Sine Wave

John Ehlers' Hilbert-transform-based phase visualiser (TA-Lib HT_SINE). Takes the dominant-cycle phase of HtDcPhase — the smoothed price correlated with one cycle of the measured dominant period — and returns sin(DCPhase) and the 45° lead sin(DCPhase + 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 (inherited from HtDcPhase)
Interpretation	sin(phase) for chart panel; pair with lead for cross signal

Formula

The phase is the dominant-cycle phase of HtDcPhase: the adaptive Hilbert engine measures the dominant cycle DC (the rounded smoothed period), then the 4-bar smoothed price is correlated with one cycle of a sine and a cosine of that period:

Real     = Σ_{i=0}^{DC−1} sin(360°·i / DC) · SmoothPrice[i]
Imag     = Σ_{i=0}^{DC−1} cos(360°·i / DC) · SmoothPrice[i]
DCPhase  = atan(Real / Imag)                 (degrees; ±90° if |Imag| ≤ 0.001)
DCPhase += 90° + 360° / SmoothPeriod         (offset + smoother-lag correction)
DCPhase += 180°   if Imag < 0                (quadrant fix)
DCPhase −= 360°   if DCPhase > 315°          (wrap)

Sine_t     = sin(DCPhase)
LeadSine_t = sin(DCPhase + 45°)

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.

TA-Lib parity. The sine and the lead sine are identical to TA-Lib HT_SINE (sine, leadsine, to 1e-9) from bar 193 on the 3000-bar TA-Lib reference series. Before that the two start-ups differ — TA-Lib primes its Hilbert state with zeros after a WMA burn-in, Wickra waits for its tap buffers to fill — and the shared recursion then converges.

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 an array.array('d') of the sine line. Node and WASM return the same single sine line.

Warmup

warmup_period() == 50, inherited from HtDcPhase: the first value is emitted on the 50th input (index 49), once the Hilbert engine's moving-average chain has filled. Early outputs are still noisy until the period 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.
• Flat input. A constant series makes Real and Imag exactly zero; the phase takes its degenerate-Imag guard (±90°) and the sine is still defined (flat_input_uses_phase_fallback test).
• Non-finite input. NaN / ±inf returns None without touching state (ignores_non_finite_input test).
• Reset. reset() clears the inner HtDcPhase estimator (its smoothing buffers and period memory), the sine 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])   # row 100: 0.7812038618938434

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. batch only emits sine — for cross signals use streaming update + lead() (available in Rust, Python, Node and WASM).
• 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. The first value arrives on bar 50, but early outputs are noisy while the dominant-period estimate settles; allow extra 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.
• TA-Lib HT_SINE — reference implementation the phase follows.

See also

• HtDcPhase — phase source (HT_DCPHASE).
• HilbertDominantCycle — dominant-period engine.
• Mama — Hilbert-transform phase used for adaptive smoothing.
• FisherTransform — different visualisation of cycle state.
• Indicators-Overview — full taxonomy.