// The MIT License (MIT)
// © mihakralj
//@version=6
indicator("Fast Fourier Transform (FFT)", "FFT", overlay=false, precision=2)

//@function Computes dominant cycle period via DFT with Hanning window
//@param source Series to analyze
//@param windowSize DFT window size (power of 2: 32, 64, 128)
//@param minPeriod Minimum detectable cycle period (>= 2)
//@param maxPeriod Maximum detectable cycle period (<= windowSize/2)
//@returns dominant cycle period in bars
//@optimized O(N * N/2) per bar; N=64 → ~2048 multiply-adds
fft(series float source, simple int windowSize, simple int minPeriod, simple int maxPeriod) =>
    if windowSize != 32 and windowSize != 64 and windowSize != 128
        runtime.error("Window size must be 32, 64, or 128")
    if minPeriod < 2
        runtime.error("Min period must be >= 2")
    if maxPeriod > windowSize / 2
        runtime.error("Max period must be <= windowSize / 2")

    int N = windowSize
    int halfN = N / 2
    float twoPiOverN = 2.0 * math.pi / N

    float maxMag = 0.0
    int peakBin = 0
    float peakMagA = 0.0
    float peakMagB = 0.0

    int minBin = math.max(1, N / maxPeriod)
    int maxBin = math.min(halfN, N / minPeriod)

    for k = minBin to maxBin
        float re = 0.0
        float im = 0.0
        float omega_k = twoPiOverN * k
        for n = 0 to N - 1
            float val = nz(source[n])
            float w = 0.5 - 0.5 * math.cos(twoPiOverN * n)
            float xw = val * w
            float angle = omega_k * n
            re += xw * math.cos(angle)
            im -= xw * math.sin(angle)
        float mag = re * re + im * im
        if mag > maxMag
            if peakBin > 0
                peakMagA := maxMag
            maxMag := mag
            peakBin := k
        else if peakBin > 0 and peakMagB == 0.0
            peakMagB := mag

    float dominantPeriod = float(N)
    if peakBin > 0
        float denom = peakMagA + 2.0 * maxMag + peakMagB
        float shift = denom > 0.0 ? (peakMagA - peakMagB) / denom : 0.0
        dominantPeriod := N / (peakBin + shift)

    math.max(float(minPeriod), math.min(float(maxPeriod), dominantPeriod))

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

// Inputs
i_source = input.source(close, "Source")
i_window = input.int(64, "Window Size", options=[32, 64, 128], tooltip="DFT window; larger = finer frequency resolution")
i_minP   = input.int(4, "Min Period", minval=2, maxval=64, tooltip="Shortest cycle to detect (bars)")
i_maxP   = input.int(32, "Max Period", minval=4, maxval=64, tooltip="Longest cycle to detect (bars)")

// Calculation
float period = fft(i_source, i_window, i_minP, i_maxP)

// Plot
plot(period, "Dominant Period", color=color.yellow, linewidth=2)
hline(8, "Fast Cycle", color=color.green, linestyle=hline.style_dashed)
hline(20, "Slow Cycle", color=color.red, linestyle=hline.style_dashed)