[GYTS] FiltersToolkit LibraryFiltersToolkit Library
🌸 Part of GoemonYae Trading System (GYTS) 🌸
🌸 --------- 1. INTRODUCTION --------- 🌸
💮 What Does This Library Contain?
This library is a curated collection of high-performance digital signal processing (DSP) filters and auxiliary functions designed specifically for financial time series analysis. It includes a shortlist of our favourite and best performing filters — each rigorously tested and selected for their responsiveness, minimal lag and robustness in diverse market conditions. These tools form an integral part of the GoemonYae Trading System (GYTS), chosen for their unique characteristics in handling market data.
The library contains two main categories:
1. Smoothing filters (low-pass filters and moving averages) for e.g. denoising, trend following
2. Detrending tools (high-pass and band-pass filters, known as "oscillators") for e.g. mean reversion
This collection is finely tuned for practical trading applications and is therefore not meant to be exhaustive. However, will continue to expand as we discover and validate new filtering techniques. I welcome collaboration and suggestions for novel approaches.
🌸 ——— 2. ADDED VALUE ——— 🌸
💮 Unified syntax and comprehensive documentation
The FiltersToolkit Library brings together a wide array of valuable filters under a unified, intuitive syntax. Each function is thoroughly documented, with clear explanations and academic sources that underline the mathematical rigour behind the methods. This level of documentation not only facilitates integration into trading strategies but also helps underlying the underlying concepts and rationale.
💮 Optimised performance and readability
The code prioritizes computational efficiency while maintaining readability. Key optimizations include:
- Minimizing redundant calculations in recursive filters
- Smart coefficient caching
- Efficient state management
- Vectorized operations where applicable
💮 Enhanced functionality and flexibility
Some filters in this library introduce extended functionality beyond the original publications. For instance, the MESA Adaptive Moving Average (MAMA) and Ehlers’ Combined Bandpass Filter incorporate multiple variations found in the literature, thereby providing traders with flexible tools that can be fine-tuned to different market conditions.
🌸 ——— 3. THE FILTERS ——— 🌸
💮 Hilbert Transform Function
This function implements the Hilbert Transform as utilised by John Ehlers. It converts a real-valued time series into its analytic signal, enabling the extraction of instantaneous phase and frequency information—an essential step in adaptive filtering.
Source: John Ehlers - "Rocket Science for Traders" (2001), "TASC 2001 V. 19:9", "Cybernetic Analysis for Stocks and Futures" (2004)
💮 Homodyne Discriminator
By leveraging the Hilbert Transform, this function computes the dominant cycle period through a Homodyne Discriminator. It extracts the in-phase and quadrature components of the signal, facilitating a robust estimation of the underlying cycle characteristics.
Source: John Ehlers - "Rocket Science for Traders" (2001), "TASC 2001 V. 19:9", "Cybernetic Analysis for Stocks and Futures" (2004)
💮 MESA Adaptive Moving Average (MAMA)
An advanced dual-stage adaptive moving average, this function outputs both the MAMA and its companion FAMA. It combines adaptive alpha computation with elements from Kaufman’s Adaptive Moving Average (KAMA) to provide a responsive and reliable trend indicator.
Source: John Ehlers - "Rocket Science for Traders" (2001), "TASC 2001 V. 19:9", "Cybernetic Analysis for Stocks and Futures" (2004)
💮 BiQuad Filters
A family of second-order recursive filters offering exceptional control over frequency response:
- High-pass filter for detrending
- Low-pass filter for smooth trend following
- Band-pass filter for cycle isolation
The quality factor (Q) parameter allows fine-tuning of the resonance characteristics, making these filters highly adaptable to different market conditions.
Source: Robert Bristow-Johnson's Audio EQ Cookbook, implemented by @The_Peaceful_Lizard
💮 Relative Vigor Index (RVI)
This filter evaluates the strength of a trend by comparing the closing price to the trading range. Operating similarly to a band-pass filter, the RVI provides insights into market momentum and potential reversals.
