Chebyshev Type I Filter (CHEBY1)

// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("Chebyshev Type I Filter (CHEBY1)", "CHEBY1", overlay=true)

//@function Calculates 2nd Order Chebyshev Type I Lowpass Filter
//@param src Series to calculate Chebyshev filter from
//@param length Cutoff period (related to cutoff frequency)
//@param ripple Passband ripple in decibels (dB) > 0
//@returns Chebyshev Type I filter value
//@optimized Uses IIR 2nd order Chebyshev Type I filter with O(1) complexity per bar
cheby1(series float src, simple int length, simple float ripple) =>
    float pi = math.pi
    int safe_length = math.max(length, 2)
    float safe_ripple = math.max(ripple, 0.01)
    float wc = 2.0 * pi / safe_length
    float Wc = math.tan(wc / 2.0)
    float epsilon = math.sqrt(math.pow(10.0, safe_ripple / 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 sigma = -sinh_mu * Wc
    float omega_d = cosh_mu * Wc
    float K = sigma * sigma + omega_d * omega_d
    float a0_z = 1.0 - 2.0 * sigma + K
    float a1_z = 2.0 * K - 2.0
    float a2_z = 1.0 + 2.0 * sigma + K
    float b0_z = K
    float b1_z = 2.0 * K
    float b2_z = K
    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
    var float filt = na
    if bar_index < 2
        filt := nz(src, 0.0)
    else
        float ssrc = nz(src, src[1])
        float src1 = nz(src[1], ssrc)
        float src2 = nz(src[2], src1)
        float filt1 = nz(filt[1], ssrc)
        float filt2 = nz(filt[2], filt1)
        filt := B0 * ssrc + B1 * src1 + B2 * src2 - A1 * filt1 - A2 * filt2
    filt

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

// Inputs
i_length = input.int(20, "Length", minval=2)
i_ripple = input.float(1.0, "Passband Ripple (dB)", minval=0.01, step=0.1)
i_source = input.source(close, "Source")

// Calculation
cheby1_val = cheby1(i_source, i_length, i_ripple)

// Plot
plot(cheby1_val, "Cheby1", color=color.yellow, linewidth=2)