Ehlers Adaptive Bandpass Filter [CC]The Adaptive Bandpass Filter was created by John Ehlers (Cycle Analytics For Traders pgs 153-156) and this uses his autocorrelation code to provide the adaptive lengths to use for the underlying bandpass filter. The bandpass filter is a common way in digital signal processing to filter out the underlying noise in the data. It can actually be turned into a leading indicator by changing the bw variable to a smaller amount. Since this indicator is adaptive using the cycle period, the buy and sell signals are different compared to the normal bandpass filter. Buy signals for this indicator according to Ehlers are when the line is red and the line is under the oversold line (also red) then you buy when the indicator line turns green and then you exit when the indicator line turns red and is above the overbought line. This indicator doesn't provide clear buy and sell signals in all circumstances but generally speaking buy when the indicator line turns green and sell when it turns red. Feel free to experiment with this one.
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Bandpas
Ehlers Truncated BandPass Filter [CC]Hot off the presses! The Truncated BandPass Filter was created by John Ehlers (Stocks & Commodities July 2020) and this is a much more reactive version of his original bandpass filter. When the indicator rises above 0 then it is an uptrend and when it falls below 0 then it is in a downtrend. Buy when the indicator line is red and sell when it is green.
Let me know if there are other scripts you would like to see me publish or if you want something custom done!
Narrow Bandpass FilterIn technical analysis most bandpass filters like the MACD, TRIX, AO, or COG will have a non-symmetrical frequency response, in fact, this one is generally right-skewed. As such these oscillators will not fully remove lower and higher frequency components from the input signal, the following indicator is a bandpass filter with a more symmetrical frequency response with the possibility to have a narrow bandwidth, this allows the indicator to potentially isolate sinusoids from the input signal.
Indicator & Settings
The filter is calculated via convolution, if we take into account that the frequency response of a filter is the Fourier transform of its weighting function we can deduce that we can get a narrow response by using a sinusoid sin(2𝛑nf) as the weighting function, with the peak of the frequency response being equal to f , this makes the filter quite easy to control by the user, as this one can choose the frequency to be isolated. The length of the weighting function controls the bandwidth of the frequency response, with a higher length returning an ever-smaller frequency response width.
In the indicator settings the "Cycle Period" determine the period of the sinusoid used as a weighting function, while "Bandwidth" determine the filter passband width, with higher values returning a narrower passband, this setting also determine the length of the convolution, because the sum of the weights must add to 0 we know that the length of the convolution must be a multiple of "Cycle Period", so the length of the convolution is equal to "Cycle Period × Bandwidth".
Finally, the windowing option determines if a window is applied to the weighting function, a weighting function allow to remove ripples in the filter frequency response
Above both indicators have a Cycle period of 100 and a Bandwidth of 4, we can see that the indicator with no windowing don't fully remove the trend component in the price, this is due to the presence of ripples allowing lower frequency components to pass, this is not the case for the windowed version.
In theory, an ultra-narrow passband would allow to fully isolate pure sinusoids, below the cycle period of interest is 20
using a bandwidth equal to 10 allow to retain that sinusoid, however, note that this sinusoid is subject to phase shift and that it might not be a dominant frequency in the price.
