Ultimate Smoother

🧪 Open Source Tool

The Ultimate Smoother does what conventional filters cannot: it smooths price data with effectively zero lag in the passband. Pioneered by John F. Ehlers and extended by our research team, it replaces averaging with a different idea from digital signal processing : cancelling the noise instead of diluting it.

Tip

Open Source: The Ultimate Smoother embodies our commitment to sharing the research we actually trade with. Both the standalone indicator and its implementation in the FiltersToolkit Library are fully open source, allowing traders to study, modify, and build upon these mathematical foundations.

Sidestepping the Lag Trade-Off

Traditional filters face an inescapable trade-off: more smoothing means more lag. Moving averages, even sophisticated ones, must choose between responsiveness and noise reduction. The Ultimate Smoother sidesteps this trade-off with a construction that maintains phase alignment at all frequencies in the passband.

Zero-Lag Response

Unlike conventional smoothers that lag behind price movements, the Ultimate Smoother maintains phase alignment in the passband. When price changes direction, the filter responds on the same bar—not several bars later.

Noise Reduction

Despite its zero-lag characteristic, the filter effectively attenuates high-frequency noise. This isn’t achieved through averaging but through sophisticated frequency cancellation.

Adaptive Smoothness

The 3-pole version offers controllable smoothness without sacrificing responsiveness. Paradoxically, longer periods create less smooth but more responsive output.

Mathematical Foundation

The Ultimate Smoother achieves these properties through a counterintuitive approach: instead of directly designing a low-pass filter, it subtracts a high-pass filter from an all-pass filter (the original input).

The Core Principle

Conceptual Model

The filter operates on a simple but profound principle:

Low-Pass Output = All-Pass Input - High-Pass Component

At very low frequencies (long-term trends), the high-pass filter contributes almost nothing, so the output closely matches the input in both amplitude and phase. At higher frequencies (noise), the high-pass filter’s response increasingly matches the input, resulting in cancellation through subtraction.

Mathematical Form

For the 2-pole Ultimate Smoother:

ω = √2 × π / period
a₁ = e^(-ω)

Coefficients:
c₀ = (1 + 2a₁cos(ω) - a₁²) / 4
c₁ = 2a₁cos(ω)
c₂ = -a₁²

Output = (1-c₀)×source + (2c₀-c₁)×source[1] - (c₀+c₂)×source[2] + c₁×output[1] + c₂×output[2]

Frequency Response

The Ultimate Smoother exhibits unique frequency characteristics:

• Passband: Near-perfect unity gain with zero phase shift
• Transition Band: Gradual attenuation begins at the critical frequency
• Stopband: Effective noise reduction through cancellation
• Group Delay : Effectively zero in the passband

Our Innovation: The 3-Pole Extension

GYTS Research Contribution

Building upon Ehlers’ 2-pole design, our research team developed a 3-pole version that extends the zero-lag principle while offering enhanced control over smoothness. The derivation is original work, and the implementation is public in the open-source code.

The 3-pole Ultimate Smoother maintains all the benefits of the original while adding:

• Enhanced Noise Reduction: The additional pole provides tunable, potentially stronger attenuation of high-frequency components
• Controllable Smoothness: Unique parameter behaviour allows fine-tuning the smoothness/responsiveness balance
• Zero-Lag Maintained: Despite the additional pole, passband phase alignment is preserved

Counterintuitive Control

In the 3-pole version, the period parameter works opposite to conventional filters:

• Longer periods: Less smooth, more responsive (closer to raw price)
• Shorter periods: Smoother output but may exhibit overshooting on large moves

This unusual characteristic provides unique flexibility in adapting to different market conditions.

Practical Implementation

Configuration Guide

1. Add the Indicator

   Search for “GYTS Ultimate Smoother” in TradingView’s indicator library. The open source version provides both 2-pole and 3-pole options.

2. Select Your Version

   • 2-pole: Classic Ehlers design, balanced performance
   • 3-pole: GYTS innovation, enhanced control with zero-lag properties

3. Adjust the Period

   Start with a period of 20. Remember that behaviour differs between versions:

   • 2-pole: Traditional behaviour (longer = smoother)
   • 3-pole: Inverted behaviour (longer = more responsive)

4. Fine-Tune Visualisation

   Use our signature colour palettes or monochromatic mode. Adjust transparency and line width for optimal chart clarity.

Choosing Between Versions

Use 2-Pole when...

• You need predictable, traditional smoothing behaviour
• Working with established strategies expecting conventional lag

Use 3-Pole when...

• Zero-lag response is absolutely critical
• You want fine control over smoothness

Integration Strategies

The Ultimate Smoother serves as a foundational component throughout our indicator suite:

Signal Generation

Use as a zero-lag price proxy for:

• Entry/exit signal generation
• Trend direction confirmation
• Support/resistance level refinement

Noise Reduction

Pre-process price data before:

• Feeding into oscillators
• Calculating divergences
• Computing market statistics

Composite Systems

Combine with other filters for:

• Multi-timeframe analysis
• Adaptive smoothing systems
• Regime-dependent strategies

Popular combinations discovered through research:

• Ultimate Smoother → MAMA: Adaptive smoothing that responds to market cycles
• Ultimate Smoother → Butterworth: Creates well-behaved oscillators

Explore Filter Combinations Discover powerful filter chains using the Ultimate Smoother with other DSP tools

Filter Mathematics Guide Comprehensive mathematical foundations of all GYTS filters

Open Source Commitment

Why We Share

Filters of this kind are often kept proprietary. We publish ours because:

• Education Empowers: Understanding these concepts elevates all traders
• Collaboration Accelerates: Community insights drive innovation
• Transparency Validates: Open methods invite scrutiny and improvement
• Excellence Speaks: Quality tools need no artificial scarcity

By making both the indicator and its library implementation open source, we invite you to:

• Study the mathematical foundations
• Adapt the code for specific needs
• Contribute improvements
• Build derivative works

Source Code:

• Ultimate Smoother Indicator - Complete TradingView implementation
• FiltersToolkit Library - Reusable filter functions

Performance Characteristics

Computational Efficiency

• 2-pole: O(1) constant time per bar
• 3-pole: O(1) constant time per bar
• Minimal memory footprint
• No repainting or lookahead bias

Signal Quality Metrics

• Phase Delay: 0° in passband
• Amplitude Response: Unity gain for trends
• Noise Attenuation: -20dB to -30dB for high frequencies
• Transient Response: Immediate direction changes

Next Steps

• Experiment with Periods: Discover how different settings affect your specific trading style
• Explore Combinations: Use the FiltersToolkit to create sophisticated filter chains
• Study the Mathematics: Dive into our Filter Methods guide
• Join the Discussion: Share discoveries in our Discord channels
• Watch Tutorials: See practical applications on our YouTube channel

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