Gaussian Noise
Posted: Sat Jan 10, 2015 6:50 pm
The standard random generators in computer-languages have a uniform distribution.
That means that each number has the same chance to occur.
In natural processes the distribution curve however has often a bell shape.
That means that the frequency of occurrence of extreme numbers is far lower than the mid-values.
A special bell-shape is the Gaussian distribution curve.
It is also called the normal distribution because it is often a characteristic of the variation in normal natural processes.
In order to simulate natural processes, I developed a Gaussian number generator according to the "Marsaglia polar method".
See http://en.wikipedia.org/wiki/Marsaglia_polar_method
By using the complex random number generator of SB, it was rather easy to do.
The following code is a program in which the distribution curve of that function 'GRAND()' is tested.
That means that each number has the same chance to occur.
In natural processes the distribution curve however has often a bell shape.
That means that the frequency of occurrence of extreme numbers is far lower than the mid-values.
A special bell-shape is the Gaussian distribution curve.
It is also called the normal distribution because it is often a characteristic of the variation in normal natural processes.
In order to simulate natural processes, I developed a Gaussian number generator according to the "Marsaglia polar method".
See http://en.wikipedia.org/wiki/Marsaglia_polar_method
By using the complex random number generator of SB, it was rather easy to do.
The following code is a program in which the distribution curve of that function 'GRAND()' is tested.
Code: Select all
'Gaussian Noise: function GRANDC() with testprogram
'by Dutchman, january 2015
twidth=3 'total width: sigma's
count=1E5 'total of random numbers
mid=12 'mid size of distribution
FontSize=FONT_SIZE()
sh=SCREEN_HEIGHT()
lines=sh/(1.2*fontsize)-5 ' number of lines to print
size=2*mid+1 'array-size
OPTION BASE 0
DIM number(size)
'---- fill array with distribution
PRINT "Calculating:"
sw=SCREEN_WIDTH()
SLIDER "run" VALUE 0 AT 0,30 SIZE sw
FOR i=1 TO count/2 'two numbers per cycle
n=GRANDC()
u=REAL(n) ! i1=mid+INT(mid/twidth*u)
v=IMAG(n) ! i2=mid+INT(mid/twidth*v)
IF i1<size AND i1>0 THEN number(i1)+=1
IF i2<size AND i2>0 THEN number(i2)+=1
IF i%100=0 THEN SLIDER "run" SET VALUE 2*i/count
NEXT i
SLIDER "run" DELETE ! TEXT CLEAR
'---- show distribution
PRINT "Distributioin within total width of";twidth;"sigma"
PRINT "Width (%)","Total (%)"
n=number(mid) ! i=0
repeat:
PRINT "####.#":100*(2*i+1)/size,"####.#":100*n/count
i+=1
IF i<=MIN(mid,lines) THEN
n=n+number(mid+i)+number(mid-i)
GOTO repeat
ENDIF
'---------- peak calculation
peak:
p=200
DO
p-=1
n=10^-p+1i*10^-p
UNTIL ABS(n)^2>1E-300
p-=1
GRANDC.preset=1
GRANDC.n=10^-p+1i*10^-p
GRANDC.s=ABS(GRANDC.n)^2
PRINT
PRINT "Peak=";GRANDC();" at seed: n=";GRANDC.n
END
DEF GRANDC()
'Generates random complex number
'with Gaussian distribution
'according to the Marsaglia polar method
'r'Remove tinted lines: is only for peak testing
IF preset THEN Transform
''Start with random complex number within limits
DO ! n=RNDC(1) ! s=ABS(n)^2
UNTIL s<1 AND s>1E-320
Transform:
m=SQR(-2*LN(s)/s)
u=SIGN(RND(1)-0.5)*REAL(n)*m
v=SIGN(RND(1)-0.5)*IMAG(n)*m
RETURN u+1i*v
END DEF
