Chebyshev Type II Filter (CHEBY2)

// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("Chebyshev Type II Filter (CHEBY2)", "CHEBY2", overlay=true)

//@function Calculates 2nd Order Chebyshev Type II Lowpass Filter
//@param src Series to calculate Chebyshev filter from
//@param length Cutoff period (related to cutoff frequency)
//@param attenuation Stopband attenuation in decibels (dB) > 0
//@returns Chebyshev Type II filter value
//@optimized Uses IIR 2nd order Chebyshev Type II filter with O(1) complexity per bar
cheby2(series float src, simple int length, simple float attenuation) =>
    float pi = math.pi
    int safe_length = math.max(length, 2)
    float safe_atten = math.max(attenuation, 0.1)
    float wc = 2.0 * pi / safe_length
    float Wc = 2.0 * math.tan(wc / 2.0)
    float epsilon = 1.0 / math.sqrt(math.pow(10.0, safe_atten / 10.0) - 1.0)
    float asinh_inv_eps = math.log(1.0 / epsilon + math.sqrt(1.0 / (epsilon * epsilon) + 1.0))
    float mu = asinh_inv_eps / 2.0
    float sinh_mu = (math.exp(mu) - math.exp(-mu)) / 2.0
    float cosh_mu = (math.exp(mu) + math.exp(-mu)) / 2.0
    float sqrt2 = math.sqrt(2.0)
    float sigma_p = -Wc * sinh_mu / sqrt2
    float omega_p = Wc * cosh_mu / sqrt2
    float omega_z = Wc / math.cos(pi / 4.0)
    float Kp = sigma_p * sigma_p + omega_p * omega_p
    float Kz = omega_z * omega_z
    float DC_gain = Kz / Kp
    float a0_z = 1.0 - 2.0 * sigma_p + Kp
    float a1_z = 2.0 * Kp - 2.0
    float a2_z = 1.0 + 2.0 * sigma_p + Kp
    float b0_z = DC_gain * (1.0 + Kz)
    float b1_z = DC_gain * (2.0 * Kz - 2.0)
    float b2_z = DC_gain * (1.0 + Kz)
    float B0 = b0_z / a0_z
    float B1 = b1_z / a0_z
    float B2 = b2_z / a0_z
    float A1 = a1_z / a0_z
    float A2 = a2_z / a0_z
    float sumB = B0 + B1 + B2
    float sumA = 1.0 + A1 + A2
    float norm = sumA / sumB
    B0 *= norm
    B1 *= norm
    B2 *= norm
    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(10, "Length", minval=2)
i_attenuation = input.float(5.0, "Stopband Attenuation (dB)", minval=0.1, step=1.0)
i_source = input.source(close, "Source")

// Calculation
cheby2_val = cheby2(i_source, i_length, i_attenuation)

// Plot
plot(cheby2_val, "Cheby2", color=color.yellow, linewidth=2)