Ehlers Hilbert Transform SineWave

// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("Ehlers Hilbert Transform SineWave (HT_SINE)", "HT_SINE", overlay=false)

//@function Calculates Hilbert Transform SineWave and LeadSine using TA-Lib algorithm
//@param source Series to analyze for dominant cycle
//@returns Tuple [sine, leadsine] - sine wave and lead sine wave (+45° phase lead)
ht_sine(series float source) =>
    var float detrender = 0.0
    var float i1 = 0.0
    var float q1 = 0.0
    var float ji = 0.0
    var float jq = 0.0
    var float i2 = 0.0
    var float q2 = 0.0
    var float re = 0.0
    var float im = 0.0
    var float period = 0.0
    var float smooth_period = 0.0
    var float dc_phase = 0.0

    float price = nz(source)

    // Step 1: WMA smoothing (4-tap: [4,3,2,1]/10)
    float smooth_price = (4.0 * price + 3.0 * nz(price[1]) + 2.0 * nz(price[2]) + nz(price[3])) / 10.0

    // Bandwidth uses period (not smooth_period) per TA-Lib
    float bandwidth = 0.075 * period + 0.54

    // Step 2: Hilbert FIR detrender
    detrender := (0.0962 * smooth_price + 0.5769 * nz(smooth_price[2]) - 0.5769 * nz(smooth_price[4]) - 0.0962 * nz(smooth_price[6])) * bandwidth

    // Step 3: Q1 computation (Hilbert FIR on detrender)
    q1 := (0.0962 * detrender + 0.5769 * nz(detrender[2]) - 0.5769 * nz(detrender[4]) - 0.0962 * nz(detrender[6])) * bandwidth

    // Step 4: I1 = detrender delayed 3 bars
    i1 := nz(detrender[3])

    // Step 5: Advance phase via JI/JQ
    ji := (0.0962 * i1 + 0.5769 * nz(i1[2]) - 0.5769 * nz(i1[4]) - 0.0962 * nz(i1[6])) * bandwidth
    jq := (0.0962 * q1 + 0.5769 * nz(q1[2]) - 0.5769 * nz(q1[4]) - 0.0962 * nz(q1[6])) * bandwidth

    // Step 6: Smooth I2/Q2 with 2-bar EMA
    i2 := 0.2 * (i1 - jq) + 0.8 * nz(i2[1])
    q2 := 0.2 * (q1 + ji) + 0.8 * nz(q2[1])

    // Step 7: Homodyne discriminator
    re := 0.2 * (i2 * nz(i2[1]) + q2 * nz(q2[1])) + 0.8 * nz(re[1])
    im := 0.2 * (i2 * nz(q2[1]) - q2 * nz(i2[1])) + 0.8 * nz(im[1])

    // Step 8: Period from atan (NOT atan2) + rate limiting + clamping
    float prev_period = period
    if math.abs(im) > 1e-12 and math.abs(re) > 1e-12
        float angle = math.atan(im / re)
        if math.abs(angle) > 1e-12
            period := 2.0 * math.pi / angle

    // Rate limit: ±50% bar-to-bar
    if prev_period > 0
        period := math.min(period, 1.5 * prev_period)
        period := math.max(period, 0.67 * prev_period)

    // Clamp to valid range
    period := math.max(6.0, math.min(50.0, period))

    // Step 9: Smooth period with 0.2/0.8 EMA
    period := 0.2 * period + 0.8 * prev_period

    // Step 10: Smooth smoothPeriod with 0.33/0.67 EMA
    smooth_period := 0.33 * period + 0.67 * smooth_period

    // Step 11: DFT-based DC Phase extraction (identical to HT_DCPHASE)
    int dc_period_int = int(smooth_period + 0.5)
    float real_part = 0.0
    float imag_part = 0.0
    for i = 0 to dc_period_int - 1
        float temp_angle = i * 2.0 * math.pi / dc_period_int
        float sp_val = nz(smooth_price[i])
        real_part += math.sin(temp_angle) * sp_val
        imag_part += math.cos(temp_angle) * sp_val

    // Phase from DFT components
    float abs_imag = math.abs(imag_part)
    if abs_imag > 0.0
        dc_phase := math.atan(real_part / imag_part) * (180.0 / math.pi)
    else if abs_imag <= 0.01
        if real_part < 0.0
            dc_phase -= 90.0
        else if real_part > 0.0
            dc_phase += 90.0

    // Phase adjustments per TA-Lib
    dc_phase += 90.0
    dc_phase += 360.0 / smooth_period

    if imag_part < 0.0
        dc_phase += 180.0

    if dc_phase > 315.0
        dc_phase -= 360.0

    // Step 12: Output sine and leadsine from DC Phase (in degrees -> radians for sin)
    float sine = math.sin(dc_phase * math.pi / 180.0)
    float leadsine = math.sin((dc_phase + 45.0) * math.pi / 180.0)
    [sine, leadsine]

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

// Inputs
i_source = input.source(hlc3, "Source")

// Calculation
[sine, leadsine] = ht_sine(i_source)

// Plot
plot(sine, "Sine", color=color.yellow, linewidth=2)
plot(leadsine, "LeadSine", color=color.blue, linewidth=2)
hline(0, "Zero", color=color.gray, linestyle=hline.style_solid)