G-Score | NAL1. Overview
G-Score | NAL is a volatility-adjusted Z-Score regime indicator built from two main components: a smoothed price Z-Score and an adaptive GARCH-based volatility Z-Score.
The indicator does not use fixed overbought or oversold levels. Instead, it builds dynamic thresholds from the current volatility structure of the market. Price is then measured against those volatility-derived boundaries to determine whether the market is entering a bullish or bearish statistical regime.
2. Calculation
The indicator starts by estimating volatility through a GARCH-style process. It calculates log returns from the selected source, converts those returns into squared variance, and then compares short-term variance behavior against a realized variance baseline.
GARCH_LogReturn = math.log(src / src )
GARCH_SquaredLogReturn = math.pow(GARCH_LogReturn, 2.0)
GARCH_RealizedVariance = ta.sma(GARCH_SquaredLogReturn, GARCH_Lookback)
The model then searches through possible beta and gamma coefficients to find weights that better fit the recent variance environment. These optimized coefficients are used to build a GARCH variance estimate from three components: long-run variance, recent shock variance, and lagged variance.
GARCH_Variance =
GARCH_Gamma * GARCH_LongRunVariance +
GARCH_Alpha * GARCH_SquaredLogReturn +
GARCH_Beta * GARCH_LaggedVariance
The final GARCH volatility value is created by taking the square root of the projected variance. This produces the volatility engine used later in the threshold system.
The indicator then calculates two separate Z-Scores. The first is a price Z-Score, measuring where price is relative to its own mean and deviation. The second is a volatility Z-Score, measuring where GARCH volatility is relative to its own historical distribution.
Both values are smoothed with a Jurik-style moving average to reduce noise while keeping the response relatively fast.
The volatility Z-Score is then mirrored into positive and negative boundaries. This creates dynamic upper and lower thresholds that expand and contract with the current volatility regime.
The final signal compares the smoothed price Z-Score against those adaptive volatility thresholds. A bullish state triggers when price strength expands above the upper volatility boundary. A bearish state triggers when price weakness falls below the lower volatility boundary. When price remains inside the volatility envelope, the previous regime is held.
3. Key Features
Adaptive GARCH-style volatility engine.
Price Z-Score measured against volatility-derived thresholds.
Dynamic upper and lower boundaries instead of fixed levels.
Jurik-style smoothing for both price and volatility components.
State-based candle coloring, background regime coloring, threshold fills, and transition labels.
Designed to capture statistical expansion when price moves outside its volatility-adjusted structure.
4. Use
G-Score is designed to identify when price begins separating from its normal statistical range after accounting for the current volatility environment. A move above the upper threshold reflects bullish statistical expansion, while a move below the lower threshold reflects bearish statistical expansion.
The strength of the indicator comes from the relationship between price displacement and volatility regime. Rather than treating every Z-Score reading the same, it lets volatility define the boundary that price must break.
This indicator is best used as a specialized module within a complete strategy framework. Its role is to isolate a specific statistical layer of market behavior, where price expansion is evaluated through the lens of adaptive volatility. The full value comes from how this regime signal is integrated into a broader process for timing, structure, and risk.
Indicator
Momentum RSI | NAL1. Overview
Momentum RSI | NAL is a momentum-regime indicator built around a Jurik-smoothed double RSI engine. It first smooths price using a Jurik-style moving average, then applies RSI twice to measure both momentum and momentum-of-momentum.
Instead of relying on raw RSI movement, the indicator uses a smoothed second RSI layer to better identify when momentum is expanding or deteriorating. The final Momentum RSI is compared against bullish and bearish thresholds to create a clean directional state.
2. Calculation
The indicator starts by smoothing the selected source with a Jurik-style moving average. This creates a cleaner input before the RSI calculation, helping reduce noise while keeping the response relatively fast.
The first RSI measures the momentum of the smoothed source. The second RSI is then applied to the first RSI, creating a double RSI structure. This second layer measures whether the original RSI itself is strengthening or weakening.
After the double RSI is calculated, it is smoothed again using the same Jurik-style smoothing method. This produces the final Momentum RSI line.
The signal is based on two thresholds. A bullish state triggers when the Momentum RSI rises above the long threshold. A bearish state triggers when the Momentum RSI falls below the short threshold.
When the Momentum RSI is between both thresholds, the indicator keeps its previous directional state. This helps avoid constant neutral flipping and gives a cleaner regime-style output.
3. Key Features
Jurik-smoothed double RSI momentum engine.
Measures both momentum and momentum-of-momentum.
Bullish and bearish threshold-based regime detection.
State-based coloring that holds the previous direction between thresholds.
Glow-style RSI plot, threshold fills, candle coloring, and transition labels.
4. Use
Works well for identifying momentum shifts and potential exhaustion areas during trending periods. The double RSI structure can react to changes in momentum before a standard RSI fully confirms the move.
A move above the long threshold suggests bullish momentum pressure. A move below the short threshold suggests bearish momentum pressure. The colored candles and transition labels make it easier to see when the indicator changes state.
Best used in confluence with other indicators, due to its unique behavior and potential for false signals in choppy or low-directional regimes. The indicator is best used as a momentum-regime tool for confirming trend continuation, spotting momentum deterioration, and visually separating bullish and bearish conditions. Indicator
Momentum RSI For Loop | NAL1. Overview
Momentum RSI For Loop | NAL is a momentum-regime indicator built around a Jurik-smoothed double RSI engine. It first smooths price using a Jurik-style moving average, then applies RSI twice to measure both momentum and momentum-of-momentum.
Instead of using a fixed RSI threshold, the indicator compares the current smoothed double RSI against many of its previous values. This creates a loop counter that shows whether current momentum is stronger or weaker than a broad section of recent history.
2. Calculation
The indicator starts by smoothing the selected source with a Jurik-style moving average. This creates a cleaner input before RSI is calculated, helping reduce noise while keeping the response relatively fast.
The first RSI measures the momentum of the smoothed source. The second RSI is then applied to the first RSI, creating a double RSI structure. This second layer measures whether the original RSI itself is strengthening or weakening.
After the double RSI is calculated, it is smoothed again using the same Jurik-style smoothing method. This produces the final momentum series used by the loop engine.
The loop mechanism then compares the current smoothed double RSI value against past values over the selected range. If the current value is greater than the value from i bars ago, the counter adds one point. If it is not greater, the counter subtracts one point.
A high positive counter means current momentum is stronger than many previous momentum readings. A deeply negative counter means current momentum is weaker than many previous readings.
