Why does physics still exist in blackcat's eyes?

The story of this cat and the subject of physics can be described as ups and downs, making people laugh. During my undergraduate years, this cat actually scored a perfect 100 in two semesters of college physics, shining like the sun in the cat world! Several years later, while continuing my graduate studies at the same school, I encountered the young female teacher who had taught physics back then. Ah, time flies, she is no longer the youthful beauty she once was. After exchanging pleasantries, she sighed and said, "Since you, no one has been able to score a perfect grade in both semesters of college physics." In that moment, a sense of pride welled up in my heart. Yes, I have truly turned physics into a supreme art, feeling invincible!

Similarly, I was enthusiastic about digital signal processing (DSP) during my college years. I scored 98 on the undergraduate exam, making me feel invincible and believing that the world of DSP is my cat's backyard. Unfortunately, a few years later, I discovered that I had to take this subject again for my graduate studies, and I was at a loss. But, being resourceful, I immediately found a solution - borrowing DSP review materials from my junior classmates.

On those photocopies, which had been copied numerous times and had some faded handwriting, I saw a familiar handwriting. To my delight, it turned out to be the review materials I had helped my classmates prepare for the exam back in my undergraduate years! Over the years, this treasure had not been lost, but had been passed down from junior to junior! The feeling at that time was truly indescribable, as if this cat was a legend in the Department of Automation. Haha, it seems that this cat's academic torch has been burning for a long time, unconsciously influencing one batch of students after another. In summary, my academic career is like a dinosaur, completely extinct, but my skills are like a torch, illuminating the path for others. This cat's aura of academic excellence is probably irresistible!

In my trading experience, my deep involvement with physics began with John Ehlers' four English textbooks. When faced with complex market conditions, my scientific background required me to trust conclusions based on solid theoretical foundations rather than those based on experience or hearsay "Holy Grails". Ehlers' theories, although profound, were greatly aided by the accumulation of my physics knowledge during school, allowing me to quickly translate many concepts into code. So, if you want to find the most comprehensive collection of Ehlers' technical indicators on the internet, you can search for "Ehlers" on my TradingView page, and you'll find a bunch. Those are all the technical indicators I have translated from Ehlers' book into TradingView scripts. Even now, this cat admires its own dedication and perseverance.

In trading, delving into physics is not an easy task. Starting with John F. Ehlers' four English textbooks, I immersed myself in the ocean of physics. Facing the complex market environment, as a science student, I tend to trust conclusions based on solid theoretical foundations rather than those based on experience or hearsay "Holy Grails".

Ehlers' theories are indeed profound, but fortunately, during my school years, I accumulated a lot of physics knowledge, which greatly helped me in trading. Not only do I understand the principles behind many things, but I can also quickly convert them into executable code. So, if you're interested in finding the most comprehensive collection of Ehlers' technical indicators on the internet, you can go to my TradingView page and search for "Ehlers," and you'll see a bunch of relevant results. Those are all the technical indicators I have translated from Ehlers' book into TradingView scripts. Ah, even now, this cat has to admire its own dedication and perseverance! Hehe, surprised, aren't you? This cat is not only a physics genius, but also a master at translating theory into practical applications! In China, this cat is considered a representative of the feline world who has taken his theoretical research to the extreme! But no matter what, this cat will always cherish this special ability, continue to explore and utilize the wonders of physics in trading. Who knows?

The previous paragraphs were all introductions. Now let's get back to the main topic and talk about what the market and technical indicators look like after studying Ehlers' theory. First of all, Ehlers is an expert in the field of digital signal processing (DSP), and he introduced this method into technical analysis. Here are his main reasons and viewpoints for using this method:

1. **Market prices as time series data**: JFE believes that the price data of financial markets can be viewed as a discrete time series system. This means that market prices are similar to digital signals (such as audio signals), consisting of a series of data points that change over time.
2. **Market periodicity**: JFE observed that financial markets often exhibit periodicity, and digital signal processing is used to analyze the periodicity and other components in signals. By appropriately applying DSP techniques, we can more accurately determine market cycles and predict future price movements.
3. **Noise filtering**: Digital signal processing techniques help analysts filter out random noise in price data, allowing clearer observation of true market trends and patterns.
4. **Adaptation to cycles**: Unlike traditional fixed-period indicators, indicators developed using DSP techniques can adapt to the current market cycle, providing more accurate and timely trading signals.
5. **Filters and transforms**: He designed a series of filters and transforms, such as MESA, Fisher transform, etc., to help identify and utilize market periodicity.
6. **Nonlinear systems**: He also believes that since the market is a nonlinear system, traditional linear methods may not always be effective. Therefore, his techniques often take into account this nonlinear nature of the market.

