EDCF: Ehlers Distance Coefficient Filter

// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("EDCF: Ehlers Distance Coefficient Filter", "EDCF", overlay = true)

//@function Calculates Ehlers Distance Coefficient Filter using distance-weighted FIR
//@param source Series to calculate EDCF from
//@param length Filter window length (>= 2)
//@returns Distance-weighted filter value
//@optimized Uses distance-squared coefficients with O(n²) complexity per bar

// ——— Inputs ———
int    p_length = input.int(15, "Length", minval = 2, maxval = 50,
                            tooltip = "Filter window length. Larger = smoother but more lag.")
string p_source = input.string("HL2", "Source",
                               options = ["Close", "HL2", "HLC3", "OHLC4", "Open", "High", "Low"])

// ——— Source selector ———
float src = switch p_source
    "Close" => close
    "HL2"   => hl2
    "HLC3"  => hlc3
    "OHLC4" => ohlc4
    "Open"  => open
    "High"  => high
    "Low"   => low

// ——— Distance Coefficient Filter ———
// Reference: John F. Ehlers, "Ehlers Filters" (MESA Software)
//            John F. Ehlers, "Nonlinear Ehlers Filters" (S&C V.19:4, pp.25-34)
//
// Algorithm:
//   For each sample position i in [0, Length-1]:
//     Distance2[i] = Σ (Price[i] - Price[i + k])^2  for k = 1 to Length-1
//   Coef[i] = Distance2[i]
//   Filter = Σ(Coef[i] * Price[i]) / Σ(Coef[i])
//
// When prices are flat, all coefficients are equal → degenerates to SMA.
// When prices shift rapidly, distant points get higher weights → faster response.
// Uses sum of squares (not sqrt of sum of squares) to heighten filter response.

edcf(float source, int length) =>
    float sumCoef = 0.0
    float num     = 0.0

    for count = 0 to length - 1
        // Compute distance-squared coefficient for this sample position
        float dist2 = 0.0
        for lookBack = 1 to length - 1
            float diff = source[count] - source[count + lookBack]
            dist2 += diff * diff
        // The distance-squared value IS the coefficient
        float coef = dist2
        sumCoef += coef
        num     += coef * source[count]

    // Normalized weighted average; fallback to current price if all coefficients zero
    float result = sumCoef != 0.0 ? num / sumCoef : source
    result

// ——— Compute ———
float filt = edcf(src, p_length)

// ——— Plot ———
plot(filt, "EDCF", color = color.yellow, linewidth = 2)