The final signal is based on two thresholds. A bullish state triggers when the loop counter rises above the upper threshold. A bearish state triggers when the loop counter falls below the lower threshold.
3. Key Features
Jurik-smoothed double RSI momentum engine.
For-loop comparison against historical momentum values.
Measures relative momentum strength instead of relying on static RSI levels.
Upper and lower loop thresholds for bullish and bearish regime detection.
Glow-style loop plot, threshold fills, candle coloring, and transition labels.
4. Use
Works well in getting out around tops and bottoms, during trending periods. Best used in confluence with other indicators, due to it's unique behaviour, and it being prone to false signals in regimes where other indicators are not.
The indicator is best used as a momentum-regime tool. It can help confirm trend continuation, detect momentum shifts, and visually separate bullish and bearish conditions through candle coloring and transition labels. Indicator
Indicator
Blau Jurik Ergodic Candlestick Oscillator (ECO)================================================================================
TECHNICAL DESCRIPTION: BLAU JURIK ERGODIC CANDLESTICK OSCILLATOR (ECO)
OVERVIEW
The Blau Jurik Ergodic Candlestick Oscillator (ECO) is a highly responsive
momentum-to-volatility ratio indicator. It is a modernized variation of William
Blau's classic Ergodic Candlestick Oscillator.
While the standard ECO uses simple or exponential moving averages for smoothing,
this implementation replaces those linear filters with a double-pass adaptive
Jurik Filter. This modification significantly reduces lag while minimizing overshoot,
resulting in a cleaner, faster signal that adapts to changing market volatility.
CORE CONSTRUCTS & MATHEMATICAL FORMULATING
The indicator processes two primary streams of candlestick data at each bar:
A. Candlestick Body Displacement (Net Directional Movement)
This measures the net price movement from open to close:
co = Close - Open
B. Candlestick High-Low Range (Total Local Volatility)
This measures the absolute range of price movement, serving as a baseline
for total market energy:
hl = High - Low
Rather than using these raw values directly—which would produce an unstable,
noisy oscillator—both "co" and "hl" are smoothed using two cascaded passes
of an adaptive Jurik Filter.
THE ADAPTIVE JURIK SMOOTHING PROCESS
The Jurik Filter adapts its smoothing speed dynamically based on localized market
volatility. When volatility spikes, the filter automatically reduces its
smoothing length (speeding up) to catch the trend. When volatility drops, it
increases its smoothing length (slowing down) to filter out noise.
The key steps in the adaptive algorithm are:
A. Volatility Calculation:
Calculate changes relative to the current and prior values:
del1 = InputValue - max(InputValue , InputValue)
del2 = InputValue - min(InputValue , InputValue)
volty = max(abs(del1), abs(del2))
B. Volatility Normalization:
The current volatility is compared to a long-term rolling average (such as
a 65-period Simple Moving Average) to determine whether the market is
experiencing higher or lower volatility than normal:
Relative Volatility = volty / AverageVolatility
C. Dynamic Speed Adjustment:
An adjustment factor (representing the filter's feedback speed) is scaled
by this Relative Volatility.
When Relative Volatility is high, the smoothing coefficient (alpha)
increases, making the filter highly responsive.
When Relative Volatility is low, alpha decreases, smoothing out market noise.
D. Phase-Correction and Double-Pass Smoothing:
The filter runs a multi-stage phase shift correction that offsets the
natural lag of moving averages.
To construct the Ergodic Oscillator, this process is run twice (cascaded):
SmoothedBody = JurikFilter(JurikFilter(co, Length1, Phase), Length2, Phase)
SmoothedRange = JurikFilter(JurikFilter(hl, Length1, Phase), Length2, Phase)
OSCILLATOR & SIGNAL CALCULATIONS
Once the body displacement and high-low range are smoothed, the ECO is calculated
as a percentage ratio of the two:
ECO = 100 * (SmoothedBody / SmoothedRange)
Because "co" can be positive or negative, the ECO oscillates between -100 and +100.
An ECO near +100 indicates that the bodies of the candlesticks are taking up
almost the entire high-low range in a positive direction (strong, clean uptrend).
An ECO near -100 indicates that the bodies are taking up almost the entire
range in a negative direction (strong, clean downtrend).
An ECO near 0 indicates range-bound, choppy, or rotating price action with
little directional progress.
Downstream Signal Lines:
To generate trade signals and identify trend changes, multiple downstream signal
lines are calculated by applying a Jurik Filter directly to the ECO output:
Signal1 = JurikFilter(ECO, SignalLength1, SignalPhase1)
Signal2 = JurikFilter(ECO, SignalLength2, SignalPhase2)
...and so on, up to five distinct signal lines.
INTERPRETATION & USE CASES
The ECO is typically used for three primary types of market analysis:
A. Zero-Line Crossovers:
When the ECO crosses above 0, it indicates that buying momentum is
overcoming the overall price range, establishing a bullish bias.
When the ECO crosses below 0, it indicates that selling momentum is
dominating, establishing a bearish bias.
B. Signal Line Crossovers:
Bullish Signal: The ECO line crosses above its primary Signal Line.
Bearish Signal: The ECO line crosses below its primary Signal Line.
C. Volatility & Compression Regimes:
When all downstream signal lines contract and cluster together, it signals
extreme price compression (a low-volatility environment). This state often
precedes an explosive expansion of volatility.
When the signal lines fan out widely, it indicates a highly directional,
mature trend.
================================================================================ Indicator
Indicator
JMA Quantum Edge: Adaptive Precision Trading System JMA Quantum Edge: Adaptive Precision Trading System - Enhanced Visuals & Risk Management
Get ready to experience a groundbreaking trading strategy that adapts in real-time to market conditions! This powerful, open-source script combines advanced technical analysis with state-of-the-art risk management tools, designed to give you the edge you need in today's dynamic markets.
What It Does:
Adaptive JMA Indicator:
Utilizes a custom Jurik Moving Average (JMA) that adjusts its sensitivity based on market volatility, ensuring you get precise signals even in the most fluctuating environments.
Dynamic Risk Management:
Features built-in support for partial exits (scaling out) to secure profits, along with an optional Kelly Criterion-based position sizing that tailors your exposure based on historical performance metrics.
Robust Error Handling:
Incorporates market condition filters—like minimum volume and maximum allowed gap percentage—to ensure trades are only executed under favorable conditions.
Vivid Visual Enhancements:
Enjoy an animated background that reflects market momentum, dynamic pivot markers, and clearly drawn trend channels. Plus, interactive tables provide real-time performance analytics and detailed error metrics.
