--- title: "Hilbert Transform SineWave: Formula" description: "The Hilbert Transform Sinewave outputs two lines, a sine and a lead sine, computed from the dominant cycle phase that a Hilbert transform measures. It is..." canonical: https://www.getswoopr.com/indicators/cycle-and-signal-processing/hilbert-transform-sinewave/ source: "Swoopr Investment: https://www.getswoopr.com" --- ## Direct Answer > The Hilbert Transform Sinewave outputs two lines, a sine and a lead sine, computed from the dominant cycle phase that a Hilbert transform measures. It is the Hilbert-based implementation of the sine-wave cycle display popularized by John Ehlers. The two lines oscillate between -1 and +1. # Hilbert Transform SineWave: Formula, Meaning, Signals, Examples and How to Use It ## How Is Hilbert Transform SineWave Calculated? The Hilbert Transform Sinewave outputs two lines, a sine and a lead sine, computed from the dominant cycle phase that a Hilbert transform measures. It is the Hilbert-based implementation of the sine-wave cycle display popularized by John Ehlers. **Formula:** `Sine = sin(DCPhase); LeadSine = sin(DCPhase + 45 degrees), with DCPhase taken from the Hilbert transform cycle measurement` **Inputs:** - Close prices - Hilbert transform dominant cycle phase **Worked example.** With a lead of 45 degrees, the sine and lead sine lines cross when the cycle phase is 67.5 degrees, and again 180 degrees later. The inputs are illustrative numbers, not market data. **Reading it.** The two lines oscillate between -1 and +1. A crossing is read as a cycle turning point, and lines that stay close and flat suggest that no dominant cycle is present, so crossings are not informative. **Limits.** It inherits all the noise of the Hilbert phase measurement. During trends the lines whipsaw, and the crossings arrive after the turn they describe. ## What is 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. It is the Hilbert-based implementation of the sine-wave cycle display popularized by John Ehlers. ## How to use Hilbert Transform SineWave The two lines oscillate between -1 and +1. A crossing is read as a cycle turning point, and lines that stay close and flat suggest that no dominant cycle is present, so crossings are not informative. A reading alone is never a buy or sell signal; it needs context from price structure, volume, volatility and the broader market regime. ## Strengths - Computing the lines from phase measured by a Hilbert transform recovers the angle without fitting a single fixed period. - Both lines are bounded between -1 and +1, so they can be drawn in a fixed panel without scale changes. - Reproducible when the formula and data convention are fixed. ## Weaknesses and limitations - The sine is flat near its peaks, so the lines change slowly just where a cycle turns, which blurs the timing near extremes. - Two lines 45 degrees apart cross twice per cycle by construction, so every measured cycle yields crossings whether or not price turned. - Correlated indicators can create false confidence by repeating the same underlying information. ## Editorial and risk note This page is educational content, not individualized investment advice. It should not imply guaranteed prediction, accuracy or outperformance. ## Frequently Asked Questions Is Hilbert Transform SineWave a buy or sell signal? No. The two lines oscillate between -1 and +1. It inherits all the noise of the Hilbert phase measurement. A trade built on it still needs a trigger, an invalidation rule, a position size and realistic execution assumptions. What is the best setting for Hilbert Transform SineWave? Hilbert Transform SineWave is computed from close prices; hilbert transform dominant cycle phase, so the choices that matter are the data convention and the window it is read over. Test those across instruments, regimes and out-of-sample periods instead of fitting one historical winner. Can Hilbert Transform SineWave be used by itself? It inherits all the noise of the Hilbert phase measurement. During trends the lines whipsaw, and the crossings arrive after the turn they describe. For that reason it is read next to measures of direction, participation, valuation, liquidity and risk, not alone. Does Hilbert Transform SineWave work on every timeframe? The calculation (Sine = sin(DCPhase); LeadSine = sin(DCPhase + 45 degrees), with DCPhase taken from the Hilbert transform cycle measurement) can be run on any bar size, but behavior is not portable: a reading on a five-minute chart describes a very different market window from the same reading on a daily chart. Validate the exact timeframe before relying on it. Why does Hilbert Transform SineWave give false signals? The sine is flat near its peaks, so the lines change slowly just where a cycle turns, which blurs the timing near extremes. Two lines 45 degrees apart cross twice per cycle by construction, so every measured cycle yields crossings whether or not price turned. Lag, noise and regime changes add to this, because market participants react to new information after the reading is calculated. How should Hilbert Transform SineWave be backtested? Rebuild Hilbert Transform SineWave from close prices using point-in-time data, write the rules before testing, include delisted securities where relevant, model realistic fills and costs, reserve a validation sample and compare with a simpler baseline. S Swoopr Editorial Team The Swoopr Editorial Team produces independent investment education, research, and tools for understanding markets, evaluating opportunities, and managing risk. All content is educational only and does not constitute personalized investment advice. See our [editorial policy](https://www.getswoopr.com/legal/editorial-policy/) and [corrections policy](https://www.getswoopr.com/legal/corrections-policy/).