# Sinewave Indicator A Statistics concept (Ehlers DSP cluster) in the LuxAlgo Library, with 2 indicator implementations. ## What is the Sinewave Indicator? The Sinewave Indicator is John Ehlers' cycle-timing tool. Instead of smoothing price the way a conventional oscillator does, it estimates the phase of the market's dominant cycle (see [dominant cycle measurement](https://www.luxalgo.com/library/concept/dominant-cycle-measurement/), classically done with the [Hilbert Transform](https://www.luxalgo.com/library/concept/hilbert-transform/)) and plots two lines: the sine of that phase, and a lead line, the sine of the phase advanced by 45 degrees. When price is genuinely cycling, the two lines cross close to cycle troughs and crests, so turns register with little of the lag a fixed-length oscillator carries. Its second property is just as useful: trend detection by silence. In a trending market the phase stops advancing at a steady rate, and the sine and lead lines flatten out and run roughly parallel without crossing. Active, regular crossings say the market is cycling and turn-timing applies; a quiet, uncrossed pair says the market is trending and cycle signals should be stood down. The indicator only anticipates turns when a reasonably stable cycle actually exists, which is why implementations condition the input first. The geometry explains the anticipation. A lagging oscillator must watch price roll over before it can turn; the sinewave pair instead crosses at a fixed phase margin ahead of the cycle extreme, because the lead line runs 45 degrees in front of its sibling. When the phase estimate is clean, the crossing therefore lands before the price turn it predicts, an advance notice bought entirely from the phase measurement rather than from any smoothing trick. The same dependence is the weakness: every degree of jitter in the measured phase translates directly into crossing noise, which is why the indicator inherits the conditioning requirements of the phase engine underneath it. Ehlers published the design within his broader cycle-analysis work around the turn of the millennium, and the Library carries both the classic and its modern descendants. jacobnie2008's Hilbert Sine Wave Support and Resistance projects the measured cycle onto price as adaptive levels; LuxAlgo's Correlated Sine Oscillator estimates cycle position by correlating price against sine shapes rather than through a Hilbert pair; and the Variable Sine Wave Fit goes a step further, fitting a sine of variable period and amplitude directly to price. All inherit the same honest constraint: the message is conditional on a stable cycle existing, and the tool's most reliable output is often its statement that none currently does. ## How to identify the Sinewave Indicator's readings Reading the tool means knowing which of its two modes the market is in; everything else follows. 1. Confirm the input is conditioned: detrended or bandpassed price, since trend leaking into the phase estimate corrupts everything downstream. 2. Locate the phase engine: a Hilbert-based estimator classically, or a correlation-based alternative in newer variants. 3. Watch the pair in cycle mode: regular alternating crossings of the sine and lead lines, arriving slightly ahead of price turns, are the tool working as designed. 4. Recognize trend mode: the two lines flattening and running parallel without crossing is a deliberate signal to stand cycle tactics down. 5. Distrust the boundary: around regime shifts the phase estimate slews, producing crossings that belong to neither mode; conservative use waits for the new mode to establish. ## How traders use it - Timing cycle turns in ranges: crossings of the sine and lead-sine lines flag expected troughs and crests of the measured cycle, so mean-reversion entries can be taken toward the opposite extreme rather than after a lagging oscillator confirms. - As a trend/cycle regime filter: when the two lines stop crossing and run parallel, the market is treated as trending and cycle-based fade signals are disabled. Some traders use the indicator purely for this mode call. - With conditioned input: the phase estimate degrades when trend and noise leak into the measurement, so implementations typically detrend or bandpass price first (a [roofing filter](https://www.luxalgo.com/library/concept/roofing-filter/) is the standard Ehlers preprocessing) before computing the sinewave. - As cycle-anchored support and resistance: projecting the measured cycle's turns onto price yields adaptive levels that shift with the rhythm, the approach packaged in Hilbert sine wave S/R tools. - Through correlation variants: estimating cycle position by [correlating](https://www.luxalgo.com/library/concept/correlation/) price against candidate sine shapes trades the Hilbert machinery for a simpler, sometimes steadier phase read, at the cost