Fully Customizable:
With a comprehensive set of inputs, you can easily tailor the strategy to your personal trading style and market preferences. Adjust everything from JMA parameters to refresh intervals for tables and labels!
How to Use It:
Add the Script:
Copy and paste the script into the Pine Script Editor on PulseWire and click “Add to Chart.”
Configure Your Settings:
Customize your risk management (capital, commission, position sizing, partial exits, etc.) and tweak the JMA settings to match your preferred trading style. Use the extensive input panel to adjust visuals, alerts, and more.
Backtest & Optimize:
Run the strategy in the Strategy Tester to analyze its historical performance. Monitor real-time analytics and error metrics via the interactive tables, and fine-tune your parameters for optimal performance.
Go Live with Confidence:
Once you're satisfied with the backtest results, use the generated signals for live trading, and let the system help you stay ahead in fast-paced markets!
How to use the imputs:
This cutting-edge strategy is designed to adapt to changing market conditions and offers you complete control over your trading parameters. Here’s a breakdown of what each group of inputs does and how you should use them:
Risk Management & Trade Settings
Recalculate on Every Tick:
What it does: When enabled, the strategy recalculates on every price update.
Recommendation: Leave it true for fast charts.
Initial Capital:
What it does: Sets your starting capital for backtesting, which influences position sizing and performance metrics.
Recommendation: Start with $10,000 (or adjust according to your trading capital).
Commission (%):
What it does: Simulates the cost per trade.
Recommendation: Use a realistic rate (e.g., 0.04%).
Position Size & Quantity Type:
What they do: Define how large each trade will be. Choose between a fixed unit amount or a percentage of equity.
Recommendation: For beginners, the default fixed value is a good start. Experiment later with percentage-based sizing if needed.
Order Comment:
What it does: Adds a label to your orders for easier tracking.
Allow Reverse Orders:
What it does: If disabled, the strategy will close opposing positions before entering a new trade, reducing conflicts.
Enable Dynamic Position Sizing:
What it does: Adjusts trade size based on current volatility.
Recommendation: Beginners may start with this disabled until they understand basic sizing.
Partial Exit Inputs:
What they do:
Enable Partial Exits: When turned on, you can scale out of your position to lock in profits.
Partial Exit Profit (%): The profit percentage that triggers a partial exit.
Partial Exit Percentage: The percentage of your current position to exit. Recommendation: Use defaults (e.g., 5% profit, 50% exit) to secure profits gradually.
Kelly Criterion Option:
What it does: When enabled, adjusts your position sizing using historical performance (win rate and profit factor).
Recommendation: Beginners might leave this disabled until comfortable with backtest performance metrics.
Market Condition Filters:
What they do:
Minimum Volume: Ensures trades occur only when there’s sufficient market activity.
Maximum Gap (%): Prevents trading if there’s an unusually large gap between the previous close and current open. Recommendation: Defaults work well for most markets. If trades seem erratic, consider tightening these limits.
JMA Settings
Price Source:
What it does: The input series for the JMA calculation, typically set to the closing price.
JMA Length:
What it does: Controls the smoothing period of the JMA. Lower values are more sensitive; higher values smooth out the noise. Recommendation: Start with 21.
JMA Phase & Power:
What they do: Adjust how responsive the JMA is. Phase controls timing; power adjusts the intensity. Recommendation: Default settings (63 phase and 3 power) are a balanced starting point.
Visual Settings & Style
Show JMA Line, Pivot Lines, and Pivot Labels:
What they do: Toggle visual elements on your chart for easier signal identification.
Pivot History Count:
What it does: Limits how many historical pivot markers are displayed.
Color Settings (Up/Down Neon Colors):
What they do: Set the visual cues for buy and sell signals.
Pivot Marker & Line Style:
What they do: Choose the style and thickness of your pivot markers and lines.
Show Stats Panel:
What it does: Displays real-time performance and error metrics.
Dynamic Background & Visual Enhancements
Animate Background:
What it does: Changes the background color based on market momentum.
Show Trend Channels & Volume Zones:
What they do: Draw trend channels and highlight areas of high volatility/volume.
Show Data-Rich Labels:
What it does: Displays key metrics like volume, error percentage, and momentum on the chart.
High Volatility Threshold:
What it does: Determines the multiplier for when the chart background should change due to high volatility.
Multi-Timeframe Settings
Higher Timeframe:
What it does: Uses a higher timeframe’s JMA for trend confirmation. Recommendation: Use Daily ('D') or Weekly ('W') for broader trend analysis.
Show HTF Trend Zone & Opacity:
What they do: Display a visual zone from the higher timeframe to help confirm trends.
6. Trailing Stop Settings
Trailing Stop ATR Factor & Offset Multiplier:
What they do: Calculate trailing stops based on the Average True Range (ATR), adjusting stop distances dynamically. Recommendation: Default settings are a good balance but can be fine-tuned based on asset volatility.
Alerts & Notifications
Alerts on Pivot Formation & JMA Crossover:
What they do: Notify you when key events occur.
Dynamic Power Threshold:
What it does: Sets the sensitivity for dynamic alerts.
8. Static Stop Loss / Take Profit
Static Stop Loss (%) & Take Profit (%):
What they do: Allow you to set fixed stop loss or take profit levels. Recommendation: Leave them at 0 to disable if you prefer dynamic risk management, or set them if you have strict risk/reward preferences.
Advanced Settings
ATR Length:
What it does: Determines the period for ATR calculation, impacting trailing stop sensitivity. Recommendation: Start with 14.
Optimization Feedback & Enhanced Error Analysis
Error Metric Length & Error Threshold (%):
What they do: Calculate error metrics (like average error, skewness, and kurtosis) to help you fine-tune the JMA. Recommendation: Use the defaults and adjust if the error metrics seem off during backtesting.
UI - User-Driven Tweaking & Table Customization
Parameter Tweaker Panel, Debug/Performance Table Settings:
What they do: Provide interactive tables that display real-time performance, error metrics, and allow you to monitor strategy parameters.
Refresh Frequency Options (Table & Label Refresh Intervals):
What they do: Set how often the tables and labels update.
Recommendation: Start with an interval of 1 bar; increase it if your chart is too busy.
Important for Beginners:
Default Settings:
All default values have been chosen for balanced performance across different markets. If you ever experience unexpected behavior, start by resetting the inputs to their defaults.
Step-by-Step Adjustments:
Experiment by changing one setting at a time while observing how the strategy’s signals and performance metrics change. This will help you understand the impact of each parameter.
