|
PureBytes Links
Trading Reference Links
|
Alex,
the relationship between L and N is mainly for you and your understanding when
you compare your _sma3(L) to a simpleMovingAverage(L). You have to define N
because the other two coefficients are depending on N and you can do this
either by defining N itself or by defining L and R so that R*L = N
I say this because I have found some interesting and surprising relations,
which becomes clear if you focus on N:
First let's move the 'origin' of your _sma3-Filter from L to N.
This is your original with N = R*L:
_sma3(L) = avg( avg( avg(Signal, rnd(N), rnd(N/1.25)), rnd(N/1.5) ),
or
sma3(N/R) = avg( avg( avg(Signal, rnd(N), rnd(N/1.25)), rnd(N/1.5) ),
Let me write (we'll see later, why) your filter:
_sma3(a/R) = avg( avg( avg(Signal, c), a), b);
So c=N and L becomes:
L = rnd(c/R) (now you select c to that L meet your needs).
Now (as I wrote to you):
a = rnd( c/1.25 ) = rnd( 0.80*c ) = rnd( c*4/5 )
and
b = rnd( c/1.50 ) = rnd( 0.6667*c) = rnd (c*2/3)
Now if you set R = 0.75, c=5 (L = 5/0.75 = 6.667) you get for a, b: 4, 3:
_sma3(6.667) = avg( avg( avg(Signal, 5), 4), 3).
These are Phythagoras' numbers from his theorem of the right-angled triangle:
The square of the long side (hypotenuse) is equal to the sum of the squared
short sides (cathetus)
c² = a² + b² (that's how we wrote it in school)
- WOW. (I have no idea, if this is just accedentally so or it has some meaning
in the context of filtering noises, but it inspires)
But the relationship
c, a=c*4/5, b=c*2/3
does not leed exactly to the Phythagoras' numbers, for this the relationship
the calculus should be:
c,
a = c*4/5 = c*0.8,
b = c*3/5 = c*0.6
( 1^2 = 0.8^2 + 0.6^2 => 1 = 0.64 + 0.36 )
so that the filter becomes
_sma3( a/0.75 ) = avg( avg( avg(Signal, c), rnd(0.8*a)), rnd(b*0.6))
Hmm, now I would like to ask you, Bob, as you had posted the *.gifs with the
'saw blade' quotes applied to Alex' filter, to compare both variations, if
there is a difference, may be you can vary a bit with the coefficients 0.8
and 0.6. Might be interesting.
Carl
Am Montag, 14. Juni 2004 01:13 schrieb Alex Matulich:
> > playing around with your formulas I found this (maybe you allready know
> > this):
> >
> > L is the length, from there you calc the N = int(0.5 + L*0.75), now
> > b=int(a/1.25), c=a/1.5, finally the sum of all (see the tab below, as
> > higher L is as more precise no. I get)
> >
> > So you can calc your formula as:
> > N=int(0.5 + 0.75*L)
> > b=int(0.5 + 0.60*L)
> > c=int(0.5 + 0.50*L)
> > and you have (without rounding):
> > _SMA3 = avg( avg( avg(Sig, 0.75*L), 0.60*L), 0.50*L).
>
> You're missing something. There's a reason to keep that original 0.75
> isolated. The factors 1.25 and 1.5 are the moving average tuning factors
> that control the phase cancellation, resulting in a steep roll-off in
> frequency response. Let's define R=0.75. Then the formula is:
>
> _SMA3 = avg( avg( avg(Sig, R*L), R*L/1.25), R*L/1.5).
>
> R determines the rolloff point, and ultimately the lag. For example, if
> you want the _SMA3 of length L to have the same lag as a simple moving
> average of length L, you would use R=0.42 instead of R=0.75. The number
> 0.75 was chosen to have 20 dB of attenuation at wavelength L -- a purely
> arbitrary choice.
>
> R is actually another input parameter, just like L. In my original code,
> I simply embedded it. I actually find R=0.42 to be more useful.
>
> -Alex
|