Cycle Spectrogram [LuxAlgo]The Cycle Spectrogram indicator is a spectral analysis tool that visualizes the power of various price cycles to identify dominant periodicities and market rhythms.
🔶 USAGE
The indicator provides a technical visualization of spectral density over time by decomposing price action into multiple cycle bands. This allows traders to identify whether the market is currently influenced by short-term noise or long-term structural cycles.
🔹 Spectrogram Interpretation
The spectrogram consists of 30 rows, each representing a specific cycle period. The vertical axis is logarithmically scaled between the "Minimum Period" and "Maximum Period" settings.
Color Intensity: Brighter or more saturated colors (depending on the selected theme) indicate higher spectral power or "energy" at that specific cycle length. Vertical Position: Higher rows represent longer cycle periods (slower cycles), while lower rows represent shorter periods (faster cycles).
🔹 Dominant Period Tracking
To help identify the most significant cycle at any given time, the script includes a Dominant Period Marker (red cross). This marker tracks the row with the highest energy, providing a real-time estimate of the current market cycle length in bars.
🔹 Dashboard Metrics
A real-time dashboard provides key analytical data:
Current DP: The period (in bars) of the most powerful cycle found in the current bar. Average DP: A 20-period moving average of the dominant period, useful for identifying stable, persistent cycles versus erratic shifts. Lowest Period: A reference for the minimum boundary of the spectral analysis.
🔶 DETAILS
A spectrogram is a visual representation of the spectrum of a signal as it varies with time. This script utilizes a series of Bandpass filters to isolate specific cycle lengths. Each filter is tuned to a period calculated using a logarithmic distribution, ensuring that the analysis covers a wide range of market periodicities without bias toward specific scales.
The "Power" of each cycle is calculated by squaring the output of the bandpass filter and applying a smoothing factor. This process helps filter out transient spikes and provides a cleaner "heat" signature for more reliable cycle identification.
🔶 SETTINGS
🔹 Aesthetics
Theme: Select from several high-contrast color maps, including Viridis, Inferno, Magma, Plasma, Cividis, and Turbo.
🔹 Settings
Minimum Period: The shortest cycle length (in bars) to include in the analysis. Maximum Period: The longest cycle length (in bars) to include in the analysis. Bandwidth: Controls the "focus" or resonance of each cycle band. Lower values result in narrower, more precise detection, while higher values allow for more overlap. Power Smoothing: Determines the amount of smoothing applied to the amplitude. Higher values reduce visual noise but may increase lag in detecting cycle shifts.
🔹 Dashboard
Dashboard: Toggles the visibility of the data table. Position: Moves the dashboard to different corners of the pane. Size: Adjusts the text and cell size of the dashboard. Indicator
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Weighted Fourier Transform: Spectral Gating & Main Frequency🙏🏻 This drop has 2 purposes:
1) to inform every1 who'd ever see it that Weighted Fourier Tranform does exist, while being available nowhere online, not even in papers, yet there's nothing incredibly complicated about it, and it can/should be used in certain cases;
2) to show PulseWire users how they can use it now in dem endevours, to show em what spectral filtering is, and what can they do with all of it in diy mode.
... so we gonna have 2 sections in the description
Section 1: Weighted Fourier Transform
It's quite easy to include weights in Fourier analysis: you just premultiply each datapoint by its corresponding weight -> feed to direct Fourier Transform, and then divide by weights after inverse Fourier transform. Alternatevely, in direct transform you just multiply contributions of each data point to the real and imaginary parts of the Fourier transform by corresponding weights (in accumulation phase), and in inverse transform you divide by weights instead during the accumulation phase. Everything else stays the same just like in non-weighted version.
If you're from the first target group let's say, you prolly know a thing or deux about how to code & about Fourier Transform, so you can just check lines of code to see the implementation of Weighted Discrete version of Fourier Transform, and port it to to any technology you desire. Pine Script is a developing technology that is incredibly comfortable in use for quant-related tasks and anything involving time series in general. While also using Python for research and C++ for development, every time I can do what I want in Pine Script, I reach for it and never touch matlab, python, R, or anything else.