Resetting to Defaults:
If things seem off or you’re not getting the expected results, you can always reset the indicator. Either reload the script or use the “Reset Inputs” option (if available) to revert to the default settings.
Jump in, experiment, and enjoy the power of adaptive precision trading. This strategy is built to grow with your skills—have fun exploring and refining your trading edge!
Happy trading!
Strategy
Indicator
Dynamic Jurik RSX w/ Fisher Transform█ Introduction
The Dynamic Jurik RSX with Fisher Transform is a powerful and adaptive momentum indicator designed for traders who seek a non-laggy view of price movements. This script is based on the classic Jurik RSX (Relative Strength Index). It also includes features such as the dynamic overbought and oversold limits, the Inverse Fisher Transform, trend display, slope calculations, and the ability to color extremes for better clarity.
█ Key Features:
• RSX: The Relative Strength Index (RSX) in this script is based on Jurik’s RSX, which is smoother than the traditional RSI and aims to reduce noise and lag. This script calculates the RSX using an exponential smoothing technique and adaptive adjustments.
• Inverse Fisher Transform: This script can optionally apply the Inverse Fisher Transform to the RSX, which helps to normalize the RSX values, compressing them between -1 and 1. The inverse transformation makes it easier to spot extreme values (overbought and oversold conditions) by enhancing the visual clarity of those extremes. It also smooths the curve over a user-defined period in hopes of providing a more consistent signal.
• Dynamic Limits: The dynamic overbought and oversold limits are calculated based on the RSX's recent high and low values. The limits adjust dynamically depending on market conditions, making them more relevant to current price action.
• Slope Display: The slope of the RSX is calculated as the rate of change between the current and previous RSX value. The slope is displayed as dots when the slope exceeds the threshold designated by the user, providing visual cues for momentum shifts.
• Trend Coloring: Optionally, the user can also enable a trend-based display. It is simply based on current value of RSX versus the previous one. If RSX is rising then the trend is bullish, if not, then the trend is bearish.
• Coloring Extremes: Users can configure the RSX to color the chart when prices enter extreme conditions, such as overbought or oversold zones, providing visual cues for market reversals.
█ Attached Chart Notes:
• Top Panel: Enabled dynamic limits, Trend display, standard Jurik RSX with 20 lookback period, and Slope display.
• Middle Panel: Enabled dynamic limits, Extremes display, and standard Jurik RSX with 20 lookback period.
• Bottom Panel: Enabled dynamic limits, Trend display, Inverse Fisher Transform with 14 lookback period and 9 smoothing period. and Slope display.
█ Credits:
Special thanks to Everget for providing the original script. The script was also slightly modified based on updates from outside sources.
█ Disclaimer:
This script is for educational purposes only and should not be considered financial advice. Always conduct your own research and consult a professional before making any trading decisions. Indicator
Goertzel Adaptive JMA T3Hello Fellas,
The Goertzel Adaptive JMA T3 is a powerful indicator that combines my own created Goertzel adaptive length with Jurik and T3 Moving Averages. The primary intention of the indicator is to demonstrate the new adaptive length algorithm by applying it on bleeding-edge MAs.
It is useable like any moving average, and the new Goertzel adaptive length algorithm can be used to make own indicators Goertzel adaptive.
Used Adaptive Length Algorithms
Normalized Goertzel Power: This uses the normalized power of the Goertzel algorithm to compute an adaptive length without the special operations, like detrending, Ehlers uses for his DFT adaptive length.
Ehlers Mod: This uses the Goertzel algorithm instead of the DFT, originally used by Ehlers, to compute a modified version of his original approach, which sticks as close as possible to the original approach.
Scoring System
The scoring system determines if bars are red or green and collects them.
Then, it goes through all collected red and green bars and checks how big they are and if they are above or below the selected MA. It is positive when green bars are under MA or when red bars are above MA.
Then, it accumulates the size for all positive green bars and for all positive red bars. The same happens for negative green and red bars.
Finally, it calculates the score by ((positiveGreenBars + positiveRedBars) / (negativeGreenBars + negativeRedBars)) * 100 with the scale 0–100.
Signals
Is the price above MA? -> bullish market
Is the price below MA? -> bearish market
Usage
Adjust the settings to reach the highest score, and enjoy an outstanding adaptive MA.
It should be useable on all timeframes. It is recommended to use the indicator on the timeframe where you can get the highest score.
Now, follows a bunch of knowledge for people who don't know about the concepts used here.
T3
The T3 moving average, short for "Tim Tillson's Triple Exponential Moving Average," is a technical indicator used in financial markets and technical analysis to smooth out price data over a specific period. It was developed by Tim Tillson, a software project manager at Hewlett-Packard, with expertise in Mathematics and Computer Science.
The T3 moving average is an enhancement of the traditional Exponential Moving Average (EMA) and aims to overcome some of its limitations. The primary goal of the T3 moving average is to provide a smoother representation of price trends while minimizing lag compared to other moving averages like Simple Moving Average (SMA), Weighted Moving Average (WMA), or EMA.
To compute the T3 moving average, it involves a triple smoothing process using exponential moving averages. Here's how it works:
Calculate the first exponential moving average (EMA1) of the price data over a specific period 'n.'
Calculate the second exponential moving average (EMA2) of EMA1 using the same period 'n.'
Calculate the third exponential moving average (EMA3) of EMA2 using the same period 'n.'
The formula for the T3 moving average is as follows:
T3 = 3 * (EMA1) - 3 * (EMA2) + (EMA3)
By applying this triple smoothing process, the T3 moving average is intended to offer reduced noise and improved responsiveness to price trends. It achieves this by incorporating multiple time frames of the exponential moving averages, resulting in a more accurate representation of the underlying price action.
JMA
The Jurik Moving Average (JMA) is a technical indicator used in trading to predict price direction. Developed by Mark Jurik, it’s a type of weighted moving average that gives more weight to recent market data rather than past historical data.
JMA is known for its superior noise elimination. It’s a causal, nonlinear, and adaptive filter, meaning it responds to changes in price action without introducing unnecessary lag. This makes JMA a world-class moving average that tracks and smooths price charts or any market-related time series with surprising agility.
In comparison to other moving averages, such as the Exponential Moving Average (EMA), JMA is known to track fast price movement more accurately. This allows traders to apply their strategies to a more accurate picture of price action.
Goertzel Algorithm
The Goertzel algorithm is a technique in digital signal processing (DSP) for efficient evaluation of individual terms of the Discrete Fourier Transform (DFT). It's particularly useful when you need to compute a small number of selected frequency components. Unlike direct DFT calculations, the Goertzel algorithm applies a single real-valued coefficient at each iteration, using real-valued arithmetic for real-valued input sequences. This makes it more numerically efficient when computing a small number of selected frequency components¹.
