// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
// Indicator algorithm (C) 2004-2024 John F. Ehlers
indicator("Ehlers Decycler (DECYCLER)", "DECYCLER", overlay=true)

//@function Calculates Ehlers Decycler by subtracting a 2-pole Butterworth high-pass filter from price
//@param source Series to calculate Decycler from
//@param period Cutoff period for the high-pass filter (>= 1)
//@returns Decycler value (source minus high-pass filtered component)
//@optimized Uses 2-pole Butterworth HP with O(1) complexity per bar
decycler(series float source, simple int period) =>

    float src = na(source) ? 0.0 : source

    // Butterworth 2-pole HP coefficient: alpha = (cos(x) + sin(x) - 1) / cos(x)
    // where x = 0.707 * 2pi / period
    float arg = 0.707 * 2.0 * math.pi / period
    float alpha = (math.cos(arg) + math.sin(arg) - 1.0) / math.cos(arg)
    float omah = 1.0 - alpha * 0.5
    float oma = 1.0 - alpha
    float a1 = omah * omah
    float b1 = 2.0 * oma
    float c1 = -(oma * oma)

    // 2-pole HP: HP[n] = a1*(x - 2*x[1] + x[2]) + b1*HP[1] + c1*HP[2]
    float diff_src = nz(src) - 2.0 * nz(src[1]) + nz(src[2])

    var float hp = 0.0
    var float hp1 = 0.0

    float new_hp = bar_index < 2 ? 0.0 : a1 * diff_src + b1 * hp + c1 * hp1

    hp1 := hp
    hp := new_hp

    // Decycler = price - high-pass
    na(source) ? na : src - new_hp

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

// Inputs
i_period = input.int(60, "Period", minval=1, tooltip="Cutoff period for the high-pass filter")
i_source = input.source(close, "Source")

// Calculation
decycler_value = decycler(i_source, i_period)

// Plot
plot(decycler_value, "DECYCLER", color=color.yellow, linewidth=2)