INVITE-ONLY SCRIPT
OLPF - Octavio Low-Pass Filter Strategy
OCTAVIO LOW-PASS FILTER (OLPF) v1.0
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DESCRIPTION
The Octavio Low-Pass Filter (OLPF) is an advanced Finite Impulse Response (FIR) low-pass filter designed for financial time series analysis. It builds upon the foundational work of the New Low-Pass Filter (NLF) by Alex Pierrefeu, introducing three key enhancements that significantly improve signal quality and reduce common filtering artifacts.
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KEY INNOVATIONS
1. HERMITE SMOOTHING POLYNOMIAL
Replaces the simple quadratic base (x²) with the cubic Hermite interpolation polynomial [x²(3-2x)]. This mathematical refinement provides C¹ continuity at kernel boundaries, ensuring smoother transitions and eliminating edge discontinuities that can introduce artificial noise into the filtered signal.
2. LANCZOS SIGMA FACTOR WINDOWING
Applies a Lanczos-type attenuation factor [sin(πi/N)/(πi/N)] to each harmonic component in the sine series. This windowing technique dramatically reduces the Gibbs phenomenon - the characteristic overshooting and ringing that occurs near sharp price transitions. The result is a cleaner signal with minimized false crossover signals.
3. ADAPTIVE WEIGHT NORMALIZATION
Implements dynamic normalization of kernel weights, guaranteeing that the sum of all filter coefficients equals unity. This ensures proper amplitude preservation across all market conditions and prevents signal drift or scaling artifacts.
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MATHEMATICAL FOUNDATION
The OLPF kernel function is defined as:
K(x, N) = x²(3-2x) + Σ[i=1 to N] (1/i) × σ(i) × sin(πxi)
Where:
- x ∈ [0,1] is the normalized position within the filter window
- N is the filter order (degree of the sine series)
- σ(i) = sin(πi/(N+1)) / (πi/(N+1)) is the Lanczos sigma factor
The filter output is computed via discrete convolution:
F(M, N) = Σ[i=1 to M] src[i-1] × [K(i/M, N) - K((i-1)/M, N)] / W
Where W is the sum of all weights for normalization.
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APPLICATIONS
- Trend identification with reduced lag compared to traditional MAs
- Noise reduction in volatile market conditions
- Generation of trading signals via fast/slow filter crossovers
- Foundation for more complex indicator development
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STRATEGY IMPLEMENTATION
This script implements a dual-filter crossover strategy with:
- Fast OLPF for responsive signal generation
- Slow OLPF for trend confirmation
- EMA filter for additional trend validation
- ATR-based dynamic stop-loss positioning
- Risk-based position sizing (percentage of equity)
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AUTHOR
Name: Hector Octavio Piccone Pacheco
Filter: Octavio Low-Pass Filter (OLPF)
Version: 1.0
Based on: New Low-Pass Filter (NLF) by Alex Pierrefeu
Date: 2025
Original Contributions:
- Hermite smoothing polynomial kernel base
- Lanczos sigma factor windowing for Gibbs reduction
- Adaptive weight normalization system
- Integrated risk management framework
---
LICENSE
This work is licensed under the Mozilla Public License 2.0. You are free to use, modify, and distribute this code with attribution.
---
DISCLAIMER
Trading involves substantial risk of loss. This indicator is provided for educational and research purposes only. Past performance does not guarantee future results. Always conduct your own analysis and risk assessment.
---
DESCRIPTION
The Octavio Low-Pass Filter (OLPF) is an advanced Finite Impulse Response (FIR) low-pass filter designed for financial time series analysis. It builds upon the foundational work of the New Low-Pass Filter (NLF) by Alex Pierrefeu, introducing three key enhancements that significantly improve signal quality and reduce common filtering artifacts.
---
KEY INNOVATIONS
1. HERMITE SMOOTHING POLYNOMIAL
Replaces the simple quadratic base (x²) with the cubic Hermite interpolation polynomial [x²(3-2x)]. This mathematical refinement provides C¹ continuity at kernel boundaries, ensuring smoother transitions and eliminating edge discontinuities that can introduce artificial noise into the filtered signal.
