DeNoised Momentum [OmegaTools]

The DeNoised Momentum by OmegaTools is a versatile tool designed to help traders evaluate momentum, acceleration, and noise-reduction levels in price movements. Using advanced mathematical smoothing techniques, this script provides a "de-noised" view of momentum by applying filters to reduce market noise. This helps traders gain insights into the strength and direction of price trends without the distractions of market volatility. Key components include a DeNoised Moving Average (MA), a Momentum line, and Acceleration bars to identify trend shifts more clearly.

Features:
- Momentum Line: Measures the percentage change of the de-noised source price over a specified look-back period, providing insights into trend direction.
- Acceleration (Ret) Bars: Visualizes the rate of change of the source price, helping traders identify momentum shifts.
- Normal and DeNoised Moving Averages: Two moving averages, one based on close price (Normal MA) and the other on de-noised data (DeNoised MA), enable a comparison of smoothed trends versus typical price movements.
- DeNoised Price Data Plot: Displays the current de-noised price, color-coded to indicate the relationship between the Normal and DeNoised MAs, which highlights bullish or bearish conditions.

Script Inputs:
- Length (lnt): Sets the period for calculations (default: 21). It influences the sensitivity of the momentum and moving averages. Higher values will smooth the indicator further, while lower values increase sensitivity to price changes.
The Length does not change the formula of the DeNoised Price Data, it only affects the indicators calculated on it.

Indicator Components:
1. Momentum (Blue/Red Line):
- Calculated using the log of the percentage change over the specified period.
- Blue color indicates positive momentum; red indicates negative momentum.
2. Acceleration (Gray Columns):
- Measures the short-term rate of change in momentum, shown as semi-transparent gray columns.
3. Moving Averages:
- Normal MA (Purple): A standard simple moving average (SMA) based on the close price over the selected period.
- DeNoised MA (Gray): An SMA of the de-noised source, reducing the effect of market noise.
4. DeNoised Price Data:
- Represented as colored circles, with blue indicating that the Normal MA is above the DeNoised MA (bullish) and red indicating the opposite (bearish).

Usage Guide:
1. Trend Identification:
- Use the Momentum line to assess overall trend direction. Positive values indicate upward momentum, while negative values signal downward momentum.
- Compare the Normal and DeNoised MAs: when the Normal MA is above the DeNoised MA, it indicates a bullish trend, and vice versa for bearish trends.

2. Entry and Exit Signals:
- A change in the Momentum line's color from blue to red (or vice versa) may indicate potential entry or exit points.
- Observe the DeNoised Price Data circles for early signs of a trend reversal based on the interaction between the Normal and DeNoised MAs.

3. Volatility and Noise Reduction:
- By utilizing the DeNoised MA and de-noised price data, this indicator helps filter out minor fluctuations and focus on larger price movements, improving decision-making in volatile markets.