Cycle & Signal Processing Indicators

Cycle and signal-processing indicators treat a price series as a signal made of a trend, one or more cycles and noise, and use filters borrowed from engineering to separate them: band-pass and high-pass filters, the Hilbert transform, the Fisher transform and John Ehlers' adaptive filters. They estimate the dominant cycle length and phase, or produce a smoothed series with less lag than a moving average.

What do Cycle & Signal Processing indicators have in common?

Every indicator in this category starts from an engineering view of price: a time series is a mixture of components at different frequencies, and the tools that separate frequencies in a radio receiver can separate them in a chart. A moving average is a crude low-pass filter with a lot of lag; the indicators here are designed filters with a chosen pass band and a known lag, which is why most of them carry the name of their designer, John Ehlers, whose published papers describe the mathematics.

The category divides by what it extracts. The cycle estimators (dominant cycle period and phase, the Hilbert transform family, the autocorrelation periodogram, phase accumulation, cycle strength) measure the length and position of the dominant cycle in the recent data. The filters (band-pass, high-pass, roofing filter, decycler, the SuperSmoother, the instantaneous trendline) remove the components that are not wanted, either the trend to leave the cycle or the cycle to leave the trend. The oscillators (cyber cycle, center of gravity, sine wave, even better sinewave, reflex, trendflex, MESA stochastic) turn the filtered cycle into a bounded indicator that can be read for turning points. The Fisher transform reshapes a bounded series so that its extremes are sharper and easier to time.

What they share is the trade-off every filter makes: less lag means less smoothing, and a cycle estimate is only as good as the assumption that a cycle of roughly stable length exists in the data. When the market is trending without a measurable cycle, the cycle tools return a number anyway, which is why several of them come paired with a trend-versus-cycle mode indicator.

How do you choose a Cycle & Signal Processing indicator?

• Decide first whether the market is in cycle mode or trend mode, using the Hilbert transform trend-versus-cycle indicator or the cycle strength reading; cycle tools misfire in a trend
• For a smoothed price with less lag than a moving average, start with the SuperSmoother or the instantaneous trendline rather than a cycle oscillator
• For turning points, use an oscillator whose pass band is set from the measured dominant cycle (the adaptive cyber cycle, MESA stochastic) rather than one with a fixed length
• Apply the roofing filter or a high-pass filter before any oscillator so that the trend and the very short noise do not dominate the reading
• Read the Fisher transform as a sharpener of an existing bounded indicator, not as a signal source on its own