Weighted version allows you to explicetly include order/time information into the operation, which is essential with every time series, although not widely used in mainstream just as many other obvious and right things. If you think deeply, you'll understand that you can apply a usual non-weighted Fourier to any 2d+ data you can (even if none of these dimensions represent time), because this is a geometric tool in essence. By applying linearly decaying weights inside Fourier transform, you're explicetly saying, "one of these dimensions is Time, and weights represent the order". And obviously you can combine multiple weightings, eg time and another characteristic of each datum, allows you to include another non-spatial dimension in your model.
By doing that, on properly processed (not only stationary but Also centered around zero data), you can get some interesting results that you won't be able to recreate without weights:
^^ A sine wave, centered around zero, period of 16. Gray line made by: DWFT (direct weighted Fourier transform) -> spectral gating -> IWFT (inverse weighted Fourier transform) -> plotting the last value of gated reconstructed data, all applied to expanding window. Look how precisely it follows the original data (the sine wave) with no lag at all. This can't be done by using non-weighted version of Fourier transform.
^^ spectral filtering applied to the whole dataset, calculated on the latest data update
And you should never forget about Fast Fourier Transform, tho it needs recursion...
Section 2: About use cases for quant trading, about this particular implementaion in Pine Script 6 (currently the latest version as of Friday 13, December 2k24).
Given the current state of things, we have certain limits on matrix size on PulseWire (and we need big dope matrixes to calculate polynomial regression -> detrend & center our data before Fourier), and recursion is not yet available in Pine Script, so the script works on short datasets only, and requires some time.
A note on detrending. For quality results, Fourier Transform should be applied to not only stationary but also centered around zero data. The rightest way to do detrending of time series
is to fit Cumulative Weighted Moving Polynomial Regression (known as WLSMA in some narrow circles xD) and calculate the deltas between datapoint at time t and this wonderful fit at time t. That's exactly what you see on the main chart of script description: notice the distances between chart and WLSMA, now look lower and see how it matches the distances between zero and purple line in WFT study. Using residuals of one regression fit of the whole dataset makes less sense in time series context, we break some 'time' and order rules in a way, tho not many understand/cares abouit it in mainstream quant industry.
Two ways of using the script:
Spectral Gating aka Spectral filtering. Frequency domain filtering is quite responsive and for a greater computational cost does not introduce a lag the way it works with time-domain filtering. Works this way: direct Fourier transform your data to get frequency & phase info -> compute power spectrum out of it -> zero out all dem freqs that ain't hit your threshold -> inverse Fourier tranform what's left -> repeat at each datapoint plotting the very first value of reconstructed array*. With this you can watch for zero crossings to make appropriate trading decisions.
^^ plot Freq pass to use the script this way, use Level setting to control the intensity of gating. These 3 only available values: -1, 0 and 1, are the general & natural ones.
* if you turn on labels in script's style settings, you see the gray dots perfectly fitting your data. They get recalculated (for the whole dataset) at each update. You call it repainting, this is for analytical & aesthetic purposes. Included for demonstration only.
Finding main/dominant frequency & period. You can use it to set up Length for your other studies, and for analytical purposes simply to understand the periodicity of your data.
^^ plot main frequency/main period to use the script this way. On the screenshot, you can see the script applied to sine wave of period 16, notice how many datapoints it took the algo to figure out the signal's period quite good in expanding window mode
Now what's the next step? You can try applying signal windowing techniques to make it all less data-driven but your ego-driven, make a weighted periodogram or autocorrelogram (check Wiener-Khinchin Theorem ), and maybe whole shiny spectrogram?
... you decide, choice is yours,
The butterfly reflect the doors ...
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Special Time PeriodWith this indicator, you can choose candles in the period you want on your chart.
