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https://github.com/mihakralj/QuanTAlib.git
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Miha Kralj
51 lines
2.7 KiB
Plaintext
51 lines
2.7 KiB
Plaintext
// AMFM: Ehlers AM Detector / FM Demodulator
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// John F. Ehlers — "A Technical Description of Market Data for Traders"
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// TASC, May 2021 (AM + FM) / June 2021 (strategy application)
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// Source: https://www.mesasoftware.com/papers/AMFM.pdf
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//
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// Decomposes price movement into amplitude (AM) and frequency (FM) components
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// using digital signal processing techniques from radio engineering.
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//
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// AM Detector: extracts volatility envelope from whitened spectrum
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// Deriv = Close - Open (whitening — removes DC, handles gaps)
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// Envel = Highest(|Deriv|, 4) (envelope detection)
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// AM = SMA(Envel, 8) (smoothed volatility)
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//
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// FM Demodulator: extracts timing/phase from whitened spectrum
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// Deriv = Close - Open
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// HL = clamp(10 * Deriv, -1, +1) (hard limiter — strips amplitude)
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// FM = SuperSmoother(HL, Period) (integration via 2-pole Butterworth IIR)
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//@version=6
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indicator("AMFM - Ehlers AM Detector / FM Demodulator", shorttitle="AMFM",
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overlay=false, precision=4)
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// ── Inputs ────────────────────────────────────────────────────────────
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int period = input.int(30, "FM Super Smoother Period", minval=1)
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// ── Common: Whitened derivative ───────────────────────────────────────
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float deriv = close - open
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// ── AM Detector ──────────────────────────────────────────────────────
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float envel = ta.highest(math.abs(deriv), 4)
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float am = ta.sma(envel, 8)
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// ── FM Demodulator ───────────────────────────────────────────────────
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// Hard limiter: 10x gain then clamp to ±1 strips all amplitude info
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float hl = math.max(-1.0, math.min(1.0, 10.0 * deriv))
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// Super Smoother (2-pole Butterworth IIR) — integrates the hard-limited signal
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float a1 = math.exp(-1.414 * math.pi / period)
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float b1 = 2.0 * a1 * math.cos(1.414 * math.pi / period)
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float c2 = b1
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float c3 = -(a1 * a1)
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float c1 = 1.0 - c2 - c3
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var float fm = 0.0
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fm := bar_index < 2 ? deriv : c1 * (hl + nz(hl[1])) / 2.0 + c2 * nz(fm[1]) + c3 * nz(fm[2])
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// ── Plots ────────────────────────────────────────────────────────────
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plot(am, "AM", color=color.new(color.orange, 0), linewidth=2)
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plot(fm, "FM", color=color.new(color.aqua, 0), linewidth=2)
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hline(0, "Zero", color=color.gray, linestyle=hline.style_dotted)
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