Source: John Ehlers – “Cybernetic Analysis for Stocks and Futures” (2004)
💮 Cyber Cycle
The Cyber Cycle filter emphasises market cycles by smoothing out noise and highlighting the dominant cyclical behaviour. It is particularly useful for detecting trend reversals and cyclical patterns in the price data.
Source: John Ehlers – “Cybernetic Analysis for Stocks and Futures” (2004)
💮 Butterworth High Pass Filter
Inspired by the classical Butterworth design, this filter achieves a maximally flat magnitude response in the passband while effectively removing low-frequency trends. Its design minimises phase distortion, which is vital for accurate signal interpretation.
Source: John Ehlers – “Cybernetic Analysis for Stocks and Futures” (2004)
💮 2-Pole SuperSmoother
Employing a two-pole design, the SuperSmoother filter reduces high-frequency noise with minimal lag. It is engineered to preserve trend integrity while offering a smooth output even in noisy market conditions.
Source: John Ehlers – “Cybernetic Analysis for Stocks and Futures” (2004)
💮 3-Pole SuperSmoother
An extension of the 2-pole design, the 3-pole SuperSmoother further attenuates high-frequency noise. Its additional pole delivers enhanced smoothing at the cost of slightly increased lag.
Source: John Ehlers – “Cybernetic Analysis for Stocks and Futures” (2004)
💮 Adaptive Directional Volatility Moving Average (ADXVma)
This adaptive moving average adjusts its smoothing factor based on directional volatility. By combining true range and directional movement measurements, it remains exceptionally flat during ranging markets and responsive during directional moves.
Source: Various implementations across platforms, unified and optimized
💮 Ehlers Combined Bandpass Filter with Automated Gain Control (AGC)
This sophisticated filter merges a highpass pre-processing stage with a bandpass filter. An integrated Automated Gain Control normalises the output to a consistent range, while offering both regular and truncated recursive formulations to manage lag.
Source: John F. Ehlers – “Truncated Indicators” (2020), “Cycle Analytics for Traders” (2013)
💮 Voss Predictive Filter
A forward-looking filter that predicts future values of a band-limited signal in real time. By utilising multiple time-delayed feedback terms, it provides anticipatory coupling and delivers a short-term predictive signal.
Source: John Ehlers - "A Peek Into The Future" (TASC 2019-08)
💮 Adaptive Autonomous Recursive Moving Average (A2RMA)
This filter dynamically adjusts its smoothing through an adaptive mechanism based on an efficiency ratio and a dynamic threshold. A double application of an adaptive moving average ensures both responsiveness and stability in volatile and ranging markets alike. Very flat response when properly tuned.
Source: @alexgrover (2019)
💮 Ultimate Smoother (2-Pole)
The Ultimate Smoother filter is engineered to achieve near-zero lag in its passband by subtracting a high-pass response from an all-pass response. This creates a filter that maintains signal fidelity at low frequencies while effectively filtering higher frequencies at the expense of slight overshooting.
Source: John Ehlers - TASC 2024-04 "The Ultimate Smoother"
Note: This library is actively maintained and enhanced. Suggestions for additional filters or improvements are welcome through the usual channels. The source code contains a list of tested filters that did not make it into the curated collection.
Gyts
[GYTS] Filters ToolkitFilters Toolkit indicator
🌸 Part of GoemonYae Trading System (GYTS) 🌸
🌸 --------- 1. INTRODUCTION --------- 🌸
💮 Overview
The GYTS Filters Toolkit indicator is an advanced, interactive interface built atop the high‐performance, curated functions provided by the FiltersToolkit library . It allows traders to experiment with different combinations of filtering methods -— from smoothing low-pass filters to aggressive detrenders. With this toolkit, you can build custom indicators tailored to your specific trading strategy, whether you're looking for trend following, mean reversion, or cycle identification approaches.
