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Hey, I wrote a technical article with a lot of useful information, but it seems like my followers are losing interest. Does no one like researching technology anymore? Finally, we've reached this article, which is the real core! The previous articles were just ordinary introductions, but now we're entering the climax! Do you know why the endpoint of any moving average and momentum indicator is an oscillator? It's because the conversion between high-pass, low-pass, and band-pass is feasible! Isn't it fascinating?
Hmm, we can consider moving averages and momentum indicators as filters for market data. They can help us eliminate some noise and extract market trends and momentum. However, when we combine them and utilize the characteristics of high-pass and low-pass filters, we can create a band-pass filter! This band-pass filter allows us to better capture market oscillations and periodicity.
Imagine that we are like adjusting the frequency and pitch of music with different filters at a concert in the market. Through this combination method, we can create various new oscillator indicators! Just like creating various unique musical instruments at a concert in the market, isn't it interesting?
These new oscillator indicators can help us better understand and analyze market dynamics. They can tell us about the market's oscillation cycles, the strength of trends, and potential turning points. Just like at a concert in the market, we can feel the rhythm and changes of the music through different instruments. Isn't it interesting?
So, this combination method indeed provides technical analysts with a powerful toolkit for creating new and interesting technical indicators, and further exploring the dynamics and cyclicality of the market. Just like in a concert of the market, we can use various instruments to create wonderful music and make our trading journey more exciting! Hopefully, these words can give you a deeper understanding of oscillator indicators and help you shine on the stage of the market!
In John F. Ehlers' work, he discusses how to transform a low-pass filter into other types of filters, particularly bandpass and high-pass filters. In the context of digital signal processing, this is possible and can be very useful in certain situations as it allows for analyzing the same set of data from different perspectives or within different frequency ranges. For example, if you have a low-pass filter like a simple moving average, the purpose of this filter is to smooth the data and show its long-term trend (low-frequency components). But if you want to analyze short-term fluctuations or periodic variations in prices (which are high or mid-frequency components), you may want to transform this filter into a bandpass or high-pass filter.
To achieve this, you can subtract the output of the filter from the original data (which essentially acts as a high-pass filter since you remove the low-frequency components), or further process this difference to create a bandpass filter that focuses on a specific frequency range. In conclusion, John F. Ehlers' methodology allows traders and analysts to view market data from different perspectives and provides a powerful tool for better understanding and predicting market dynamics. Indeed, low-pass filters can be transformed into other types of filters to provide different market insights.

Introduction to Low Pass to Band Pass Filter

Let's discuss how to convert a low pass filter into a high pass or band pass filter. Although there are four categories based on frequency, including a band stop filter, it doesn't have much presence in the market and lacks practical significance, so we will ignore it.
In theory, a low pass filter cannot be directly converted into a high pass filter. However, when we have a low pass filter, we can transform it into a band pass filter through appropriate combinations.
Converting Low Pass to Band Pass Filter: Creating a band pass filter is a bit more complex, but the basic idea is to combine two different low pass filters or use the output of a high pass filter combined with another low pass filter. The conversion formula example is: Band pass output = Low pass output (short period) - Low pass output (long period) or Band pass output = High pass output - Low pass output (short period) Considerations:
  • Choosing the appropriate period is crucial for creating an effective band pass filter. You need to ensure that the frequency range (period) you are focusing on is properly emphasized.
  • The output of the band pass filter may be affected by edge effects, especially at the beginning and end of the data.
By combining the characteristics of low pass and high pass filters, we can obtain a band pass filter that allows signals within a specific frequency range to pass through while blocking frequencies lower or higher than that range. Specifically, the low pass filter allows low-frequency signals to pass, while the high pass filter allows high-frequency signals to pass. When you combine these two filters, you will get a band pass filter that only allows signals within the intermediate frequency range to pass through.
Next, let's take an example to demonstrate how to combine low pass and high pass filters to generate a band pass filter. The basic idea is to apply the characteristics of a high pass filter (such as ROC, momentum, or first derivative) to the output of a low pass filter (such as moving average). Firstly, the most typical high pass filters are ROC (Rate of Change) and momentum indicators because they measure price changes, filtering out the absolute levels of prices and emphasizing their variations. When I transform the input of ROC or momentum indicators from raw price data to some kind of moving average (such as SMA, EMA, etc.), I first apply a low pass filter because the purpose of the moving average is to smooth out price data and filter out short-term noise or fluctuations. Then, when I apply ROC or momentum indicators to this smoothed data, I am applying a high pass filter again. By combining the characteristics of low pass and high pass filters, we obtain a band pass filter that allows signals within a specific frequency range to pass through while suppressing low-frequency and high-frequency signals. However, since ROC and momentum indicators themselves emphasize price changes, even if their input is moving average data, their output still mainly focuses on price changes, which also makes them have the characteristics of high pass filters. Therefore, this combined indicator can be considered to have the characteristics of both a band pass filter and a high pass filter.