Discrete Fourier Transform
The Discrete Fourier Transform (DFT) is a mathematical technique used in signal processing to convert a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency . The DFT provides a frequency domain representation of the original input sequence .
Usage of DFT/Goertzel In Adaptive Length Algorithms
Adaptive length algorithms are automated trading systems that can dynamically adjust their parameters in response to real-time market data. This adaptability enables them to optimize their trading strategies as market conditions fluctuate. Both the Goertzel algorithm and DFT can be used in these algorithms to analyze market data and detect cycles or patterns, which can then be used to adjust the parameters of the trading strategy.
The Goertzel algorithm is more efficient than the DFT when you need to compute a small number of selected frequency components. However, for covering a full spectrum, the Goertzel algorithm has a higher order of complexity than fast Fourier transform (FFT) algorithms.
I hope this can help you somehow.
Thanks for reading, and keep it up.
Best regards,
simwai
---
Credits to:
@ClassicScott
@yatrader2
@cheatcountry
@loxx
Indicator
Variety Step RSI w/ Dynamic Zones [Loxx]Variety Step RSI w/ Dynamic Zones is a stepped RSI calculation with Discontinued Signal Lines. This indicator includes 7 types of RSI to choose from. The addition of the Discontinued Signal Lines allows this indicator to better identify momentum shifts in price so traders have better defined long/short signals.
Enhanced Moving Average Calculation with Stepped Moving Average and the Advantages over Regular RSI
Technical analysis plays a crucial role in understanding and predicting market trends. One popular indicator used by traders and analysts is the Relative Strength Index (RSI). However, an enhanced approach called Stepped Moving Average, in combination with the Slow RSI function, offers several advantages over regular RSI calculations.
█ Stepped Moving Average and Moving Averages:
The Stepped Moving Average function serves as a crucial component in the calculation of moving averages. Moving averages smooth out price data over a specific period to identify trends and potential trading signals. By employing the Stepped Moving Average function, traders can enhance the accuracy of moving averages and make more informed decisions.
Stepped Moving Average takes two parameters:
The current RSI value and a size parameter. It computes the next step in the moving average calculation by determining the upper and lower bounds of the moving average range. It accomplishes this by adjusting the values of smax and smin based on the given RSI and size.
Furthermore, Stepped Moving Average introduces the concept of a trend variable. By comparing the previous trend value with the current RSI and the previous upper and lower bounds, it updates the trend accordingly. This feature enables traders to identify potential shifts in market sentiment and make timely adjustments to their trading strategies.
█ Advantages over Regular RSI:
Enhanced Range Boundaries:
The inclusion of size parameters in Stepped Moving Average allows for more precise determination of the upper and lower bounds of the moving average range. This feature provides traders with a clearer understanding of the potential price levels that can influence market behavior. Consequently, it aids in setting more effective entry and exit points for trades.
Improved Trend Identification:
The trend variable in Stepped Moving Average helps traders identify changes in market trends more accurately. By considering the previous trend value and comparing it to the current RSI and previous bounds, Stepped Moving Average captures trend reversals with greater precision. This capability empowers traders to respond swiftly to market shifts and potentially capture more profitable trading opportunities.
Smoother Moving Averages:
Stepped Moving Average's ability to adjust the moving average range bounds based on trend changes and size parameters results in smoother moving averages. Regular RSI calculations may produce jagged or erratic results due to abrupt market movements. Stepped Moving Average mitigates this issue by dynamically adapting the range boundaries, thereby providing traders with more reliable and consistent moving average signals.
Complementary Functionality with Slow RSI:
Stepped Moving Average and Slow RSI function in harmony to provide a comprehensive trading analysis toolkit. While Stepped Moving Average refines the moving average calculation process, Slow RSI offers a more accurate representation of market strength. The combination of these two functions facilitates a deeper understanding of market dynamics and assists traders in making better-informed decisions.
What is a Discontinued Signal Line (DSL)?
Many indicators employ signal lines to more easily identify trends or desired states of the indicator. The concept of a signal line is straightforward: by comparing a value to its smoothed, slightly lagging state, one can determine the current momentum or state.
The Discontinued Signal Line builds on this fundamental idea by extending it: rather than having a single signal line, multiple lines are used based on the indicator's current value.
The "signal" line is calculated as follows:
When a specific level is crossed in the desired direction, the EMA of that value is calculated for the intended signal line.
When that level is crossed in the opposite direction, the previous "signal" line value is "inherited," becoming a sort of level.
This approach combines signal lines and levels, aiming to integrate the advantages of both methods.
In essence, DSL enhances the signal line concept by inheriting the previous signal line's value and converting it into a level.
Extras
-Alerts
-Signals
Related indicators:
Step RSI
Indicator
Universal MA Trend(Republishing in Open source)
Hello traders,
Many existing moving average indicators have not been satisfactory in terms of the number, types, and length adjustments of moving averages.
Feeling the inconvenience, I created a moving average indicator and collected numerous famous moving averages.
Fortunately, there was a PineCoder "andre_007" who had already compiled various Moving Averages,
so I was able to find a new Moving Average and combine it with the indicator. Here is the link below
Among these, for the JMA, which has not been publicly disclosed, I utilized the source code from PulseWire Wizard everget:
For VIDYA, I also used everget's source code:
And also MAMA / FAMA Coded from Pinescript Wizard everget :
Ehlers MESA Adaptive Moving Averages (MAMA & FAMA)
For Frama, I used the code from nemozny's source code :
Thanks to all these Pinecoders.
---
By using these excellent moving averages together, I found that the simultaneous Up/Down changes of various moving averages with different characteristics tend to be maintained for quite a long time.
Therefore, this indicator not only collects various moving averages but also displays areas with simultaneous trends as background.
An example can be found here:
Furthermore, to prevent the up/down changes of the moving averages due to factors like whipsaws, a smoothing filter has been introduced.
And Also, Alert is able when trend changes.
---
(오픈소스화 후 재발행)
안녕하세요 트레이더여러분.
기존의 이동평균선 지표들은, 이동평균선의 갯수, 종류, 길이조절 등에서 만족스럽지 못한 점들이 많았습니다.
불편함을 느끼고 직접 이동평균선 지표를 만들면서, 유명한 수 많은 이동평균선들을 모았습니다.
