Ehlers Laguerre Filter

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

//@function Calculates Laguerre Filter using 4 cascaded all-pass IIR elements
//@param source Series to calculate Laguerre filter from
//@param gamma Damping factor controlling smoothing (0 = FIR, higher = more smoothing)
//@returns Laguerre filter value with frequency-dependent smoothing
//@optimized Uses 4-element all-pass cascade with O(1) complexity per bar
laguerre(series float src, simple float gamma) =>
    var float L0 = 0.0
    var float L1 = 0.0
    var float L2 = 0.0
    var float L3 = 0.0
    var float pL0 = 0.0
    var float pL1 = 0.0
    var float pL2 = 0.0
    var bool initialized = false
    float ssrc = nz(src, src[1])
    if not initialized
        L0 := ssrc
        L1 := ssrc
        L2 := ssrc
        L3 := ssrc
        pL0 := ssrc
        pL1 := ssrc
        pL2 := ssrc
        initialized := true
    else
        pL0 := L0
        pL1 := L1
        pL2 := L2
        float omg = 1.0 - gamma
        L0 := omg * ssrc + gamma * pL0
        L1 := -gamma * L0 + pL0 + gamma * pL1
        L2 := -gamma * L1 + pL1 + gamma * pL2
        L3 := -gamma * L2 + pL2 + gamma * L3
    float filt = (L0 + 2.0 * L1 + 2.0 * L2 + L3) / 6.0
    filt

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

// Inputs
i_gamma = input.float(0.8, "Gamma", minval=0.0, maxval=0.99, step=0.01)
i_source = input.source(close, "Source")

// Calculation
laguerre_val = laguerre(i_source, i_gamma)

// Plot
plot(laguerre_val, "Laguerre", color=color.yellow, linewidth=2)