🌸 --------- 2. FILTER METHODS AND TYPES --------- 🌸
💮 Filter categories
The available filters fall into four main categories, each marked with a distinct symbol:
🌗 Low Pass Filters (Smoothers)
These filters attenuate high-frequency components (noise) while allowing low-frequency components (trends) to pass through. Examples include:
Ultimate Smoother
Super Smoother (2-pole and 3-pole variants)
MESA Adaptive Moving Average (MAMA) and Following Adaptive Moving Average (FAMA)
BiQuad Low Pass Filter
ADXvma (Adaptive Directional Volatility Moving Average)
A2RMA (Adaptive Autonomous Recursive Moving Average)
Low pass filters are displayed on the price chart by default, as they follow the overall price movement. If they are combined with a high-pass or bandpass filter, they will be displayed in the subgraph.
🌓 High Pass Filters (Detrenders)
These filters do the opposite of low pass filters - they remove low-frequency components (trends) while allowing high-frequency components to pass through. Examples include:
Butterworth High Pass Filter
BiQuad High Pass Filter
High pass filters are displayed as oscillators in the subgraph below the price chart, as they fluctuate around a zero line.
🌑 Band Pass Filters (Cycle Isolators)
These filters combine aspects of both low and high pass filters, isolating specific frequency ranges while attenuating both higher and lower frequencies. Examples include:
Ehlers Bandpass Filter
Cyber Cycle
Relative Vigor Index (RVI)
BiQuad Bandpass Filter
Band pass filters are also displayed as oscillators in a separate panel.
🔮 Predictive Filter
Voss Predictive Filter: A special filter that attempts to predict future values of band-limited signals (only to be used as post-filter). Keep its prediction horizon short (1–3 bars) for reasonable accuracy.
Note that the the library contains elaborate documentation and source material of each filter.
🌸 --------- 3. INDICATOR FEATURES --------- 🌸
💮 Multi-filter configuration
One of the most powerful aspects of this indicator is the ability to configure multiple filters. compare them and observe their combined effects. There are four primary filters, each with its own parameter settings.
💮 Post-filtering
Process a filter’s output through an additional filter by enabling the post-filter option. This creates a filter chain where the output of one filter becomes the input to another. Some powerful combinations include:
Ultimate Smoother → MAMA: Creates an adaptive smoothing effect that responds well to market changes, good for trend-following strategies
Butterworth → Super Smoother → Butterworth: Produces a well-behaved oscillator with minimal phase distortion, John Ehlers also calls a "roofing filter". Great for identifying overbought/oversold conditions with minimal lag.
A bandpass filter → Voss Prediction filter: Attempts to predict future movements of cyclical components, handy to find peaks and troughs of the market cycle.
💮 Aggregate filters
Arguably the coolest feature: aggregating filters allow you to combine multiple filters with different weights. Important notes about aggregation:
You can only aggregate filters that appear on the same chart (price chart or oscillator panel).
The weights are automatically normalised, so only their relative values matter
Setting a weight to 0 (zero) excludes that filter from the aggregation
Filters don't need to be visibly displayed to be included in aggregation
💮 Rich visualisation & alerts
The indicator intelligently determines whether a filter is displayed on the price chart or in the subgraph (as an oscillator) based on its characteristics.
Dynamic colour palettes, adjustable line widths, transparency, and custom fill between any of enabled filters or between oscillators and the zero-line.
A clear legend showing which filters are active and how they're configured
Alerts for direction changes and crossovers of all filters
🌸 --------- 4. ACKNOWLEDGEMENTS --------- 🌸
This toolkit builds on the work of numerous pioneers in technical analysis and digital signal processing:
John Ehlers, whose groundbreaking research forms the foundation of many filters.
Robert Bristow-Johnson for the BiQuad filter formulations.
The TradingView community, especially @The_Peaceful_Lizard, @alexgrover, and others mentioned in the code of the library.
Everyone who has provided feedback, testing and support!
