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+# Laguerre Filter Professional
+
+## 1. Summary (Introduction)
+
+> **Part of the Laguerre Indicator Family**
+>
+> This indicator is a member of a family of tools based on John Ehlers' Laguerre filter. Each member utilizes the filter's extremely low-lag and smooth characteristics to analyze different aspects of market behavior.
+>
+> * **Laguerre Filter:** A fast, responsive moving average.
+> * **Laguerre RSI:** A smooth, noise-filtered momentum oscillator.
+
+The Laguerre Filter, developed by John Ehlers, is a sophisticated, low-lag moving average based on the principles of digital signal processing. It applies a weighted average to the components of a Laguerre-transformed price series, resulting in a unique balance between smoothness and responsiveness.
+
+It serves as an advanced trendline, and optionally, it can display a comparative **FIR (Finite Impulse Response) filter** to visually demonstrate the smoothing effect of the Laguerre transformation.
+
+Our `Laguerre_Filter_Pro` implementation is a unified, professional version that allows the calculation to be based on either **standard** or **Heikin Ashi** price data.
+
+## 2. Mathematical Foundations and Calculation Logic
+
+The indicator's logic is centered around the recursive Laguerre filter and a final weighted summation.
+
+### Required Components
+
+* **Gamma (γ):** A coefficient between 0 and 1 that controls the filter's smoothing.
+* **Source Price (P):** The price series used for the calculation.
+
+### Calculation Steps (Algorithm)
+
+1. **Calculate Laguerre Filter Components:** For each bar `i`, the four internal filter components (`L0`...`L3`) are updated recursively.
+    * $L0_i = (1 - \gamma) \times P_i + \gamma \times L0_{i-1}$
+    * $L1_i = -\gamma \times L0_i + L0_{i-1} + \gamma \times L1_{i-1}$
+    * ...and so on for `L2` and `L3`.
+2. **Calculate the Final Weighted Filter:** The final output is a weighted sum of the four components, as defined by Ehlers.
+    * $\text{Laguerre Filter}_i = \frac{L0_i + 2 \times L1_i + 2 \times L2_i + L3_i}{6}$
+3. **(Optional) Calculate the FIR Filter:** For comparison, a standard FIR filter with the same weights is calculated on the raw price data.
+    * $\text{FIR Filter}_i = \frac{P_i + 2 \times P_{i-1} + 2 \times P_{i-2} + P_{i-3}}{6}$
+
+## 3. MQL5 Implementation Details
+
+* **Modular "Family" Architecture:** The core Laguerre filter calculation is encapsulated in a central `Laguerre_Engine.mqh` file. The `Laguerre_Filter_Calculator.mqh` is a thin adapter that includes this engine and performs the final weighted summation for both the Laguerre and the optional FIR filters.
+* **Heikin Ashi Integration:** An inherited `CLaguerreEngine_HA` class allows the calculation to be performed seamlessly on smoothed Heikin Ashi data.
+* **Stability via Full Recalculation:** We employ a full recalculation within `OnCalculate` for maximum stability.
+
+## 4. Parameters
+
+* **Gamma (`InpGamma`):** The Laguerre filter coefficient, a value between 0.0 and 1.0. This parameter controls the trade-off between smoothing and lag.
+  * **High Gamma (e.g., 0.7 - 0.9):** Results in a **smoother** line with **more lag**.
+  * **Low Gamma (e.g., 0.1 - 0.3):** Results in a **faster, more responsive** line (less lag) that is less smooth. At `gamma = 0`, the Laguerre Filter becomes identical to the FIR filter.
+* **Applied Price (`InpSourcePrice`):** The source price for the calculation.
+* **Show FIR (`InpShowFIR`):** A boolean switch to show or hide the comparative FIR filter line on the chart.
+
+## 5. Usage and Interpretation
+
+The Laguerre Filter is used as a superior, low-lag alternative to traditional moving averages.
+
+* **Trend Identification:** It serves as a highly responsive trendline.
+  * When the price is consistently above the Laguerre Filter and the line is rising, the trend is bullish.
+  * When the price is consistently below the Laguerre Filter and the line is falling, the trend is bearish.
+* **Crossover Signals:**
+  * **Price Crossover:** A crossover of the price and the Laguerre Filter line can be used as a trade signal, similar to a standard moving average crossover. Due to its low lag, these signals are often more timely.
+  * **Two-Line Crossover:** A classic fast/slow system can be created by placing two Laguerre Filter indicators on the chart with different `gamma` values (e.g., `0.5` for the fast line and `0.2` for the slow line). A crossover of the fast line above the slow line is a buy signal, and vice versa.
+* **Dynamic Support and Resistance:** In a trending market, the Laguerre Filter line often acts as a dynamic level of support (in an uptrend) or resistance (in a downtrend), providing potential entry points on pullbacks.
+
+### **Combined Strategy with Laguerre Momentum (Advanced)**
+
+The filter's characteristics can be better understood when used with its companion oscillator, the `Laguerre_Momentum_Pro`. A key predictive relationship exists between them:
+
+* **The Momentum Oscillator's zero-cross predicts the Filter's turning point.**
+  * When the `Laguerre_Momentum` oscillator crosses **above its zero line**, it provides an early warning that the `Laguerre_Filter` on the main chart is about to form a **trough (a bottom)**.
+  * When the `Laguerre_Momentum` oscillator crosses **below its zero line**, it provides an early warning that the `Laguerre_Filter` is about to form a **peak (a top)**.
+
+This relationship allows a trader to use the momentum oscillator as a **leading indicator** to anticipate the turning points of the smoother, lagging Laguerre Filter.