Cycle & Signal Processing indicators at a glance

Indicator	What it measures	How it is read
Hilbert Transform Dominant Cycle Period	Hilbert Transform dominant cycle period is the estimated length, in bars, of the strongest cycle in price, taken from the rate of phase change that the Hilbert transform measures.	Higher values mean longer cycles, so an indicator tuned to this period uses a longer lookback.
Hilbert Transform Dominant Cycle Phase	Hilbert Transform dominant cycle phase is the angle, in degrees, of where the market currently sits within its dominant cycle, as derived from a Hilbert transform.	A steadily advancing phase reflects a steady cycle.
Hilbert Transform Phasor Components	The Hilbert Transform phasor components are the in-phase (I) and quadrature (Q) parts of the price cycle.	The pair is a building block rather than a signal.
Hilbert Transform SineWave	The Hilbert Transform Sinewave outputs two lines, a sine and a lead sine, computed from the dominant cycle phase that a Hilbert transform measures.	The two lines oscillate between -1 and +1.
Hilbert Transform Trend vs Cycle Mode	The Hilbert Transform trend-versus-cycle mode is a binary classifier.	A value of 1 says price is behaving as a trend relative to the measured cycle, so cycle-based oscillators are less appropriate.
Hilbert Transform Instantaneous Trendline	The Hilbert Transform Instantaneous Trendline is a trend estimate built by averaging price over a window equal to the measured dominant cycle period, then applying a short weighted smoothing.	Price above the trendline means price sits above its cycle-neutral average and below means the reverse.
Dominant Cycle Period	Dominant cycle period is the length in bars of the strongest recurring cycle in a price series, found for example from a spectral estimate such as a discrete Fourier transform, an autocorrelation periodogram, or a Hilbert transform.	It is used to set adaptive lookbacks, for instance half the dominant period for an oscillator.
Dominant Cycle Phase	Dominant cycle phase is the position, as an angle from 0 to 360 degrees, of the market within its strongest measured cycle.	Phase that rotates steadily indicates a stable cycle, and where it sits in the circle tells where price is within the swing, for example the bottom, rising half, top and falling half.
Sine Wave Indicator	The Sine Wave indicator plots the sine of the current dominant cycle phase together with a lead line shifted forward by 45 degrees.	Both lines oscillate between -1 and +1.
Ehlers Fisher Transform	The Ehlers Fisher Transform converts a price series that has been normalized to the range -1 to +1 into one with a nearly Gaussian distribution using the inverse hyperbolic tangent.	The line is compared with a one-bar delayed copy, and crossings and sharp peaks at large positive or negative values are read as potential turning points.
Cyber Cycle	The Cyber Cycle is an oscillator from John Ehlers that isolates the cyclic component of price using a smoothing step followed by a two-pole high-pass-style recursion.	The line oscillates around zero.
Roofing Filter	The Roofing Filter is a John Ehlers band-pass construction that chains a high-pass filter and a Super Smoother.	The output swings around zero.
Decycler	The Decycler is a John Ehlers trend indicator made by subtracting a high-pass filtered copy of price from price itself.	The line tracks price at trend scale, and price above it means the high-pass component is positive.
Center of Gravity Oscillator	The Center of Gravity oscillator is a John Ehlers indicator that treats the last N prices as weights on a balance beam and finds the balance point.	The line oscillates in a narrow band, often re-centered around zero by adding (N + 1) / 2.
Ehlers Instantaneous Trendline	The Ehlers Instantaneous Trendline is a low-lag trend filter from John Ehlers' early work.	A rising line indicates upward drift and a falling line downward drift.
Ehlers Super Smoother	The Ehlers Super Smoother is a two-pole recursive low-pass filter, designed by John Ehlers to approximate a Butterworth response.	The filtered line follows price with rounded, noise-free swings.
High-Pass Filter	A high-pass filter removes slow components such as trend and passes short-period fluctuations.	Output oscillates around zero and retains movements shorter than the cutoff.
Band-Pass Filter	A band-pass filter keeps cycles near a chosen center period and attenuates both longer and shorter cycles.	The output oscillates around zero and is strongest when price contains a cycle near the center period.
Autocorrelation Periodogram	The autocorrelation periodogram, popularized by John Ehlers, computes the autocorrelation of a filtered price series at many lags and then takes a discrete Fourier transform of those correlations.	The period with the highest power is the dominant cycle estimate.
Even Better Sinewave	The Even Better Sinewave is a John Ehlers indicator that high-pass filters price, smooths it with a Super Smoother, and divides a 3-bar average of the result by the square root of its 3-bar average power.	Readings near +1 or -1 are the cycle extremes, and zero crossings mark the midpoints.
Reflex Indicator	Reflex is a John Ehlers oscillator that measures how far the smoothed price departs from a straight line drawn between its current and N-bar-ago values.	Positive values show the smoothed series bulging above its own straight-line path across the window and negative values show it sagging below it.
Trendflex Indicator	Trendflex is a John Ehlers oscillator that keeps the trend component of price.	Values above zero mean the smoothed price sits above its recent history on average, values below zero the opposite.
Mesa Stochastic	MESA Stochastic is a John Ehlers refinement that applies the stochastic formula to roofing-filtered data instead of raw price, then smooths it with a Super Smoother.	Values run between 0 and 1, where readings near 1 mean the filtered price is at the top of its recent range and readings near 0 mean the bottom.
Adaptive Cyber Cycle	The Adaptive Cyber Cycle is a version of the Cyber Cycle in which the smoothing constant changes with the measured dominant cycle period, so the filter tunes itself to the cycle length instead of using a fixed value.	It reads like the Cyber Cycle, an oscillator around zero whose turns and crossings with its delayed copy mark local cycle turns.
Smoothing Filter Response	Smoothing filter response is the gain a smoothing filter applies to a cycle of a given period.	A gain of 1 means a cycle passes unchanged and a gain near 0 means it is removed.
Cycle Strength	Cycle strength gauges how dominant the leading cycle is relative to everything else in the series.	Higher values mean one cycle accounts for more of the variation, which is when cycle-based tools are most applicable.
Phase Accumulation	Phase accumulation is a method for measuring the dominant cycle period.	The resulting period is the length in bars of the cycle the method detects, so rising output means the cycle is lengthening.

Each row is the opening sentence of that indicator's own definition and reading, so the table says exactly what the profile says.

What limits do Cycle & Signal Processing indicators share?

A filter has a fixed lag that is known in advance, and reducing it always admits more noise, so there is no setting that is both fast and smooth. Cycle estimators assume a dominant cycle of roughly stable length and will report one whether or not it exists, which makes them unreliable in trending or news-driven markets. The mathematics is published, but the parameters (pass band, smoothing length, lookback) are chosen by the user and the results are sensitive to them, and most of these indicators have no long public performance record outside their designer's own articles.

Frequently Asked Questions

What is a dominant cycle in technical analysis?

The dominant cycle is the periodic component with the most energy in a window of recent prices, measured in bars from one peak to the next. The Hilbert transform, phase accumulation and the autocorrelation periodogram are three different ways to estimate it, and each returns a length and a phase that the adaptive indicators then use to set their own lookback.

How is a signal-processing filter different from a moving average?

A moving average is itself a filter, but one with poor frequency selectivity and a lag of about half its length. Designed filters such as the SuperSmoother or a band-pass filter choose which frequencies to keep and attenuate the rest more sharply, so they can smooth with less lag or isolate a cycle that a moving average would blur.

What does the Fisher transform do?

The Fisher transform converts a bounded series, such as a price normalized to its recent range, into one that is approximately normally distributed. Its extremes become sharper and its turning points more distinct, which is why it is applied to oscillators to time entries; it does not add information, it reshapes what is already there.

Do cycle indicators work in a trending market?

Poorly. A cycle estimator returns a period and a phase whether or not a stable cycle is present, and in a trend its oscillator will signal turns that do not come. The designer's own recommendation is to check the trend-versus-cycle mode indicator first and to use the trend-following tools when the market is in trend mode.