[blackcat] L2 Ehlers DFT Spectral Estimate

6 nov 2020

Level: 2

Background

John F. Ehlers introduced DFT Spectral Estimate in his "Cycle Analytics for Traders" chapter 9 on 2013.


Function

The DFT is accomplished by correlating the data with the cosine and sine of each period of interest over the selected window period. The sum of the squares of each of these correlated values represents the relative power at each period. The only user input is whether to select Spectral Dilation compensation. The default selection is NOT to use the compensation.

The spectrum values vary between 0 and 1 after being normalized. These values are converted to colors. When the spectrum is greater than 0.5 the colors combine red and yellow, with yellow being the result when spectrum = 1 and red being the result when the spectrum = 0.5. When the spectrum is less than 0.5, the red saturation is decreased, with the result that the color is black when spectrum = 0.


Key Signal


DominantCycle --> Dominant Cycle signal


Pros and Cons

100% John F. Ehlers definition translation of original work, even variable names are the same. This help readers who would like to use pine to read his book. If you had read his works, then you will be quite familiar with my code style.


Remarks

The 51th script for Blackcat1402 John F. Ehlers Week publication.


Readme

In real life, I am a prolific inventor. I have successfully applied for more than 60 international and regional patents in the past 12 years. But in the past two years or so, I have tried to transfer my creativity to the development of trading strategies. Tradingview is the ideal platform for me. I am selecting and contributing some of the hundreds of scripts to publish in Tradingview community. Welcome everyone to interact with me to discuss these interesting pine scripts.

The scripts posted are categorized into 5 levels according to my efforts or manhours put into these works.

Level 1 : interesting script snippets or distinctive improvement from classic indicators or strategy. Level 1 scripts can usually appear in more complex indicators as a function module or element.

Level 2 : composite indicator/strategy. By selecting or combining several independent or dependent functions or sub indicators in proper way, the composite script exhibits a resonance phenomenon which can filter out noise or fake trading signal to enhance trading confidence level.

Level 3 : comprehensive indicator/strategy. They are simple trading systems based on my strategies. They are commonly containing several or all of entry signal, close signal, stop loss, take profit, re-entry, risk management, and position sizing techniques. Even some interesting fundamental and mass psychological aspects are incorporated.

Level 4 : script snippets or functions that do not disclose source code. Interesting element that can reveal market laws and work as raw material for indicators and strategies. If you find Level 1~2 scripts are helpful, Level 4 is a private version that took me far more efforts to develop.

Level 5 : indicator/strategy that do not disclose source code. private version of Level 3 script with my accumulated script processing skills or a large number of custom functions. I had a private function library built in past two years. Level 5 scripts use many of them to achieve private trading strategy.

24 nov 2020

Note di rilascio

I use low resolution to cover more area of heat map in compliance with tradingview server side max 64 plots limitation.

14 apr

Note di rilascio

OVERVIEW
The Ehlers Discrete Fourier Transform Spectral Estimate is an advanced technical analysis tool that identifies market cycles and their dominant frequencies using discrete Fourier transform (DFT) techniques.

FUNCTIONALITY

This indicator performs the following key operations:

Applies dual filtering to remove noise and trends
Calculates spectral estimates using DFT
Identifies dominant cycle periods
Visualizes cycle strength through color-coded bars
INPUT PARAMETERS

• SpectralDilationCompensation: Toggle for amplitude compensation based on cycle period

HOW TO USE

Add the indicator to your chart

Adjust SpectralDilationCompensation as needed:
• Enable for better accuracy in longer cycles
• Disable for simpler interpretation

Interpret the results:
• Color intensity indicates cycle strength
• White line shows dominant cycle period
• Yellow-red spectrum represents positive correlation

INTERPRETATION

• Strong colors indicate significant cyclic activity
• Sharp color transitions suggest potential cycle changes
• Dominant cycle line helps identify primary market rhythm

LIMITATIONS

• Requires sufficient historical data
• Performance may vary in non-cyclical markets
• Results depend on proper parameter settings

NOTES

• Uses highpass and super smoother filtering techniques
• Spectral estimates are normalized between 0 and 1
• Color intensity varies based on spectral power

THANKS

This implementation is based on Ehlers' original work and has been adapted for TradingView's Pine Script platform.