그리고 이미 이러한 수많은 이동평균선을 손수 모아서 정리해주신 고마우신 파인코더(andere_007 님)가 있어서, 그 분의 코드를 많이 이용했습니다. 링크는 아래와 같습니다.
이 중 소스가 공개되지 않은 이동평균선 중 JMA는 트레이딩뷰 위자드이신 everget의 소스코드를 이용했습니다.
VIDYA 역시 everget의 소스코드를 이용했습니다.
MAMA와 FAMA의 코드 역시 everget님의 코드를 가져왔습니다.
Ehlers MESA Adaptive Moving Averages (MAMA & FAMA)
Frama는 nemozny님의 코드를 이용했습니다.
의 코드를 이용했습니다.
이 자리를 빌어 위의 파인코더님들께 감사의 말씀을 전합니다.
---
이러한 좋은 이동평균선을 모아서 사용해보니, 다양한 특성을 갖고 있는 이동평균선의 동시적인 Up/Down 변화는 꽤 오랫동안 유지된다는 점을 발견했습니다.
그래서 이 지표는, 위의 여러가지 이동평균선을 모아놓은 것 뿐만 아니라,
그것에서 동시적인 트랜드가 나오는 곳을 배경화면으로 표시해두었습니다.
예시는 다음과 같습니다.
나아가 휩쏘 등으로 이동평균선의 up/down이 바뀌는 것을 막고자, Smoothing 필터도 도입했습니다.
또한 트랜드가 바뀔 때 얼러트가 울리도록, 얼러트 기능을 설정해놓을 수 있게 해놓았으며, 현재 이동평균선과 상태를 보기 쉽도록 테이블을 만들어놓았습니다. Indicator
STD-Filtered Jurik Volty Adaptive TEMA [Loxx]The STD-Filtered Jurik Volty Adaptive TEMA is an advanced moving average overlay indicator that incorporates adaptive period inputs from Jurik Volty into a Triple Exponential Moving Average (TEMA). The resulting value is further refined using a standard deviation filter to minimize noise. This adaptation aims to develop a faster TEMA that leads the standard, non-adaptive TEMA. However, during periods of low volatility, the output may be noisy, so a standard deviation filter is employed to decrease choppiness, yielding a highly responsive TEMA without the noise typically caused by low market volatility.
█ What is Jurik Volty?
Jurik Volty calculates the price volatility and relative price volatility factor.
The Jurik smoothing includes 3 stages:
1st stage - Preliminary smoothing by adaptive EMA
2nd stage - One more preliminary smoothing by Kalman filter
3rd stage - Final smoothing by unique Jurik adaptive filter
Here's a breakdown of the code:
1. volty(float src, int len) => defines a function called volty that takes two arguments: src, which represents the source price data (like close price), and len, which represents the length or period for calculating the indicator.
2. int avgLen = 65 sets the length for the Simple Moving Average (SMA) to 65.
3. Various variables are initialized like volty, voltya, bsmax, bsmin, and vsum.
4. len1 is calculated as math.max(math.log(math.sqrt(0.5 * (len-1))) / math.log(2.0) + 2.0, 0); this expression involves some mathematical transformations based on the len input. The purpose is to create a dynamic factor that will be used later in the calculations.
5. pow1 is calculated as math.max(len1 - 2.0, 0.5); this variable is another dynamic factor used in further calculations.
6. del1 and del2 represent the differences between the current src value and the previous values of bsmax and bsmin, respectively.
7. volty is assigned a value based on a conditional expression, which checks whether the absolute value of del1 is greater than the absolute value of del2. This step is essential for determining the direction and magnitude of the price change.
8. vsum is updated based on the previous value and the difference between the current and previous volty values.
9. The Simple Moving Average (SMA) of vsum is calculated with the length avgLen and assigned to avg.
10. Variables dVolty, pow2, len2, and Kv are calculated using various mathematical transformations based on previously calculated variables. These variables are used to adjust the Jurik Volty indicator based on the observed volatility.
11. The bsmax and bsmin variables are updated based on the calculated Kv value and the direction of the price change.
12. inally, the temp variable is calculated as the ratio of avolty to vsum. This value represents the Jurik Volty indicator's output and can be used to analyze the market trends and potential reversals.
Jurik Volty can be used to identify periods of high or low volatility and to spot potential trade setups based on price behavior near the volatility bands.
█ What is the Triple Exponential Moving Average?
The Triple Exponential Moving Average (TEMA) is a technical indicator used by traders and investors to identify trends and price reversals in financial markets. It is a more advanced and responsive version of the Exponential Moving Average (EMA). TEMA was developed by Patrick Mulloy and introduced in the January 1994 issue of Technical Analysis of Stocks & Commodities magazine. The aim of TEMA is to minimize the lag associated with single and double exponential moving averages while also filtering out market noise, thus providing a smoother, more accurate representation of the market trend.
To understand TEMA, let's first briefly review the EMA.
Exponential Moving Average (EMA):
EMA is a weighted moving average that gives more importance to recent price data. The formula for EMA is:
EMA_t = (Price_t * α) + (EMA_(t-1) * (1 - α))
Where:
EMA_t: EMA at time t
Price_t: Price at time t
α: Smoothing factor (α = 2 / (N + 1))
N: Length of the moving average period
EMA_(t-1): EMA at time t-1
Triple Exponential Moving Average (TEMA):
Triple Exponential Moving Average (TEMA):
TEMA combines three exponential moving averages to provide a more accurate and responsive trend indicator. The formula for TEMA is:
TEMA = 3 * EMA_1 - 3 * EMA_2 + EMA_3
Where:
EMA_1: The first EMA of the price data
EMA_2: The EMA of EMA_1
EMA_3: The EMA of EMA_2
Here are the steps to calculate TEMA:
1. Choose the length of the moving average period (N).
2. Calculate the smoothing factor α (α = 2 / (N + 1)).
3. Calculate the first EMA (EMA_1) using the price data and the smoothing factor α.
4. Calculate the second EMA (EMA_2) using the values of EMA_1 and the same smoothing factor α.
5. Calculate the third EMA (EMA_3) using the values of EMA_2 and the same smoothing factor α.
5. Finally, compute the TEMA using the formula: TEMA = 3 * EMA_1 - 3 * EMA_2 + EMA_3
The Triple Exponential Moving Average, with its combination of three EMAs, helps to reduce the lag and filter out market noise more effectively than a single or double EMA. It is particularly useful for short-term traders who require a responsive indicator to capture rapid price changes. Keep in mind, however, that TEMA is still a lagging indicator, and as with any technical analysis tool, it should be used in conjunction with other indicators and analysis methods to make well-informed trading decisions.
