HT_SINE: Hilbert Transform - SineWave

// The MIT License (MIT)
// © mihakralj
//@version=6
indicator("HT_SINE: Hilbert Transform - SineWave", "HT_SINE", overlay=false)

//@function Numerically stable atan2 implementation for quadrant-aware angle calculation
//@param y Y-coordinate (imaginary/quadrature component)
//@param x X-coordinate (real/in-phase component)
//@returns Angle in radians from -π to π
atan2(series float y, series float x) =>
    if y == 0.0 and x == 0.0
        runtime.error("atan2: Both y and x cannot be zero")
    ay = math.abs(y)
    ax = math.abs(x)
    angle = 0.0
    if ax > ay
        angle := math.atan(ay / ax)
    else
        angle := (math.pi / 2.0) - math.atan(ax / ay)
    if x < 0.0
        angle := math.pi - angle
    if y < 0.0
        angle := -angle
    angle

//@function Calculates Hilbert Transform SineWave and LeadSine
//@param source Series to analyze for dominant cycle
//@returns Tuple [sine, leadsine] - sine wave and lead sine wave
ht_sine(series float source) =>
    var float smooth_price = 0.0
    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 = 15.0
    var float smooth_period = 15.0
    var float phase = 0.0
    var float sine = 0.0
    var float leadsine = 0.0
    float price = nz(source)
    float bandwidth = 0.075 * smooth_period + 0.54
    smooth_price := (4.0 * price + 3.0 * nz(price[1]) + 2.0 * nz(price[2]) + nz(price[3])) / 10.0
    detrender := (0.0962 * smooth_price + 0.5769 * nz(smooth_price[2]) - 0.5769 * nz(smooth_price[4]) - 0.0962 * nz(smooth_price[6])) * bandwidth
    q1 := (0.0962 * detrender + 0.5769 * nz(detrender[2]) - 0.5769 * nz(detrender[4]) - 0.0962 * nz(detrender[6])) * bandwidth
    i1 := nz(detrender[3])
    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
    i2 := i1 - jq
    q2 := q1 + ji
    i2 := 0.2 * i2 + 0.8 * nz(i2[1])
    q2 := 0.2 * q2 + 0.8 * nz(q2[1])
    re := i2 * nz(i2[1]) + q2 * nz(q2[1])
    im := i2 * nz(q2[1]) - q2 * nz(i2[1])
    re := 0.2 * re + 0.8 * nz(re[1])
    im := 0.2 * im + 0.8 * nz(im[1])
    if im != 0.0 or re != 0.0
        float angle = atan2(im, re)
        if angle != 0.0
            period := 2.0 * math.pi / angle
    period := math.max(6.0, math.min(50.0, period))
    smooth_period := 0.33 * period + 0.67 * smooth_period
    if i2 != 0.0 or q2 != 0.0
        phase := atan2(q2, i2)
    sine := math.sin(phase)
    leadsine := math.sin(phase + math.pi / 4.0)
    [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)