How ?
• If your chart is 5 minutes, the duration should be greater than 5 on this indicator.
If you do not do it this way, there will be gaps in the price, it will not give the right result.
• If you want to see it in minutes, you must enter a direct numerical value. For example, to see 2 hours, you must enter the number 120. Because 2 hours is 120 minutes.
Like the warning above, if you want to plot a 2-hour chart with this indicator, a maximum of 1 hour should be selected on your main chart.
• Resolution, eg. '60' - 60 minutes, 'D' - daily, 'W' - weekly, 'M' - monthly, '5D' - 5 days, '12M' - one year, '3M' - one quarter
• For example, if you want to see the 2-day chart, you should have a maximum of 1 day chart open on your home screen and write "2D" to the indicator value.
• You will get much better results if the period on your main chart and the period on this indicator are multiples of each other.
• In the image below, the period on the main chart is 30 minutes, but the period on the indicator is 90
• Click on the facing brackets at the top right of the legend and your chart will enlarge.
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Previous Period Levels - X Alerts====== ABOUT THIS INDICATOR
- A simple but highly customisable display of previous higher time-frame
OHLC values, drawn using line.new and label.new. Nothing fancy but...
- Customised resolution input which excludes time frames lower than 1 hour
while extending the common higher reference inputs to include:
• 6, and 12 Hour
• 5 Day
• 3, and 6 Month
• 1 Year
- Alert conditions using an adjustable SMA to help reduce false positive
spam.
- Full visual customisation options for (almost) every aspect, so it can be
tuned to suit most individual preferences.
- In line with the miriad visual customisation options is the ability to
change the display format of the Labels, to show more or less information,
or disable them altogether.
====== REASON FOR STUDY
- To practice advanced user input option handling to allow for a full visual
customisation experience without stepping outside of, or interfering with,
the intended function of the indicator.
- Provide reasonably clear code commenting and structure in order to be
useful as a potential learning aid for others, and future reference for
myself.
====== DISCLAIMER
Any trade decisions you make are entirely your own responsibility.
I've made an effort to squash all the bugs, but you never know!
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[blackcat] L2 Ehlers Phase Accumulator Cycle Period MeasurerLevel: 2
Background
John F. Ehlers introuced Phase Accumulation technique of cycle period measurement in his "Rocket Science for Traders" chapter 7. It is perhaps the easiest to comprehend. In this technique, John Ehlers measures the phase at each sample by taking the arctangent of the ratio of the Quadrature component to the In-phase component. A delta phase is generated by taking the difference of the phase between successive samples. At each sample Dr. Ehlers then looks backward, adding up the delta phases. When the sum of the delta phases reaches 360 degrees (2*pi in pulsewire), we must have passed through one full cycle, on average. The process is repeated for each new sample.
Function
blackcat L2 Ehlers Phase Accumulator Cycle Period Measurer is used to measure Dominant Cycle (DC). This is one of John Ehlers three major methods to measure DC. The Phase Accumulation method of cycle measurement always uses one full cycle’s worth of historical data. This is both an advantage and disadvantage. The advantage is the lag in obtaining the answer scales directly with the cycle period. That is, the measurement of a short cycle period has less lag than the measurement of a longer cycle period. However, the number of samples used in making the measurement means the averaging period is variable with cycle period. Longer averaging reduces the noise level compared to the signal. Therefore, shorter cycle periods necessarily have a higher output Signal-to-Noise Ratio (SNR).
Key Signal
Smooth --> 4 bar WMA w/ 1 bar lag
Detrender --> The amplitude response of a minimum-length HT can be improved by adjusting the filter coefficients by
trial and error. HT does not allow DC component at zero frequency for transformation. So, Detrender is used to remove DC component/ trend component.
Q1 --> Quadrature phase signal
I1 --> In-phase signal
Period --> Dominant Cycle in bars
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 2nd 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. Indicator
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