// The MIT License (MIT)
// © mihakralj
//@version=6
indicator("Ehlers Hilbert Transform Instantaneous Trend (HTIT)", "HTIT", overlay=true)

//@function Calculates the Hilbert Transform Instantaneous Trendline (HTIT)
//@param source Series to calculate HTIT from
//@returns HTIT value using Hilbert Transform with adaptive period estimation
//@optimized Uses Hilbert Transform quadrature components for O(1) complexity per bar
htit(series float source) =>
    var float price = na
    var float smooth = na
    var float detrender = 0.0
    var float I1 = 0.0
    var float Q1 = 0.0
    var float I2 = 0.0
    var float Q2 = 0.0
    var float Re = 0.0
    var float Im = 0.0
    var float periodEst = 10.0
    var float iTrend = na
    var float iTrend1 = na
    var float iTrend2 = na
    float result = na
    price := (4 * source + 3 * source[1] + 2 * source[2] + source[3]) / 10
    smooth := (4 * price + 3 * price[1] + 2 * price[2] + price[3]) / 10
    float padAdj = 0.075 * periodEst + 0.54
    detrender := (0.0962 * smooth + 0.5769 * smooth[2] - 0.5769 * smooth[4] - 0.0962 * smooth[6]) * padAdj
    I1 := nz(detrender[3])
    Q1 := (0.0962 * detrender + 0.5769 * detrender[2] - 0.5769 * detrender[4] - 0.0962 * detrender[6]) * padAdj
    float jI = (0.0962 * I1 + 0.5769 * I1[2] - 0.5769 * I1[4] - 0.0962 * I1[6]) * padAdj
    float jQ = (0.0962 * Q1 + 0.5769 * Q1[2] - 0.5769 * Q1[4] - 0.0962 * Q1[6]) * padAdj
    I2 := 0.2 * (I1 - jQ) + 0.8 * nz(I2[1])
    Q2 := 0.2 * (Q1 + jI) + 0.8 * nz(Q2[1])
    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])
    float newP = Im != 0 and Re != 0 ? 2 * math.pi / math.atan(Im / Re) : periodEst
    periodEst := math.max(6, math.min(50, 0.2 * newP + 0.8 * periodEst))
    float angle = I1 != 0 ? math.atan(Q1 / I1) : math.pi / 2 * math.sign(Q1)
    angle += I1 < 0 ? math.pi : Q1 < 0 and I1 > 0 ? 2 * math.pi : 0
    angle := angle % (2 * math.pi)
    float trendPower = math.sqrt(I1 * I1 + Q1 * Q1)
    float newITrendComponent = smooth + 0.07 * trendPower * math.sin(angle)
    float currentITrend2 = nz(iTrend1[1], smooth)
    float currentITrend1 = nz(iTrend[1], smooth)
    float currentITrend = 0.9 * newITrendComponent + 1.1 * currentITrend1 - 1.0 * currentITrend2
    iTrend2 := currentITrend1
    iTrend1 := currentITrend
    iTrend := currentITrend
    result := currentITrend
    result

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

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

// Calculation
htit_value = htit(i_source)

// Plot
plot(htit_value, "HTIT", color=color.yellow, linewidth=2)