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Indicators/MyIndicators/Authors/Ehlers/1_Smoothers/Butterworth_Filter_MTF_Pro.md
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# Butterworth Filter MTF Professional
## 1. Summary (Introduction)
The `Butterworth_Filter_MTF_Pro` is a multi-timeframe (MTF) version of John Ehlers' Higher-Order Butterworth Filter. This indicator calculates the filter on a **higher, user-selected timeframe** and projects its smooth, responsive trendline onto the current, lower-timeframe chart.
This allows traders to visualize the underlying trend from a broader perspective. The higher-timeframe Butterworth Filter acts as a superior dynamic benchmark for support, resistance, and overall market direction, offering a cleaner signal than traditional moving averages.
The indicator is highly versatile: if the user selects the current chart's timeframe, it functions identically to the standard `Butterworth_Filter_Pro` indicator. It also fully supports both **standard** and **Heikin Ashi** price data.
## 2. Mathematical Foundations and Calculation Logic
The underlying calculation is identical to the standard Butterworth Filter, utilizing a recursive IIR formula with multiple poles. The key innovation here is the multi-timeframe application.
### Calculation Steps (Algorithm)
1. **Fetch Higher Timeframe Data:** The indicator retrieves the OHLC price data for the user-selected higher timeframe (`htf`).
2. **Calculate Filter on the Higher Timeframe:** The complete recursive calculation (2-pole or 3-pole) is performed using the `htf` price data.
3. **Project to Current Chart:** The calculated `htf` filter values are mapped to the current chart, creating a characteristic "step-like" line that represents the higher timeframe's trend.
## 3. MQL5 Implementation Details
* **Self-Contained and Robust:** This indicator is fully self-contained and does not depend on any external indicator files (`iCustom`). It directly fetches the required higher-timeframe price data using built-in `Copy...` functions for maximum stability.
* **Modular Calculation Engine (`Butterworth_Calculator.mqh`):** The indicator reuses the exact same calculation engine as the standard `Butterworth_Filter_Pro`. This ensures mathematical consistency across all versions.
* **Optimized Incremental Calculation (O(1)):**
Unlike basic MTF indicators that recalculate the entire history on every tick, this indicator employs a sophisticated incremental algorithm:
* **HTF State Tracking:** It tracks the calculation state of the higher timeframe separately (`g_htf_prev_calculated`).
* **Persistent Buffers:** The internal buffer for the higher timeframe is maintained globally, preserving the recursive state (`Filt[i-1]`, `Filt[i-2]`) between ticks.
* **Efficient Mapping:** The projection loop only updates the bars corresponding to the new data.
* This ensures the indicator remains lightweight and high-performance even on heavy load.
* **Dual-Mode Logic:** The `OnCalculate` function contains a smart branching logic.
* If a higher timeframe is selected, it performs the optimized MTF data fetching and projection process.
* If the current timeframe is selected, it bypasses the MTF logic and functions identically to the standard `Butterworth_Filter_Pro`.
## 4. Parameters
* **Upper Timeframe (`InpUpperTimeframe`):** The higher timeframe on which the filter will be calculated. If set to `PERIOD_CURRENT`, the indicator will run on the current chart's timeframe.
* **Period (`InpPeriod`):** The "critical period" of the filter. (Default: `20`).
* **Poles (`InpPoles`):** The number of poles for the filter (2 or 3).
* **Applied Price (`InpSourcePrice`):** The source price for the calculation (Standard or Heikin Ashi).
## 5. Usage and Interpretation
The MTF version of the Butterworth Filter is an exceptionally powerful tool for multi-timeframe trend analysis.
* **Major Trend Filter:** The slope and position of the MTF filter line provide a clear view of the dominant market condition.
* If the price is consistently above a **rising** MTF filter, the market is in a strong uptrend.
* If the price is consistently below a **falling** MTF filter, the market is in a strong downtrend.
* **Dynamic Support and Resistance:** The MTF filter line acts as a strong support/resistance level. Because the Butterworth filter is smoother than an EMA, it often provides cleaner bounce levels.