Ehlers Roofing Filter (ROOFING)

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

//@function Calculates Ehlers Roofing Filter (2-pole HPF → Super Smoother composite)
//@param source Series to calculate Roofing Filter from
//@param hpLength Cutoff period for the highpass stage (removes trend below this period)
//@param ssLength Cutoff period for the super smoother stage (removes noise above this period)
//@returns Bandpass-filtered value oscillating around zero
//@optimized Uses two cascaded 2-pole IIR filters with O(1) complexity per bar
roofing(series float src, simple int hpLength, simple int ssLength) =>
    var float SQRT2_PI = math.sqrt(2.0) * math.pi

    // --- Stage 1: 2-pole Butterworth Highpass Filter (removes trend) ---
    int safe_hp = math.max(hpLength, 1)
    var float hp_c1 = 0.0
    var float hp_c2 = 0.0
    var float hp_c3 = 0.0
    var int prev_hp = 0
    if prev_hp != safe_hp
        float hp_arg = SQRT2_PI / float(safe_hp)
        float hp_exp_arg = math.exp(-hp_arg)
        hp_c2 := 2.0 * hp_exp_arg * math.cos(hp_arg)
        hp_c3 := -hp_exp_arg * hp_exp_arg
        hp_c1 := (1.0 + hp_c2 - hp_c3) / 4.0
        prev_hp := safe_hp

    var float hp = 0.0
    float ssrc = nz(src, src[1])
    float src1 = nz(src[1], ssrc)
    float src2 = nz(src[2], src1)
    float hp1 = nz(hp[1], 0.0)
    float hp2 = nz(hp[2], 0.0)
    hp := hp_c1 * (ssrc - 2.0 * src1 + src2) + hp_c2 * hp1 + hp_c3 * hp2

    // --- Stage 2: Super Smoother Filter (removes noise from HP output) ---
    int safe_ss = math.max(ssLength, 1)
    var float ss_c1 = 0.0
    var float ss_c2 = 0.0
    var float ss_c3 = 0.0
    var int prev_ss = 0
    if prev_ss != safe_ss
        float ss_arg = SQRT2_PI / float(safe_ss)
        float ss_exp_arg = math.exp(-ss_arg)
        ss_c2 := 2.0 * ss_exp_arg * math.cos(ss_arg)
        ss_c3 := -ss_exp_arg * ss_exp_arg
        ss_c1 := 1.0 - ss_c2 - ss_c3
        prev_ss := safe_ss

    var float roof = 0.0
    float hp_cur = hp
    float hp_prev1 = nz(hp[1], hp_cur)
    roof := ss_c1 * hp_cur + ss_c2 * nz(roof[1], hp_prev1) + ss_c3 * nz(roof[2], nz(hp[2], hp_prev1))
    roof

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

// Inputs
i_hpLength = input.int(48, "HP Length", minval=1, tooltip="Highpass cutoff period — removes cycles longer than this")
i_ssLength = input.int(10, "SS Length", minval=1, tooltip="Super Smoother cutoff period — removes cycles shorter than this")
i_source   = input.source(close, "Source")

// Calculation
roof_val = roofing(i_source, i_hpLength, i_ssLength)

// Plot
plot(roof_val, "Roofing", color=color.yellow, linewidth=2)
hline(0, "Zero", color=color.gray, linestyle=hline.style_dotted)