basis.

-- 
						   Wm. Randolph Franklin
Internet: wrf@ecse.rpi.edu (or @cs.rpi.edu)    Bitnet: Wrfrankl@Rpitsmts
Telephone: (518) 276-6077;  Telex: 6716050 RPI TROU; Fax: (518) 276-6261
Paper: ECSE Dept., 6026 JEC, Rensselaer Polytechnic Inst, Troy NY, 12180