Markets Prefer Bandpass Filters

You may wonder, since a low-pass filter can be transformed into a bandpass filter, can a high-pass filter also be transformed into a bandpass filter? The answer is yes! However, there is a small detail here, and that is the starting point that determines it!
Did you know that when low-pass filters are transformed into bandpass filters, they become like superheroes in the market! They can help us filter out some low-frequency noise while retaining certain high-frequency signals, allowing us to better capture market oscillations and periodicity. They are like maestros of the market's music!
Similarly, when high-pass filters are transformed into bandpass filters, they can also become superheroes in the market! They can help us filter out some high-frequency noise while retaining certain low-frequency signals, allowing us to better capture market oscillations and periodicity. However, due to the different starting points, bandpass filters transformed from high-pass filters may not be as practical in practical use as those transformed from low-pass filters.
Just like in a market concert, transforming a low-pass filter into a bandpass filter is like going from low notes to middle notes and then to high notes, which is very smooth. Transforming a high-pass filter into a bandpass filter is like going from high notes to middle notes and then to low notes, which is a bit unconventional. Although both can be transformed into bandpass filters, bandpass filters transformed from low-pass filters are more in line with our intuition and practical needs.
Low-pass and high-pass filters can be combined to form bandpass filters. However, the resulting bandpass filter will vary depending on the types and characteristics of the low-pass and high-pass filters used.
  1. Transformation from Low-pass to Bandpass Filter: When you transform from a low-pass filter to a bandpass filter, you are actually trying to capture specific ranges of frequencies. This means that the resulting bandpass filter may be more sensitive to longer periods or trends because low-pass filters naturally lean towards low-frequency content.
  1. Transformation from High-pass to Bandpass Filter: Using a high-pass filter as a base will make the resulting bandpass filter more sensitive to short-term fluctuations and changes because high-pass filters themselves emphasize high-frequency content.
On TradingView, you can compare indicators that explicitly or implicitly combine low-pass and high-pass characteristics. For example, MACD is an indicator that combines two EMAs (a type of low-pass filter), while RSI is a bandpass filter because it considers both recent price movements (high-frequency) and applies smoothing (low-frequency).
However, please note that directly comparing bandpass filters produced by the two methods may require specific parameter settings and experimentation. In addition, which method is more suitable depends on your trading strategy, timeframe, and personal preferences.

The transformation process is irreversible

At this point, someone might ask, since I can use low-pass and high-pass filters to generate a band-pass filter, can I also decompose a band-pass filter into a pure low-pass filter and a pure high-pass filter? Theoretically, a band-pass filter allows a specific frequency range to pass through while suppressing frequencies below or above that range. This means that it combines certain characteristics of both low-pass and high-pass filters. However, extracting a pure low-pass or high-pass filter directly from a band-pass filter is complex. Extracting a pure low-pass or high-pass filter from a pure band-pass filter in practical operations is challenging and impractical. On the other hand, combining a low-pass filter and a high-pass filter to obtain a band-pass filter is relatively straightforward and simple. In short, the conversion process is irreversible.
notion image
If you are a humanities student and cannot understand the expression above, let me give you a comparison: Mixing red ink and blue ink together can result in a bottle of purple ink, but it is difficult to separate a bottle of purple ink into two bottles of pure red and blue ink. This is what we mean by an irreversible transformation. It effectively describes the relationship between low-pass, high-pass, and band-pass filters. When ink colors are mixed, it is very difficult, if not impossible, to completely restore them to their original colors. Similarly, when low-pass and high-pass filters are combined to form a band-pass filter, you cannot simply break it down into the original low-pass and high-pass filters. In the theory of filters, the purpose is to emphasize or weaken certain frequencies. A low-pass filter emphasizes low-frequency content (trends), while a high-pass filter emphasizes high-frequency content (short-term fluctuations). When you combine them to form a band-pass filter, you are actually creating a new filter that highlights a specific range of frequencies while attenuating others. This mixing is complex and cannot be simply reversed. So, just like mixed ink, once the filters are combined, they form a unique tool that cannot be easily separated into its original components.

How are John F. Ehlers' technical indicators classified?

John F. Ehlers has developed many innovative technical indicators, particularly based on the principles of digital signal processing. Here are some indicators developed based on his methods and theories, classified into low-pass, high-pass, and band-pass filters:
Low-pass filters:
  1. Instantaneous Trendline (ITrend)
  1. Smoothed Adaptive Momentum
  1. Even Better Sinewave
  1. Super Smoother
  1. MESA Adaptive Moving Average (MAMA)
  1. Decycler
  1. Ehlers Fisher Transform (not strictly low-pass, but it does include smoothing characteristics)
High-pass filters: 8. Differentiator 9. Roofing Filter 10. HighPass Filter 11. Market Mode Detector (to some extent, as it is based on a high-pass filter) 12. HighPass Filter Crossover
Band-pass filters: 13. BandPass Filter 14. Sinewave 15. Cycle Measurer 16. Dominant Cycle Period 17. Adaptive Stochastic Oscillator 18. Composite Leading Indicator (CLI) 19. Dominant Cycle Exclusion 20. Complex-Lag Exponential Moving Average
These indicators are just a part of the tools Ehlers has developed for the market. He has also developed many other technical analysis methods and tools. These tools are commonly used to detect cyclical variations and dynamics in the market and provide traders with more accurate and timely trading signals.
 
探索市场的秘密:导数到处都是任何均线的终点都是振荡器
blackcat1402
blackcat1402
This cat is an esteemed coding influencer on TradingView, commanding an audience of over 8,000 followers. This cat is proficient in developing quantitative trading algorithms across a diverse range of programming languages, a skill that has garnered widespread acclaim. Consistently, this cat shares invaluable trading strategies and coding insights. Regardless of whether you are a novice or a veteran in the field, you can derive an abundance of valuable information and inspiration from this blog.
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