Elliptic 2nd Order Filter

// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("Elliptic 2nd Order Filter (ELLIPTIC)", "ELLIPTIC", overlay=true)

//@function Calculates 2nd Order Elliptic Lowpass Filter (Rp=1dB, Rs=40dB)
//@param src Series to calculate Elliptic filter from
//@param length Cutoff period (related to cutoff frequency)
//@returns Elliptic filter value
//@optimized Uses IIR 2nd order Elliptic filter with O(1) complexity per bar
elliptic(series float src, simple int length) =>
    var float C_wz = 2.15499
    var float C_sigma = -0.31323
    var float C_omega_d = 0.90436
    var float C_Kp_norm = 0.91598
    var float C_k = 0.14735
    float pi = math.pi
    int safe_length = math.max(length, 2)
    float Wc = math.tan(pi / safe_length)
    if Wc < 1e-9
        Wc := 1e-9
    float omega_z_scaled = C_wz * Wc
    float sigma_scaled = C_sigma * Wc
    float Kp_scaled = C_Kp_norm * Wc * Wc
    float a0_denom = 1.0 - 2.0 * sigma_scaled + Kp_scaled
    if math.abs(a0_denom) < 1e-9
        a0_denom := 1e-9
    float norm_factor = C_Kp_norm / (C_k * C_wz * C_wz)
    float b0 = norm_factor * C_k * (1.0 + omega_z_scaled * omega_z_scaled) / a0_denom
    float b1 = norm_factor * C_k * (2.0 * omega_z_scaled * omega_z_scaled - 2.0) / a0_denom
    float b2 = b0
    float a1 = (2.0 * Kp_scaled - 2.0) / a0_denom
    float a2 = (1.0 + 2.0 * sigma_scaled + Kp_scaled) / a0_denom
    var float filt = na
    if bar_index < 2
        filt := nz(src, 0.0)
    else
        float s0 = nz(src, 0.0)
        float s1 = nz(src[1], s0)
        float s2 = nz(src[2], s1)
        float f1 = nz(filt[1], s0)
        float f2 = nz(filt[2], f1)
        filt := b0 * s0 + b1 * s1 + b2 * s2 - a1 * f1 - a2 * f2
    filt

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

// Inputs
i_length = input.int(20, "Length", minval=2)
i_source = input.source(close, "Source")

// Calculation
elliptic_val = elliptic(i_source, i_length)

// Plot
plot(elliptic_val, "Elliptic (Rp=1, Rs=40)", color=color.yellow, linewidth=2)