docs(indicators): Optimized for incremental calculation

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## 1. Summary (Introduction)
The Windowed MA Pro is an indicator based on John Ehlers' research into advanced **Finite Impulse Response (FIR) filters**. It serves as a superior alternative to the Simple Moving Average (SMA) by employing "windowing" functions to create a smoother, more responsive output.
The Windowed MA Pro is an indicator based on John Ehlers' research into advanced **Finite Impulse Response (FIR) filters**. It serves as a superior alternative to the Simple Moving Average (SMA) by employing a **Hann Window** function to create a smoother, more responsive output.
A standard SMA uses a "rectangular window," giving equal weight to all prices in the lookback period, which results in poor filtering characteristics. This indicator allows the user to apply mathematically superior weighting schemes:
1. **Triangular Window:** A simple weighting that gives the most emphasis to the middle of the lookback period.
2. **Hann Window:** A more advanced, cosine-based weighting function that provides excellent smoothing and is Ehlers' recommended choice for most trading applications.
A standard SMA uses a "rectangular window," giving equal weight to all prices in the lookback period, which results in poor filtering characteristics. This indicator applies a mathematically superior cosine-based weighting scheme (Hann Window) that provides excellent smoothing and is Ehlers' recommended choice for most trading applications.
The result is a high-fidelity moving average that produces a cleaner representation of the trend with less noise than a standard SMA.
## 2. Mathematical Foundations and Calculation Logic
The indicator is a weighted moving average, where the weights are determined by the selected windowing function.
The indicator is a weighted moving average, where the weights are determined by the Hann window function.
### Calculation Steps (Algorithm)
For each bar, the indicator looks back over the last `N` periods.
1. **Calculate Weights:** For each position `j` within the `N`-period window, a specific weight is calculated based on the chosen `Window Type`.
* **SMA:** `Weight = 1`
* **Triangular:** The weight increases linearly to the midpoint of the window and then decreases.
* **Hann:** The weight is calculated using a cosine formula, creating a smooth, bell-shaped curve: $W_j = 0.5 \times (1 - \cos(\frac{2\pi \times j}{N-1}))$
1. **Calculate Weights:** For each position `j` within the `N`-period window, a specific weight is calculated using a cosine formula, creating a smooth, bell-shaped curve:
$W_j = 0.5 \times (1 - \cos(\frac{2\pi \times j}{N-1}))$
2. **Calculate Weighted Sum:** The source price at each position is multiplied by its corresponding weight and summed up.
3. **Normalize:** The final indicator value is the weighted sum divided by the sum of all weights.
## 3. MQL5 Implementation Details
* **Unified Calculator (`Windowed_MA_Calculator.mqh`):** The calculation for all window types is handled by a single, flexible calculator class. The user's choice determines which weighting formula is used inside the calculation loop.
* **Unified Calculator (`Windowed_MA_Calculator.mqh`):** The calculation is handled by a dedicated calculator class.
* **Optimized Incremental Calculation (O(1)):**
Unlike basic implementations that recalculate the entire history on every tick, this indicator employs an intelligent incremental algorithm.
* **State Tracking:** It utilizes `prev_calculated` to process only new bars.
* **Persistent Buffers:** The internal price buffer persists its state between ticks.
* **Pre-calculated Weights:** The Hann weights are calculated only once during initialization, making the runtime calculation extremely fast.
* **Heikin Ashi Integration:** The indicator fully supports calculation on smoothed Heikin Ashi data.
* **FIR-based Logic:** This is a non-recursive (FIR) filter. Its calculation at any given bar depends only on the last `N` prices.
* **Stability via Full Recalculation:** The indicator employs a full recalculation on every `OnCalculate` call.
## 4. Parameters
* **Window Type (`InpWindowType`):** Allows the user to select the weighting function: `SMA`, `Triangular`, or `Hann`. **`Hann` is recommended for the best smoothing.**
* **Period (`InpPeriod`):** The lookback period (`N`) for the moving average.
* **Applied Price (`InpSourcePrice`):** The source price for the calculation (e.g., Close, Open, etc.).
* **Candle Source (`InpCandleSource`):** Selects between `Standard` and `Heikin Ashi` candles.
* **Period (`InpPeriod`):** The lookback period (`N`) for the moving average. (Default: `20`).
* **Applied Price (`InpSourcePrice`):** The source price for the calculation. (Standard or Heikin Ashi).
## 5. Usage and Interpretation
@@ -46,7 +42,6 @@ The Windowed MA should be used as a high-quality replacement for a standard Simp
* **Trend Identification:** Use it to identify the direction of the trend. Price trading above the line indicates an uptrend; price below indicates a downtrend.
* **Dynamic Support and Resistance:** The line acts as a dynamic S/R level. Due to its superior smoothing, it often provides more reliable support/resistance than a standard SMA.
* **Crossover Systems:** A two-line crossover system using a fast and a slow Windowed MA (especially with the Hann window) will produce smoother and potentially cleaner signals than a standard SMA crossover system.
### **Combined Strategy with Windowed Momentum (Advanced)**