Sunday, July 15, 2012 11:35:55 PM
Re: Band Pass filter.
Here is a brief discussion.
Hi techcharter
Let’s start with an ideal case:
In the chart top section, there are 3 cycles, 80TDs (Trading Days), 100TDs, and 125TDs. The lumped sum cycle in the middle section, and the restored 100TDs (at the bottom of the chart). The restored 100TDs came out of a 97.5TDs-102.5TDs band-pass filter. The filter type is Butterworth. external second order, internal 4th order. In basic, the cycles lies outside the band has been rejected. This chart demonstrated that an embedding cycle can be restored correctly by proper filtering process.
The following chart is a band pass magnitude and phase chart.
In the center of the band, the gain is normalized to 1.0. The gain drops quickly off the center band.
The phase on lower frequency (longer cycle) side has a leading phase shift, depends on the filter type and order, it is close to +180 degrees. Conversely, the phase on shorter frequency (shorter cycle) side has a lagging phase shift. it is close to -180 degrees.
The phasing problem causes a big puzzle in the cycle study. A particular cycle may drift so that it is hard to quantize. If our goal is try to sense the rough direction, we can take the advantage of the leading/lagging characteristic. Since +/- 180 degrees involves only a sign flip. i.e, sin(45 degrees)=0.707, sin(225 degrees)=sin(-135 degrees)= -0.707.
The phase shift needs to be corrected, it came from the cycle drifting. The band-pass filter phase chart tells you how much it will be. At this moment I can do the correction manually. It is a very time consuming job,
the filter has a noticeable settling time ( http://en.wikipedia.org/wiki/Settling_time ), and its step response shows rich ‘rings’. Thus why a small changes (in the S&P500 index) can cause an apparent reverse polarity and magnitude 'ramp' in the cycle chart
At this moment, if you see magnitude starting to show resonant frequency, it is an evidence that the hutting cycle is active but there is no easy way to get reliable quantitative data.
My 2 cents
Here is a brief discussion.
Hi techcharter
Let’s start with an ideal case:
In the chart top section, there are 3 cycles, 80TDs (Trading Days), 100TDs, and 125TDs. The lumped sum cycle in the middle section, and the restored 100TDs (at the bottom of the chart). The restored 100TDs came out of a 97.5TDs-102.5TDs band-pass filter. The filter type is Butterworth. external second order, internal 4th order. In basic, the cycles lies outside the band has been rejected. This chart demonstrated that an embedding cycle can be restored correctly by proper filtering process.
The following chart is a band pass magnitude and phase chart.
In the center of the band, the gain is normalized to 1.0. The gain drops quickly off the center band.
The phase on lower frequency (longer cycle) side has a leading phase shift, depends on the filter type and order, it is close to +180 degrees. Conversely, the phase on shorter frequency (shorter cycle) side has a lagging phase shift. it is close to -180 degrees.
The phasing problem causes a big puzzle in the cycle study. A particular cycle may drift so that it is hard to quantize. If our goal is try to sense the rough direction, we can take the advantage of the leading/lagging characteristic. Since +/- 180 degrees involves only a sign flip. i.e, sin(45 degrees)=0.707, sin(225 degrees)=sin(-135 degrees)= -0.707.
The phase shift needs to be corrected, it came from the cycle drifting. The band-pass filter phase chart tells you how much it will be. At this moment I can do the correction manually. It is a very time consuming job,
the filter has a noticeable settling time ( http://en.wikipedia.org/wiki/Settling_time ), and its step response shows rich ‘rings’. Thus why a small changes (in the S&P500 index) can cause an apparent reverse polarity and magnitude 'ramp' in the cycle chart
At this moment, if you see magnitude starting to show resonant frequency, it is an evidence that the hutting cycle is active but there is no easy way to get reliable quantitative data.
My 2 cents
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