Regarding the question of whether this methodology is correct, like all technical analysis methods, there is no one method that is absolutely correct. However, JFE's methods and indicators have been accepted by many traders and analysts and are considered to be very effective tools under certain market conditions. But like all trading tools, they should be used in conjunction with other analysis methods and strategies, always considering risk management.

JFE views market prices as discrete time series systems because price data is usually reported at fixed time intervals (such as daily, hourly, or minute-by-minute), with each time point having a specific value. This is very similar to discrete signals in digital signal processing, where signals are also composed of a series of data points with a fixed interval in time.

If the above was too profound, let's explain Ehlers' market physics with a simple concept: Do you think the essence of moving averages and oscillators in technical indicators is the same?

According to Ehlers' viewpoint, moving averages and oscillators are essentially similar. His view is that all technical indicators, whether moving averages or oscillators, are filters that extract certain information from market data. In some of his work, JFE points out that oscillators can be seen as a variation of moving averages, or more specifically, they are different types of filters. For example, a simple moving average (SMA) is a low-pass filter that allows low-frequency price movements to pass while filtering out high-frequency noise. Oscillators, such as RSI or MACD, can be seen as band-pass filters that extract signals in specific frequency ranges. Therefore, JFE's view is that different technical indicators only apply different mathematical methods to process and interpret market data, but they are essentially filters. This is why he uses advanced signal processing techniques, such as Hilbert transforms, in designing indicators.

Therefore, according to John F. Ehlers (JFE), filters can be classified. He believes that all technical indicators in the market are some form of filters. According to his classification method, filters can be divided into the following types:

1. **Low Pass Filter (LPF)**: This type of filter allows low-frequency components to pass through while filtering out high-frequency components. The Simple Moving Average (SMA) is an example of a low pass filter.
2. **High Pass Filter (HPF)**: In contrast to the low pass filter, it allows high-frequency components to pass through while filtering out low-frequency components.
3. **Band Pass Filter (BPF)**: This filter only allows components within a specific frequency range to pass through. Many oscillators, such as RSI or MACD, can be considered as some form of band pass filter as they typically focus on price movements within a specific range.
4. **Band Stop Filter (BRF)**: This filter blocks components within a specific frequency range while allowing signals of other frequencies to pass through.

Here are some common low pass filter technical indicators:

**Simple Moving Average (SMA)**

**Exponential Moving Average (EMA)**

**Weighted Moving Average (WMA)**

**Triple Exponential Moving Average (TEMA)**

**Double Exponential Moving Average (DEMA)**

**Hull Moving Average (HMA)**

These indicators work by averaging or weighted averaging the price or other indicator's historical data in some form, hence they are all referred to as low pass filters. The goal of a low pass filter is to allow low-frequency (long-term) price trends to pass through while filtering out high-frequency (short-term) noise or volatility.

In technical analysis, high pass filters (HPF) are not as common as low pass filters like moving averages because they primarily focus on quick, short-term changes in price, which are often considered market "noise". However, in some applications, this "noise" or short-term changes can be valuable. Here are some indicators that can be considered high pass filters or at least have high pass filter characteristics:

**Rate of Change (ROC)**: ROC is an indicator that measures the rate of price change and focuses on quick price changes.

**Momentum**: Similar to ROC, the momentum indicator measures the change in price relative to a past period.

**First Derivative**: Although not a common indicator, calculating the first derivative of price or other indicators can be considered a high pass filter. This is an interesting fusion of mathematics and physics, and I plan to write a separate article about it. Learning about trading can definitely enhance your application of mathematical and physical knowledge, haha.

