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Congratulations to them both.
- #526
- Edited 7:35pm Oct 14, 2009 7:27pm | Edited 7:35pm
Hi All !
for those still interested in ultra low lag filters that CB talked about here (on page 10) : http://www.forexfactory.com/showpost...&postcount=147, I made an exact replication of the 4 filters in MQL4 and Matlab language : .
Also, playing with lowpass FIR design I made one who has the same length (39 bars) and has the following caracteristics over CB's implementation "Type 0" (I call "Type 0" the filter with the lowest cutoff frequency you can see on post 147) : much less lag, better phase linearity and lower overshot but with poorer high frequency attenuation.
You can get my coefficients from the MQL4 indicator I made.
Everything is in this zip file :
Philippe
for those still interested in ultra low lag filters that CB talked about here (on page 10) : http://www.forexfactory.com/showpost...&postcount=147, I made an exact replication of the 4 filters in MQL4 and Matlab language : .
Also, playing with lowpass FIR design I made one who has the same length (39 bars) and has the following caracteristics over CB's implementation "Type 0" (I call "Type 0" the filter with the lowest cutoff frequency you can see on post 147) : much less lag, better phase linearity and lower overshot but with poorer high frequency attenuation.
You can get my coefficients from the MQL4 indicator I made.
Everything is in this zip file :
Philippe
- #528
- Oct 15, 2009 5:58am Oct 15, 2009 5:58am
- Joined Apr 2006 | Status: Metatrader Programmer | 1,422 Posts
- #531
- Oct 15, 2009 6:32am Oct 15, 2009 6:32am
- Joined Mar 2008 | Status: Still testing and trading | 1,454 Posts
- #533
- Oct 15, 2009 7:19am Oct 15, 2009 7:19am
- Joined Mar 2008 | Status: Still testing and trading | 1,454 Posts
thanks for your contribution Philippe and thanks for sharing. very much appreciated.
i wondered if perhaps you could also share the derivation of the formulas. arguably the coefficients are all that count, but i was hoping to apply the filter in another subject.
please PM if you prefer. unfortunately i have just started looking at dsp and understand that i have a long way ahead of me - any shortcut would help
all the best
i wondered if perhaps you could also share the derivation of the formulas. arguably the coefficients are all that count, but i was hoping to apply the filter in another subject.
please PM if you prefer. unfortunately i have just started looking at dsp and understand that i have a long way ahead of me - any shortcut would help
all the best
thanks for your contribution Philippe and thanks for sharing. very much appreciated.
i wondered if perhaps you could also share the derivation of the formulas. arguably the coefficients are all that count, but i was hoping to apply the filter in another subject.
please PM if you prefer. unfortunately i have just started looking at dsp and understand that i have a long way ahead of me - any shortcut would help
all the best
Get an answer without searching for oneself is useless, so, I can help you understand :
a. First we have a simple lowpass filter. There are 2 manners of generating such coefficients :
1. The Sinc function.
2. The inverse Fourier transform of a gate function.
Note : The results of booth solutions are not really identicals.
b. The tricks is : The frequency of the lowpass impulse must vary over the time.
c. To have a more linear phase you have to window the coefficients. There is a lot of possible windowing methods (Blackman, Kaiser, Gaussian, Hamming, Bartlett... are well-known), but mine is custom.
I recommend Matlab to do such investigations.
Here's some wiki links if you are new to DSP :
http://en.wikipedia.org/wiki/Sinc_function
http://en.wikipedia.org/wiki/Fourier_transform
http://en.wikipedia.org/wiki/Window_function
Philippe
- #537
- Edited Oct 16, 2009 3:08am Oct 15, 2009 7:40pm | Edited Oct 16, 2009 3:08am
I don't agree when CB said his filter's smoothing factor is equivalent to a 39 bar SMA. It's not because your filter's length is 39 the cutoff period is 39.
So we have to compare the CB's ullma type 0 and my filter with a 6 bars and a 39 bars simple moving average :
We may notice the smoothing equivalent looks more to 6 bars SMA than 39.
For a symetric filter, the "center of gravity", which acts for the "present", is the sample at the center of the window, it's the sample with "most energy". All symetric filters are linear phase filters.
Because we don't know future data we have to SHIFT the filter's response in the PAST... And it's where the filter's lag comes from !
A 6 bars SMA is simply a 5th order symetric FIR Filter so his phase delay (the filter's lag) is constant over all the frequencies and equals to 2.5 bars.
