Ehlers Voss Predictive Filter (VOSS)

// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("Ehlers Voss Predictive Filter (VOSS)", "VOSS", overlay=false)

//@function Ehlers Voss Predictive Filter — negative group delay bandpass predictor
//@param source Series to filter
//@param period Primary cycle period (bars)
//@param predict Prediction bars (negative delay amount)
//@param bandwidth Bandpass tolerance (fraction of period)
//@returns [filt, voss] — bandpass output and predictive filter output
//@optimized Two-pole BPF + weighted feedback predictor, O(Order) per bar
voss(series float src, simple int period, simple int predict, simple float bandwidth) =>
    // --- Filter constants (computed once, recomputed if params change) ---
    var int _order = 0
    var float _f1 = 0.0
    var float _s1 = 0.0
    var int _prev_period = 0
    var int _prev_predict = 0
    var float _prev_bw = 0.0

    if _prev_period != period or _prev_predict != predict or _prev_bw != bandwidth
        _order := 3 * predict
        _f1 := math.cos(2.0 * math.pi / float(period))
        float g1 = math.cos(bandwidth * 2.0 * math.pi / float(period))
        _s1 := 1.0 / g1 - math.sqrt(1.0 / (g1 * g1) - 1.0)
        _prev_period := period
        _prev_predict := predict
        _prev_bw := bandwidth

    // --- Stage 1: Two-pole Bandpass Filter ---
    // Filt = 0.5*(1-S1)*(src - src[2]) + F1*(1+S1)*Filt[1] - S1*Filt[2]
    var float filt = na
    float ssrc = nz(src, src[1])
    float src2 = nz(src[2], ssrc)
    float filt1 = nz(filt[1], 0.0)
    float filt2 = nz(filt[2], 0.0)
    filt := 0.5 * (1.0 - _s1) * (ssrc - src2) + _f1 * (1.0 + _s1) * filt1 - _s1 * filt2
    if bar_index <= 5
        filt := 0.0

    // --- Stage 2: Voss Predictor ---
    // SumC = sum of ((count+1)/Order) * Voss[Order - count] for count = 0 to Order-1
    // Voss = ((3 + Order) / 2) * Filt - SumC
    var float voss_val = na
    float sumC = 0.0
    for count = 0 to _order - 1
        int idx = _order - count
        sumC += (float(count + 1) / float(_order)) * nz(voss_val[idx], 0.0)
    voss_val := (float(3 + _order) / 2.0) * filt - sumC
    [filt, voss_val]

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

// Inputs
i_period    = input.int(20, "Period", minval=2, tooltip="Primary cycle period in bars")
i_predict   = input.int(3, "Predict", minval=1, tooltip="Prediction bars (negative delay)")
i_bandwidth = input.float(0.25, "Bandwidth", minval=0.01, maxval=0.99, step=0.05,
              tooltip="Bandpass tolerance as fraction of period")
i_source    = input.source(close, "Source")

// Calculation
[filt, voss_out] = voss(i_source, i_period, i_predict, i_bandwidth)

// Plot
plot(filt, "Bandpass", color=color.red, linewidth=1)
plot(voss_out, "Voss", color=color.new(color.blue, 0), linewidth=2)
hline(0, "Zero", color=color.gray, linestyle=hline.style_dotted)