// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("Continuous Wavelet Transform (CWT)", "CWT", overlay=false, precision=6)

//@function Computes CWT magnitude using Morlet wavelet at a given scale
//@param source Series to analyze
//@param scale Wavelet scale parameter (controls frequency resolution)
//@param omega Central frequency of Morlet wavelet (default 6.0)
//@returns CWT magnitude (power) at the specified scale
cwt(series float source, simple float scale, simple float omega) =>
    if scale <= 0.0
        runtime.error("Scale must be greater than 0")
    if omega <= 0.0
        runtime.error("Omega must be greater than 0")

    int halfWin = math.max(1, int(math.round(3.0 * scale)))
    float invScale = 1.0 / scale
    float normFactor = 1.0 / math.sqrt(scale)

    float realSum = 0.0
    float imagSum = 0.0

    for k = -halfWin to halfWin
        float srcVal = nz(source[halfWin - k])
        float t = float(k) * invScale
        float gauss = math.exp(-0.5 * t * t)
        float angle = omega * t
        realSum += srcVal * gauss * math.cos(angle)
        imagSum += srcVal * gauss * math.sin(angle)

    float magnitude = math.sqrt(realSum * realSum + imagSum * imagSum) * normFactor
    magnitude

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

// Inputs
i_source = input.source(close, "Source")
i_scale = input.float(10.0, "Scale", minval=0.5, maxval=200.0, step=0.5,
     tooltip="Wavelet scale — higher values capture lower frequencies")
i_omega = input.float(6.0, "Omega (Central Frequency)", minval=1.0, maxval=20.0, step=0.5,
     tooltip="Morlet central frequency — standard value is 6.0")

// Calculation
cwt_value = cwt(i_source, i_scale, i_omega)

// Plot
plot(cwt_value, "CWT", color.new(color.yellow, 0), 2)