Extras
Signals
Alerts
Bar coloring
Loxx's Expanded Source Types (see below):
Indicator
JFD-Adaptive, GKYZ-Filtered KAMA [Loxx]JFD-Adaptive, GKYZ-Filtered KAMA is a Kaufman Adaptive Moving Average with the option to make it Jurik Fractal Dimension Adaptive. This also includes a Garman-Klass-Yang-Zhang Historical Volatility Filter to reduce noise.
What is KAMA?
Developed by Perry Kaufman, Kaufman's Adaptive Moving Average ( KAMA ) is a moving average designed to account for market noise or volatility . KAMA will closely follow prices when the price swings are relatively small and the noise is low. KAMA will adjust when the price swings widen and follow prices from a greater distance. This trend-following indicator can be used to identify the overall trend, time turning points and filter price movements.
What is Jurik Fractal Dimension?
There is a weak and a strong way to measure the random quality of a time series.
The weak way is to use the random walk index ( RWI ). You can download it from the Omega web site. It makes the assumption that the market is moving randomly with an average distance D per move and proposes an amount the market should have changed over N bars of time. If the market has traveled less, then the action is considered random, otherwise it's considered trending.
The problem with this method is that taking the average distance is valid for a Normal (Gaussian) distribution of price activity. However, price action is rarely Normal, with large price jumps occuring much more frequently than a Normal distribution would expect. Consequently, big jumps throw the RWI way off, producing invalid results.
The strong way is to not make any assumption regarding the distribution of price changes and, instead, measure the fractal dimension of the time series. Fractal Dimension requires a lot of data to be accurate. If you are trading 30 minute bars, use a multi-chart where this indicator is running on 5 minute bars and you are trading on 30 minute bars.
What is Garman-Klass-Yang-Zhang Historical Volatility?
Yang and Zhang derived an extension to the Garman Klass historical volatility estimator that allows for opening jumps. It assumes Brownian motion with zero drift. This is currently the preferred version of open-high-low-close volatility estimator for zero drift and has an efficiency of 8 times the classic close-to-close estimator. Note that when the drift is nonzero, but instead relative large to the volatility , this estimator will tend to overestimate the volatility . The Garman-Klass-Yang-Zhang Historical Volatility calculation is as follows:
GKYZHV = sqrt((Z/n) * sum((log(open(k)/close( k-1 )))^2 + (0.5*(log(high(k)/low(k)))^2) - (2*log(2) - 1)*(log(close(k)/open(2:end)))^2))
Included
Alerts
Signals
Loxx's Expanded Source Types
Bar coloring
Indicator
Indicator
Indicator
CFB-Adaptive Trend Cipher Candles [Loxx]CFB-Adaptive Trend Cipher Candles is a candle coloring indicator that shows both trend and trend exhaustion using Composite Fractal Behavior price trend analysis. To do this, we first calculate the dynamic period outputs from the CFB algorithm and then we injection those period inputs into a correlation function that correlates price input price to the candle index. The closer the correlation is to 1, the lighter the green color until the color turns yellow, sometimes, indicating upward price exhaustion. The closer the correlation is to -1, the lighter the red color until it reaches Fuchsia color indicating downward price exhaustion. Green means uptrend, red means downtrend, yellow means reversal from uptrend to downtrend, fuchsia means reversal from downtrend to uptrend.
What is Composite Fractal Behavior ( CFB )?
All around you mechanisms adjust themselves to their environment. From simple thermostats that react to air temperature to computer chips in modern cars that respond to changes in engine temperature, r.p.m.'s, torque, and throttle position. It was only a matter of time before fast desktop computers applied the mathematics of self-adjustment to systems that trade the financial markets.
Unlike basic systems with fixed formulas, an adaptive system adjusts its own equations. For example, start with a basic channel breakout system that uses the highest closing price of the last N bars as a threshold for detecting breakouts on the up side. An adaptive and improved version of this system would adjust N according to market conditions, such as momentum, price volatility or acceleration.
Since many systems are based directly or indirectly on cycles, another useful measure of market condition is the periodic length of a price chart's dominant cycle, (DC), that cycle with the greatest influence on price action.
The utility of this new DC measure was noted by author Murray Ruggiero in the January '96 issue of Futures Magazine. In it. Mr. Ruggiero used it to adaptive adjust the value of N in a channel breakout system. He then simulated trading 15 years of D-Mark futures in order to compare its performance to a similar system that had a fixed optimal value of N. The adaptive version produced 20% more profit!
This DC index utilized the popular MESA algorithm (a formulation by John Ehlers adapted from Burg's maximum entropy algorithm, MEM). Unfortunately, the DC approach is problematic when the market has no real dominant cycle momentum, because the mathematics will produce a value whether or not one actually exists! Therefore, we developed a proprietary indicator that does not presuppose the presence of market cycles. It's called CFB (Composite Fractal Behavior) and it works well whether or not the market is cyclic.
CFB examines price action for a particular fractal pattern, categorizes them by size, and then outputs a composite fractal size index. This index is smooth, timely and accurate
Essentially, CFB reveals the length of the market's trending action time frame. Long trending activity produces a large CFB index and short choppy action produces a small index value. Investors have found many applications for CFB which involve scaling other existing technical indicators adaptively, on a bar-to-bar basis.
Included
Loxx's Expanded Source Types
Related indicators:
Adaptive Trend Cipher loxx]
Dynamic Zones Polychromatic Momentum Candles
RSI Precision Trend Candles
Indicator
TDI w/ Variety RSI, Averages, & Source Types [Loxx]This hybrid indicator is developed to assist traders in their ability to decipher and monitor market conditions related to trend direction, market strength, and market volatility. Even though comprehensive, the Traders Dynamic Index (TDI) is easy to read and use. This version of TDI has 7 different types of RSI, 38 different types of Moving Averages, 33 source types, and 5 types of signals as well as alerts and coloring. Default RSI type is set to Jurik's RSX. This indicator can be used on any timeframe.