of assuming the cycle shape more strongly. ## Sinewave Indicator vs related cycle tools - **Hilbert Transform** (https://www.luxalgo.com/library/concept/hilbert-transform/): The Hilbert transform is the measurement engine, producing per-bar phase and amplitude; the Sinewave Indicator is a display built on that phase. The division of labor matters: most sinewave problems are phase-estimate problems, inherited from the engine rather than the readout. - **FFT/Spectral Analysis** (https://www.luxalgo.com/library/concept/fft-spectral-analysis/): An FFT decomposes a window into its full spectrum, revealing several cycles at once but assuming they held still across the window. The sinewave tracks one dominant cycle live, bar by bar. Survey versus tracker: one maps the terrain, the other follows the target. - **Autocorrelation** (https://www.luxalgo.com/library/concept/autocorrelation/): Autocorrelation methods find the period by matching the series against its own lags, a robust but coarser read that Ehlers himself later favored for period estimation in noise. The sinewave needs finer phase information than autocorrelation provides, which is why the two often cooperate: period from one, timing from the other. ## FAQ ### How is the Sinewave Indicator different from a normal oscillator? A conventional oscillator transforms recent price and therefore lags it. The Sinewave Indicator plots the sine of a measured dominant-cycle phase, so in a cleanly cycling market its crossings can coincide with price turns instead of trailing them. The cost is conditionality: the phase estimate is only meaningful when a stable cycle exists, and the indicator deliberately goes quiet in trends. ### What do the two lines of the Sinewave Indicator represent? One line is the sine of the current dominant-cycle phase; the other is a lead line, the sine of that phase advanced by 45 degrees. Crossings of the pair mark expected cycle turns. When the lines flatten and run parallel without crossing, Ehlers reads the market as trending rather than cycling, which is itself the signal. ### Why is the lead line advanced by 45 degrees? The offset is what moves the crossings ahead of the cycle extremes: with the lead line running a fixed phase margin in front, the pair intersects before the sine itself peaks or troughs, converting phase knowledge into advance notice. Ehlers chose 45 degrees as the practical compromise, enough lead to be useful, small enough that the two lines still describe the same cycle rather than two different ones. ### What cycle lengths can the indicator track? Whatever its phase engine can measure. Hilbert-based implementations inherit the usual chart-scale constraints, roughly 6 to 50 bars in Ehlers' filter designs: shorter cycles are under-sampled, longer ones drift beyond the short quadrature filters' accuracy. The standard escape for slower rhythms is a higher timeframe, where the same bar-count limits cover a longer span of calendar time. ### Does the Sinewave Indicator repaint? The classic causal implementation does not: each bar's phase is estimated from data up to that bar, so history stands. It does jitter, which is different, live values wobble as the phase estimate updates bar to bar. Fitted variants are another matter: a tool that refits a variable sine to the visible window revises its past as the fit updates, and deserves the same live-versus-history skepticism as any refitted curve. ### Is the Sinewave Indicator useful in trending markets? Deliberately not for entries, and that is its second job: the flattened, non-crossing state is the tool's way of reporting that no tradable cycle currently exists. Traders who respect that report use the indicator as a regime gate, enabling cycle tactics only when crossings are regular. Forcing fade entries from a sinewave that has gone quiet is using the tool against its own stated reading. ## Implementations in the Library - Correlated Sine Oscillator (LuxAlgo): https://www.luxalgo.com/library/indicator/correlated-sine-oscillator/ - Variable Sine Wave Fit (LuxAlgo): https://www.luxalgo.com/library/indicator/variable-sine-wave-fit/ ## Related concepts - Dominant Cycle Measurement: https://www.luxalgo.com/library/concept/dominant-cycle-measurement/ - Roofing Filter: https://www.luxalgo.com/library/concept/roofing-filter/ - Decycler: https://www.luxalgo.com/library/concept/decycler/ - Even-better Sinewave: https://www.luxalgo.com/library/concept/even-better-sinewave/ - Adaptive-parameter Technique: https://www.luxalgo.com/library/concept/adaptive-parameter-technique/ - Autocorrelation Periodogram: https://www.luxalgo.com/library/concept/autocorrelation-periodogram/ --- Source: https://www.luxalgo.com/library/concept/sinewave-indicator/ (LuxAlgo Library, the encyclopedia of trading & technical analysis). Free to use with attribution: https://www.luxalgo.com/library/license/