// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("Ehlers Hann-Windowed RSI (RSIH)", "RSIH", overlay = false)

//@function Ehlers Hann-Windowed RSI — a zero-mean RSI variant using Hann window
//          coefficients to weight price differences. Produces a bounded [-1, +1]
//          oscillator with inherent smoothing via the Hann window. FIR filter.
//@param source Series to analyze
//@param period Lookback window for RSI calculation (>= 1)
//@returns RSIH oscillator value [-1, +1]
//@reference Ehlers, J.F. (2022). "(Yet Another) Improved RSI."
//           Technical Analysis of Stocks & Commodities, Jan 2022.
//@optimized O(N) per bar — FIR scan over Hann-weighted window
rsih(series float source, simple int period) =>
    if period < 1
        runtime.error("Period must be at least 1")

    float price = nz(source)

    // --- Hann window coefficients precomputed per bar ---
    float angle_step = 2.0 * math.pi / (period + 1)
    float cu = 0.0
    float cd = 0.0

    for k = 1 to period
        float newer = nz(source[k - 1])
        float older = nz(source[k])
        float diff = newer - older
        float w = 1.0 - math.cos(angle_step * k)
        if diff > 0
            cu += w * diff
        if diff < 0
            cd += w * (-diff)

    float result = (cu + cd) != 0.0 ? (cu - cd) / (cu + cd) : 0.0
    result

// ── Inputs ──
int   p_period = input.int(14, "Period", minval = 1)
float p_src    = input.source(close, "Source")

// ── Calculation ──
float out = rsih(p_src, p_period)

// ── Plot ──
plot(out, "RSIH", color.yellow, 2)
hline(0, "Zero", color.gray)
hline(0.5, "+0.5", color.new(color.red, 60))
hline(-0.5, "-0.5", color.new(color.green, 60))