Sine Wave

John Ehlers' Hilbert-transform-based phase visualiser. Uses the same Hilbert-transform machinery as HilbertDominantCycle to derive the instantaneous phase, then returns sin(phase) and the 45° lead sin(phase + 45°). The two lines cross deep in trends but oscillate rapidly during cycles, providing a visual lead/lag signal.

Quick reference

Item	Value
Family	Ehlers / Cycle (DSP)
Input type	f64
Output type	f64 — the primary sin(phase) line
Output range	[-1, +1]
Default parameters	none — SineWave::new()
Warmup period	~50 bars (Hilbert chain stabilisation)
Interpretation	sin(phase) for chart panel; pair with lead for cross signal

Formula

phase_t  = atan2(im, re)               (from HilbertDominantCycle internals)
sine_t   = sin(phase_t)
lead_t   = sin(phase_t + π/4)           (45° lead)

Only the primary sine is exposed via update; the 45° lead is available via the lead() accessor after each update. See crates/wickra-core/src/indicators/sine_wave.rs.

Parameters

No parameters. SineWave::new() returns a default-constructed indicator; Default is also implemented.

Inputs / Outputs

Indicator<Input = f64, Output = f64> — returns the sin(phase) value:

use wickra::{Indicator, SineWave};

let mut sw = SineWave::new();
let px = 100.0;
let sine = sw.update(px); // Option<f64>

Python: SineWave().batch(prices) returns a 1-D np.ndarray of the sine line. Node and WASM return the same single sine line.

Warmup

~50 bars before stable output (inherits the Hilbert chain warmup). Early outputs are noisy until the phase estimator settles.

Edge cases

• Trending input. Phase rotates slowly; sine and lead closely match each other.
• Cyclical input. Phase rotates rapidly; sine and lead cross frequently, providing the canonical Ehlers cycle-state visual.
• Lead accessor before warmup. lead() returns 0.0 until the indicator has emitted at least one value — it is not None / null, just zero.
• Reset. reset() clears the inner cycle estimator, the smoothing buffers, the phase memory, and the lead value.

Examples

Rust

use wickra::{Indicator, SineWave};

fn main() {
    let prices: Vec<f64> = (0..200)
        .map(|i| 100.0 + (f64::from(i) * 0.4).sin() * 5.0)
        .collect();
    let mut sw = SineWave::new();
    for &p in &prices {
        if let Some(s) = sw.update(p) {
            let l = sw.lead();
            // s, l in [-1, +1]; cross detects momentum shift in cycle regime
        }
    }
}

Python

import numpy as np
import wickra as ta

t = np.arange(200)
prices = 100 + np.sin(t * 0.4) * 5
sw = ta.SineWave()
out = sw.batch(prices)
print('row 100:', out[100])

Node

const wickra = require('wickra');
const sw = new wickra.SineWave();
const prices = Array.from({ length: 200 }, (_, i) => 100 + Math.sin(i * 0.4) * 5);
console.log('row 100:', sw.batch(prices)[100]);

Streaming with lead access

use wickra::{Indicator, SineWave};

let mut sw = SineWave::new();
let mut prev_diff: Option<f64> = None;
let price_stream: Vec<f64> = Vec::new(); // your live price feed
for px in price_stream {
    if let Some(s) = sw.update(px) {
        let l = sw.lead();
        let diff = l - s;
        if let Some(p) = prev_diff {
            if p < 0.0 && diff > 0.0 { /* lead crossed above sine — bullish */ }
            if p > 0.0 && diff < 0.0 { /* lead crossed below sine — bearish */ }
        }
        prev_diff = Some(diff);
    }
}

Interpretation

• Cycle vs trend regime. When sine and lead track close to each other, the market is trending; when they oscillate independently and cross frequently, the market is in a cycle.
• Cross direction. lead crossing above sine is a bullish cycle-momentum signal (the cycle is bottoming); lead below sine is bearish.
• Saturation. When both lines saturate near ±1 for an extended period, the market is in a strong trend and cycle-based signals shouldn't be used.

Common pitfalls

• Trading the primary sine alone. The point of the indicator is the sine/lead pair. Reading the bindings, only sine is emitted from batch — for cross signals you must use streaming update + lead() in Rust, not the binding APIs.
• Treating it like an oscillator. This is a phase-state visualiser, not an overbought/oversold tool. ±0.8 is not "extreme" — it's just where the phase is right now.
• Warmup expectations. Early outputs are noisy. Wait at least 50 bars before treating signals as actionable.

References

• John F. Ehlers, Rocket Science for Traders (2001), ch. 9 — original Sine Wave indicator.
• John F. Ehlers, Cybernetic Analysis for Stocks and Futures (2004) — refinements and practical usage.

See also

• HilbertDominantCycle — phase source.
• Mama — uses the same phase for adaptive smoothing.
• FisherTransform — different visualisation of cycle state.
• Indicators-Overview — full taxonomy.