It should be noted that the above indicators may not be true high pass filters, but they focus on quick and temporary changes in price, hence they have high pass filter characteristics to some extent.

Band pass filters (BPF) are not as evident in technical analysis as low pass and high pass filters, but they do exist. Band pass filters only allow signals within a specific frequency range to pass through while filtering out others. This can help analysts focus more on specific market cycles. Many technical indicators, although not entirely band pass filters (not 100% conforming to the physics definition of a band pass filter), have similar characteristics because they focus on specific price change periods or ranges. Here are some technical indicators that may have band pass filter characteristics:

**Stochastic Oscillator**: This indicator measures the current price relative to its past range. Although it is not a pure band pass filter, it does focus on a specific price change range.

**Relative Strength Index (RSI)**: RSI measures the relative strength of price increases and decreases and typically ranges from 0 to 100.

**Moving Average Convergence Divergence (MACD)**: Although based on the difference between two moving averages, MACD focuses on the specific relationship between these two averages, thereby having some band pass characteristics.

**Commodity Channel Index (CCI)**: CCI measures the deviation of commodity or stock prices from their average prices.

The above-listed indicators may not be pure band pass filters, but to some extent, they all emphasize a specific range or period of price data. These band pass filter indicators are often used to identify overbought or oversold market conditions or to identify potential market turning points. Overbought and oversold signals are often signs to identify them.

Band stop filters (also known as notch filters) are not commonly used directly in technical analysis. The purpose of this filter is to suppress or filter out signals within a specific frequency range while allowing signals of other frequencies to pass through. 99% of indicators do not possess the characteristics of pure band stop filters. However, considering the working principle of band stop filters, there are some similar indicators, such as:

**High-Low Difference**: Some strategies and indicators may use the difference between the high and low prices to measure intra-day price changes. This method can filter out intra-day noise to some extent, especially when the market trading range is narrow.

However, the above-mentioned indicators are not truly designed as band stop filters. In practical financial market analysis, pure band stop filters are less common, and there are more applications of low pass, high pass, or band pass filters. If you have specific needs or purposes, you may need customized strategies or indicators to achieve similar effects to band stop filters.

The reason why I consider the high-low difference to some extent as a band stop filter is that it removes specific price movements within the day and retains a broader range of fluctuations. However, this analogy is relative because in traditional signal processing, band stop filters are usually based on frequency rather than time, as high-low difference does. In summary, although the high-low difference is not a band stop filter in the traditional sense, it does provide similar effects to some extent, namely filtering out specific intra-day price dynamics and retaining their range of fluctuations.

Based on our previous discussion and the typical characteristics of technical indicators, the technical indicators seen by me can be classified as follows:

**Low Pass Filters**: These filters allow long-term (low-frequency) trends to pass through while suppressing short-term (high-frequency) noise.

- Moving Averages (e.g., SMA, EMA, WMA, etc.)
- Bollinger Bands

**High Pass Filters**: These filters allow short-term (high-frequency) fluctuations to pass through while reducing long-term (low-frequency) trends.

- Some difference or rate of change indicators, such as Momentum or Rate of Change (these indicators can be considered as emphasizing short-term price changes)

**Band Pass Filters**: These filters emphasize price changes within a specific time range or period while suppressing changes that are too long or too short.

- Stochastic Oscillator (focuses on a specific price change range)
- RSI (considers price dynamics within a specific time window)
- MACD (although its core is based on the difference between two EMAs, it emphasizes price dynamics within a specific time range to some extent)

**Band Stop Filters**: Within commonly used technical indicators, true band stop filters are not common. However, the high-low difference can be approximated as having band stop characteristics as it aims to remove long-term trends to better analyze short-term or periodic fluctuations in price.

It should be noted that these classifications are a broad interpretation based on the concept of filters, combined with the common uses and characteristics of technical indicators. Many technical indicators were not designed with filtering as their primary purpose, so strictly classifying them as a certain type of filter may have some ambiguity. However, regardless, did today's article provide you with a different perspective? If so, give me a thumbs up.