Ehlers Sine Wave (SINE)

// The MIT License (MIT)
// © mihakralj
//@version=6
indicator("Ehlers Sine Wave (SINE)", "SINE", overlay=false)

//@function Calculates Ehlers’ original Sine Wave using a two‑pole High‑Pass, a Super‑Smoother,
//         and a Hilbert‑transform FIR pair (In‑phase I / Quadrature Q).
//@param src Series to calculate the Sine Wave from
//@param hpLength High‑Pass filter length (detrending period)
//@param ssfLength Super‑Smoother filter length (cycle smoothing period)
//@returns single normalized sine‑wave value in [‑1 … +1]
sine(series float src, simple int hpLength, simple int ssfLength) =>
    if hpLength <= 0 or ssfLength <= 0
        runtime.error("Periods must be > 0")
    float pi = 2 * math.asin(1)
    float angHP = 2 * pi / hpLength
    float aHP = (1 - math.sin(angHP)) / math.cos(angHP)
    var float hp = 0.0
    hp := 0.5 * (1 + aHP) * (src - nz(src[1])) + aHP * nz(hp[1])
    float angSSF = math.sqrt(2) * pi / ssfLength
    float aSSF = math.exp(-angSSF)
    float bSSF = 2 * aSSF * math.cos(angSSF)
    float c2 = bSSF
    float c3 = -aSSF * aSSF
    float c1 = 1 - c2 - c3
    var float filt = 0.0
    filt := c1 * (hp + nz(hp[1])) / 2 + c2 * nz(filt[1]) + c3 * nz(filt[2])
    float Q =  0.0962 * nz(filt[3])  + 0.5769 * nz(filt[1])
             - 0.5769 * nz(filt[5])  - 0.0962 * nz(filt[7])
    float I =  filt
    float pwr = I*I + Q*Q
    float sineWave = pwr == 0 ? 0 : I / math.sqrt(pwr)
    math.min(1, math.max(-1, sineWave))

// ---------- Main loop ----------

// Inputs
i_source    = input.source(close,  "Source")
i_hpLength  = input.int(40,        "High‑Pass Filter Length",      minval=1)
i_ssfLength = input.int(10,        "Super‑Smoother Filter Length", minval=1)

// Calculation
sine_wave = sine(i_source, i_hpLength, i_ssfLength)

// Plot
plot(sine_wave, "SINE", color=color.yellow, linewidth=2)
hline(0, "Zero Line", color.gray, linestyle=hline.style_dashed)