ULLMA are not symetrics and there are not either minimum phase.
You can transform a linear phase filter into a minimum phase one with the polystab.m Matlab function, but if you do so, the phase delay will never goes under zero. However, the magnitude remains the same but phase response turn non linear so the lag isn't constant and remains below to the lag of an equivalent linear phase filter.
So, obviously, the center of gravity of all non linear phase filters depends on the frequency.
So if you put this center sample to be the first of your impulse you have a predictive filter which "compensates" his negative phase delay by a poor high frequency attenuation.
It's why they are not so smooth.
There are 2 majors type of transfert function : FIR (finite impulse response) and IIR (infinite impulse response).
A direct form FIR filter has the form :
y[n] = x[n]*b0 + x[n-1]*b1 + x[n-2]*b2 + x[n-3]*b3 ...
A direct form I - IIR filter's transfert function has the form :
y[n] = x[n]*b0 + x[n-1]*b1 + x[n-2]*b2 ... - y[n-1]*a1 - y[n-2]*a2 ...
Where "n" is the present value (the lastest), "x" the input timeserie, "y" the output timeserie, "b" the numerator coefficients and "a" the denominator.
Because IIRs are recursives they are not practical to design and like CB said their phase response can't be optimal, so we must concentrate our efforts on FIRs.
We call the coefficients the "impulse response", ie, the response of a "Linear Time Invariant System" to a Dirac delta.
The filtering process is called convolution.
All linear filters do convolution and nothing else.
All linear filters are causals.
Once we have an impulse response we can get all the caracteristics of the filter and we have to design filters according to the caracteristics we necessitate.
http://en.wikipedia.org/wiki/Finite_impulse_response
http://en.wikipedia.org/wiki/IIR
http://en.wikipedia.org/wiki/LTI_system_theory
http://en.wikipedia.org/wiki/Dirac_delta_function
http://en.wikipedia.org/wiki/Minimum_phase
So we have to compare the CB's ullma type 0 and my filter with a 6 bars and a 39 bars simple moving average :
We may notice the smoothing equivalent looks more to 6 bars SMA than 39.
For a symetric filter, the "center of gravity", which acts for the "present", is the sample at the center of the window, it's the sample with "most energy". All symetric filters are linear phase filters.
Because we don't know future data we have to SHIFT the filter's response in the PAST... And it's where the filter's lag comes from !
A 6 bars SMA is simply a 5th order symetric FIR Filter so his phase delay (the filter's lag) is constant over all the frequencies and equals to 2.5 bars.
ULLMA are not symetrics and there are not either minimum phase.
You can transform a linear phase filter into a minimum phase one with the polystab.m Matlab function, but if you do so, the phase delay will never goes under zero. However, the magnitude remains the same but phase response turn non linear so the lag isn't constant and remains below to the lag of an equivalent linear phase filter.
So, obviously, the center of gravity of all non linear phase filters depends on the frequency.
So if you put this center sample to be the first of your impulse you have a predictive filter which "compensates" his negative phase delay by a poor high frequency attenuation.
It's why they are not so smooth.
There are 2 majors type of transfert function : FIR (finite impulse response) and IIR (infinite impulse response).
A direct form FIR filter has the form :
y[n] = x[n]*b0 + x[n-1]*b1 + x[n-2]*b2 + x[n-3]*b3 ...
A direct form I - IIR filter's transfert function has the form :
y[n] = x[n]*b0 + x[n-1]*b1 + x[n-2]*b2 ... - y[n-1]*a1 - y[n-2]*a2 ...
Where "n" is the present value (the lastest), "x" the input timeserie, "y" the output timeserie, "b" the numerator coefficients and "a" the denominator.
Because IIRs are recursives they are not practical to design and like CB said their phase response can't be optimal, so we must concentrate our efforts on FIRs.
We call the coefficients the "impulse response", ie, the response of a "Linear Time Invariant System" to a Dirac delta.
The filtering process is called convolution.
All linear filters do convolution and nothing else.
All linear filters are causals.
Once we have an impulse response we can get all the caracteristics of the filter and we have to design filters according to the caracteristics we necessitate.
http://en.wikipedia.org/wiki/Finite_impulse_response
http://en.wikipedia.org/wiki/IIR
http://en.wikipedia.org/wiki/LTI_system_theory
http://en.wikipedia.org/wiki/Dirac_delta_function
http://en.wikipedia.org/wiki/Minimum_phase
