mirror of
https://github.com/mihakralj/QuanTAlib.git
synced 2026-08-13 16:18:05 +00:00
76 lines
2.8 KiB
Plaintext
76 lines
2.8 KiB
Plaintext
// 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)
|