Green/Red line = RSI Price line
White line = Trade Signal line
Dark Green/Red lines = Volatility Band
Yellow line = Market Base Line
Gray dashed lines = Horizontal boundary lines, oversold/overbought
5 Signal Types w/ Alerts
Signal Crosses = Green/Red line crosses over or under White line
Floating Boundary Crosses = Green/Red line crosses over or under upper Dark Green/ lower Red lines
Horizontal Boundary Crosses = Green/Red line crosses over or under Gray dashed upper/lower lines
Floating Middle Crosses = Green/Red line crosses over or under Yellow line
Horizontal Middle Crosses = Green/Red line crosses over or under Gray dashed middle line
Manual Signal Types (no alerts included, this requires manual analysis)
Volatility Band Signals (Dark Green/Red lines) = When the Dark Green/Red lines are expanding, the market is strong and trending. When Dark Green/Red lines are constricting, the market is weak and in a range. When the Dark Green/Red lines are extremely tight in a narrow range, expect an economic announcement or other market condition to spike the market
Beyond these simple signal rules, there are various other signals or methods that can be used to derive long/short/exit signals from TDI included slope of the Green/Red line and bounces off the Yellow line.
Included
Loxx's Expanded Source Types
Loxx's Variety RSI
Loxx's Moving Averages
Signals
Alerts
Bar coloring
Indicator
Indicator
CFB-Adaptive, Jurik DMX Histogram [Loxx]Jurik DMX Histogram is the ultra-smooth, low lag version of your classic DMI indicator. This is a momentum indicator. You can use this indicator standalone or as part of a system with a moving average and a mean reversion indicator. This indicator has both composite fractal behavior adaptive inputs and fixed inputs. The default is CFB adaptive. Dark green means strong push up, dark red, strong push down. Light green means weak push up, and light red means weak push down.
What is the directional movement index?
The directional movement index (DMI) is an indicator developed by J. Welles Wilder in 1978 that identifies in which direction the price of an asset is moving. The indicator does this by comparing prior highs and lows and drawing two lines: a positive directional movement line ( +DI ) and a negative directional movement line ( -DI ). An optional third line, called the average directional index ( ADX ), can also be used to gauge the strength of the uptrend or downtrend.
When +DI is above -DI , there is more upward pressure than downward pressure in the price. Conversely, if -DI is above +DI , then there is more downward pressure on the price. This indicator may help traders assess the trend direction. Crossovers between the lines are also sometimes used as trade signals to buy or sell.
What is Composite Fractal Behavior ( CFB )?
All around you mechanisms adjust themselves to their environment. From simple thermostats that react to air temperature to computer chips in modern cars that respond to changes in engine temperature, r.p.m.'s, torque, and throttle position. It was only a matter of time before fast desktop computers applied the mathematics of self-adjustment to systems that trade the financial markets.
Unlike basic systems with fixed formulas, an adaptive system adjusts its own equations. For example, start with a basic channel breakout system that uses the highest closing price of the last N bars as a threshold for detecting breakouts on the up side. An adaptive and improved version of this system would adjust N according to market conditions, such as momentum, price volatility or acceleration.
Since many systems are based directly or indirectly on cycles, another useful measure of market condition is the periodic length of a price chart's dominant cycle, (DC), that cycle with the greatest influence on price action.
The utility of this new DC measure was noted by author Murray Ruggiero in the January '96 issue of Futures Magazine. In it. Mr. Ruggiero used it to adaptive adjust the value of N in a channel breakout system. He then simulated trading 15 years of D-Mark futures in order to compare its performance to a similar system that had a fixed optimal value of N. The adaptive version produced 20% more profit!
This DC index utilized the popular MESA algorithm (a formulation by John Ehlers adapted from Burg's maximum entropy algorithm, MEM). Unfortunately, the DC approach is problematic when the market has no real dominant cycle momentum, because the mathematics will produce a value whether or not one actually exists! Therefore, we developed a proprietary indicator that does not presuppose the presence of market cycles. It's called CFB (Composite Fractal Behavior) and it works well whether or not the market is cyclic.
CFB examines price action for a particular fractal pattern, categorizes them by size, and then outputs a composite fractal size index. This index is smooth, timely and accurate
Essentially, CFB reveals the length of the market's trending action time frame. Long trending activity produces a large CFB index and short choppy action produces a small index value. Investors have found many applications for CFB which involve scaling other existing technical indicators adaptively, on a bar-to-bar basis.
What is Jurik Volty used in the Juirk Filter?
One of the lesser known qualities of Juirk smoothing is that the Jurik smoothing process is adaptive. "Jurik Volty" (a sort of market volatility ) is what makes Jurik smoothing adaptive. The Jurik Volty calculation can be used as both a standalone indicator and to smooth other indicators that you wish to make adaptive.
What is the Jurik Moving Average?
Have you noticed how moving averages add some lag (delay) to your signals? ... especially when price gaps up or down in a big move, and you are waiting for your moving average to catch up? Wait no more! JMA eliminates this problem forever and gives you the best of both worlds: low lag and smooth lines.
Ideally, you would like a filtered signal to be both smooth and lag-free. Lag causes delays in your trades, and increasing lag in your indicators typically result in lower profits. In other words, late comers get what's left on the table after the feast has already begun.
Included:
Alerts
Loxx's Expanded Source Types
Signals
Bar coloring
Indicator
Indicator
Variety RSI of Fast Discrete Cosine Transform [Loxx]Variety RSI of Fast Discrete Cosine Transform is an RSI indicator with 7 types of RSI that is calculated on the Fast Discrete Cosine Transform of source. The source inputs are 33 different source types from Loxx's Expanded Source Types.
What is Discrete Cosine Transform?
A discrete cosine transform (DCT) expresses a finite sequence of data points in terms of a sum of cosine functions oscillating at different frequencies. The DCT, first proposed by Nasir Ahmed in 1972, is a widely used transformation technique in signal processing and data compression. It is used in most digital media, including digital images (such as JPEG and HEIF, where small high-frequency components can be discarded), digital video (such as MPEG and H.26x), digital audio (such as Dolby Digital, MP3 and AAC), digital television (such as SDTV, HDTV and VOD), digital radio (such as AAC+ and DAB+), and speech coding (such as AAC-LD, Siren and Opus). DCTs are also important to numerous other applications in science and engineering, such as digital signal processing, telecommunication devices, reducing network bandwidth usage, and spectral methods for the numerical solution of partial differential equations.
Fast Discrete Cosine Transform
The algorithm performs a fast cosine transform of the real function defined by nn samples on the real axis.
Depending on the passed parameters, it can be executed both direct and inverse conversion.
Input parameters:
tnn - Number of function values minus one. Should be 1024 degree of two. The algorithm does not check correct value passed.
a - array of Real 1025 Function values.
InverseFCT - the direction of the transformation. True if reverse, False if direct.
Output parameters: a - the result of the transformation. For more details, see description on the site. www.alglib.net
Included:
7 types of RSI
33 source inputs from Loxx's Expanded Source Types
2 types of signals
Alerts
Indicator
Indicator
