// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("Lanczos (Sinc) Window Moving Average (LANCZOS)", "LANCZOS", overlay=true)

//@function Calculates LANCZOS using sinc window weighting
//@param source Series to calculate LANCZOS from
//@param period Lookback period - FIR window size
//@returns LANCZOS value, calculates from first bar using available data
//@reference Lanczos, C. (1956). "Applied Analysis." Prentice-Hall.
lanczos(series float source, simple int period) =>
    if period < 2
        runtime.error("Period must be at least 2")

    float price = nz(source)

    // --- Circular buffer for rolling window ---
    var array<float> buffer = array.new_float(period, na)
    var int head = 0
    array.set(buffer, head, price)
    head := (head + 1) % period

    // --- Precompute Lanczos (sinc) window weights once ---
    // w(k) = sinc(2k/(N-1) - 1), sinc(x) = sin(pi*x)/(pi*x), sinc(0) = 1
    var array<float> weights = array.new_float(0)
    if barstate.isfirst
        float nm1 = (period - 1) * 1.0
        float wsum = 0.0
        for k = 0 to period - 1
            float x = nm1 > 0 ? (2.0 * k / nm1) - 1.0 : 0.0
            float pix = math.pi * x
            // Ternary guarantees lazy evaluation — avoids 0/0 when pix≈0
            float w = math.abs(pix) < 1e-8 ? 1.0 : math.sin(pix) / pix
            array.push(weights, w)
            wsum += w
        // Normalize weights to sum = 1
        if wsum > 1e-15
            for j = 0 to period - 1
                array.set(weights, j, array.get(weights, j) / wsum)

    int count = math.min(bar_index + 1, period)
    if count < period
        price
    else
        // --- Apply Lanczos window convolution via circular buffer ---
        // Buffer: head points to next-write = oldest entry
        // Weight[0] = oldest bar, Weight[period-1] = newest
        float result = 0.0
        for j = 0 to period - 1
            int idx = (head + j) % period
            float val = nz(array.get(buffer, idx))
            result += val * array.get(weights, j)
        result

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

// Inputs
i_period = input.int(14, "Period", minval=2)
i_source = input.source(close, "Source")

// Calculation
lanczos_value = lanczos(i_source, i_period)

// Plot
plot(lanczos_value, "LANCZOS", color=color.yellow, linewidth=2)