2. LANCZOS SIGMA FACTOR WINDOWING
Applies a Lanczos-type attenuation factor [sin(πi/N)/(πi/N)] to each harmonic component in the sine series. This windowing technique dramatically reduces the Gibbs phenomenon - the characteristic overshooting and ringing that occurs near sharp price transitions. The result is a cleaner signal with minimized false crossover signals.
3. ADAPTIVE WEIGHT NORMALIZATION
Implements dynamic normalization of kernel weights, guaranteeing that the sum of all filter coefficients equals unity. This ensures proper amplitude preservation across all market conditions and prevents signal drift or scaling artifacts.
---
MATHEMATICAL FOUNDATION
The OLPF kernel function is defined as:
K(x, N) = x²(3-2x) + Σ[i=1 to N] (1/i) × σ(i) × sin(πxi)
Where:
- x ∈ [0,1] is the normalized position within the filter window
- N is the filter order (degree of the sine series)
- σ(i) = sin(πi/(N+1)) / (πi/(N+1)) is the Lanczos sigma factor
The filter output is computed via discrete convolution:
F(M, N) = Σ[i=1 to M] src[i-1] × [K(i/M, N) - K((i-1)/M, N)] / W
Where W is the sum of all weights for normalization.
---
APPLICATIONS
- Trend identification with reduced lag compared to traditional MAs
- Noise reduction in volatile market conditions
- Generation of trading signals via fast/slow filter crossovers
- Foundation for more complex indicator development
---
STRATEGY IMPLEMENTATION
This script implements a dual-filter crossover strategy with:
- Fast OLPF for responsive signal generation
- Slow OLPF for trend confirmation
- EMA filter for additional trend validation
- ATR-based dynamic stop-loss positioning
- Risk-based position sizing (percentage of equity)
---
AUTHOR
Name: Hector Octavio Piccone Pacheco
Filter: Octavio Low-Pass Filter (OLPF)
Version: 1.0
Based on: New Low-Pass Filter (NLF) by Alex Pierrefeu
Date: 2025
Original Contributions:
- Hermite smoothing polynomial kernel base
- Lanczos sigma factor windowing for Gibbs reduction
- Adaptive weight normalization system
- Integrated risk management framework
---
LICENSE
This work is licensed under the Mozilla Public License 2.0. You are free to use, modify, and distribute this code with attribution.
---
DISCLAIMER
Trading involves substantial risk of loss. This indicator is provided for educational and research purposes only. Past performance does not guarantee future results. Always conduct your own analysis and risk assessment.
僅限邀請腳本
僅作者批准的使用者才能訪問此腳本。您需要申請並獲得使用許可，通常需在付款後才能取得。更多詳情，請依照作者以下的指示操作，或直接聯絡octa_piccone。
TradingView不建議在未完全信任作者並了解其運作方式的情況下購買或使用腳本。您也可以在我們的社群腳本中找到免費的開源替代方案。
作者的說明
Want access to the OLPF Strategy? Reach out to me!
Discord: octa_0001
免責聲明
這些資訊和出版物並非旨在提供，也不構成TradingView提供或認可的任何形式的財務、投資、交易或其他類型的建議或推薦。請閱讀使用條款以了解更多資訊。
僅限邀請腳本
僅作者批准的使用者才能訪問此腳本。您需要申請並獲得使用許可，通常需在付款後才能取得。更多詳情，請依照作者以下的指示操作，或直接聯絡octa_piccone。
TradingView不建議在未完全信任作者並了解其運作方式的情況下購買或使用腳本。您也可以在我們的社群腳本中找到免費的開源替代方案。
作者的說明
Want access to the OLPF Strategy? Reach out to me!
Discord: octa_0001
免責聲明
這些資訊和出版物並非旨在提供，也不構成TradingView提供或認可的任何形式的財務、投資、交易或其他類型的建議或推薦。請閱讀使用條款以了解更多資訊。