Inverse Fast Fourier Transform (IFFT)

// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("Inverse Fast Fourier Transform (IFFT)", "IFFT", overlay=true, precision=6)

//@function Spectral filter via forward DFT + frequency zeroing + inverse DFT
//@param source Series to filter
//@param windowSize DFT window size (power of 2: 32, 64, 128)
//@param numHarmonics Number of lowest-frequency harmonics to keep (1..windowSize/2)
//@returns reconstructed (filtered) value at the current bar
//@optimized Forward O(N*H) + inverse O(H); H = numHarmonics
ifft(series float source, simple int windowSize, simple int numHarmonics) =>
    if windowSize != 32 and windowSize != 64 and windowSize != 128
        runtime.error("Window size must be 32, 64, or 128")
    if numHarmonics < 1
        runtime.error("Number of harmonics must be >= 1")

    int N = windowSize
    int halfN = N / 2
    int H = math.min(numHarmonics, halfN)
    float twoPiOverN = 2.0 * math.pi / N

    float dcRe = 0.0
    for n = 0 to N - 1
        float val = nz(source[n])
        float w = 0.5 - 0.5 * math.cos(twoPiOverN * n)
        dcRe += val * w

    float result = dcRe / N

    for k = 1 to H
        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)

        result += 2.0 * re / N

    result

// ---------- 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_harmonics  = input.int(5, "Harmonics", minval=1, maxval=32, tooltip="Number of lowest-frequency components to keep; fewer = smoother")

// Calculation
float filtered = ifft(i_source, i_window, i_harmonics)

// Plot
plot(filtered, "IFFT", color=color.yellow, linewidth=2)