Discrete Wavelet Transform (DWT)

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

//@function À trous (stationary) Haar DWT decomposition — returns selected component
//@param src Input series to decompose
//@param levels Number of decomposition levels (1-8, each doubles effective window)
//@param output Which component to return: 0 = approximation at deepest level,
//       1-8 = detail coefficient at that level
//@returns Selected wavelet component (approximation or detail at chosen level)
//@optimized O(levels) per bar using Pine native series indexing, no arrays needed
dwt(series float src, simple int levels, simple int output) =>
    if levels < 1 or levels > 8
        runtime.error("Levels must be between 1 and 8")
    if output < 0 or output > levels
        runtime.error("Output must be 0 (approximation) or 1-levels (detail)")

    float c0 = nz(src, 0.0)

    float c1 = (c0 + nz(src[1], c0)) * 0.5
    float d1 = c0 - c1

    float c2 = levels >= 2 ? (c1 + nz(c1[2], c1)) * 0.5 : c1
    float d2 = levels >= 2 ? c1 - c2 : 0.0

    float c3 = levels >= 3 ? (c2 + nz(c2[4], c2)) * 0.5 : c2
    float d3 = levels >= 3 ? c2 - c3 : 0.0

    float c4 = levels >= 4 ? (c3 + nz(c3[8], c3)) * 0.5 : c3
    float d4 = levels >= 4 ? c3 - c4 : 0.0

    float c5 = levels >= 5 ? (c4 + nz(c4[16], c4)) * 0.5 : c4
    float d5 = levels >= 5 ? c4 - c5 : 0.0

    float c6 = levels >= 6 ? (c5 + nz(c5[32], c5)) * 0.5 : c5
    float d6 = levels >= 6 ? c5 - c6 : 0.0

    float c7 = levels >= 7 ? (c6 + nz(c6[64], c6)) * 0.5 : c6
    float d7 = levels >= 7 ? c6 - c7 : 0.0

    float c8 = levels >= 8 ? (c7 + nz(c7[128], c7)) * 0.5 : c7
    float d8 = levels >= 8 ? c7 - c8 : 0.0

    float approx = levels == 1 ? c1 : levels == 2 ? c2 : levels == 3 ? c3 :
         levels == 4 ? c4 : levels == 5 ? c5 : levels == 6 ? c6 :
         levels == 7 ? c7 : c8

    float result = output == 0 ? approx :
         output == 1 ? d1 : output == 2 ? d2 : output == 3 ? d3 :
         output == 4 ? d4 : output == 5 ? d5 : output == 6 ? d6 :
         output == 7 ? d7 : d8

    result

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

// Inputs
i_source = input.source(close, "Source")
i_levels = input.int(4, "Decomposition Levels", minval=1, maxval=8,
     tooltip="Number of levels — lookback = 2^levels bars")
i_output = input.int(0, "Output Component", minval=0, maxval=8,
     tooltip="0 = approximation (trend), 1-8 = detail at that level (noise/cycles)")

// Calculation
dwt_value = dwt(i_source, i_levels, i_output)

// Plot
plot(dwt_value, "DWT", color.new(color.yellow, 0), 2)
hline(0, "Zero", color=color.gray, linestyle=hline.style_dotted)