B.11: LUT-кривая уровень->маска извлечена (rmse 0.072 dB, 36 точек, 3 уровня): коллапс dual+t1kq+t1k на ОДНУ кривую x=log10(L0/res); степенной закон C~L0^p НЕ работает на 0dB (p_eff 0.19 vs 0.085) - LUT насыщающая gamma из FUN_180563440 (param_1+0x188); форма резонанса стабильна; model_lut.py канонический + roadmap B.11

2026-08-18 13:02:56 +03:00
parent 9abecb60d5
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+#!/usr/bin/env python3
+"""fit_level.py — расширенная B.10: три уровня входа (0, -7, -18 dBFS).
+
+Проверяем, что резонансная форма |2B/A| одна для всех уровней, а глубина
+масштабируется законом C(dB). Вопрос: степенной ли закон C ~ L0^p или
+экспоненциальный по dB C ~ 10^(dB/k) с k=dB-независимым?
+"""
+import numpy as np
+from scipy.optimize import least_squares
+
+FS = 44100.0
+DEPTH = 0.8639736175537109
+
+QS = [0.1, 0.2, 0.3, 0.5, 0.7, 1.0, 1.5, 2.0, 3.0, 5.0, 10.0]
+DUAL = np.array([(10.220, 15.224), (10.219, 13.963), (10.219, 12.947),
+                 (10.219, 11.725), (10.218, 11.119), (10.216, 10.689),
+                 (10.210, 10.412), (10.203, 10.305), (10.182, 10.225),
+                 (10.113, 10.183), (9.822, 10.165)])
+FCS = [800.0, 900.0, 950.0, 1000.0, 1050.0, 1100.0, 1200.0]
+# измеренные (компонент-корреляция 1к, надёжно):
+T1KQ = np.array([7.868, 8.536, 8.726, 8.788, 8.729, 8.575, 8.115])   # -18.06 dB
+T1K  = np.array([14.548, 15.332, 15.553, 15.626, 15.557, 15.378, 14.840])  # 0 dB
+L_DUAL = 10 ** (-7.142 / 20)
+L_T1KQ = 10 ** (-18.063 / 20)
+L_T1K  = 1.0
+
+
+def res_at(f_tone, fc, Q, gain):
+    w0 = fc * 2 * np.pi / FS
+    c, s = np.cos(w0), np.sin(w0)
+    p = (s * 0.5) / Q
+    a, a2 = p * gain, p / gain
+    A = [a + 1, -2 * c, 1 - a]
+    B = [a2 + 1, -2 * c, 1 - a2]
+    w = 2 * np.pi * f_tone / FS
+    z = np.exp(-1j * w)
+    return np.abs(2.0 * (B[0] + B[1] * z + B[2] * z * z) /
+                  (A[0] + A[1] * z + A[2] * z * z))
+
+
+def model(p):
+    Q, gain, p0, p1, D0, t1000 = p          # p(dB) = p0 + p1*dB
+    out = []
+    for q in QS:
+        for f in (500.0, 2000.0):
+            r = res_at(f, 500, q, gain)
+            tilt = t1000 if f == 2000 else 1.45
+            c = DEPTH * tilt * D0 * (L_DUAL / r) ** (p0 + p1 * (-7.142))
+            out.append(-20 * np.log10(max(1 - c, 1e-9)))
+    for i, fc in enumerate(FCS):
+        r = res_at(1000, fc, 0.9999978, gain)
+        c = DEPTH * t1000 * D0 * (L_T1KQ / r) ** (p0 + p1 * (-18.063))
+        out.append(-20 * np.log10(max(1 - c, 1e-9)))
+        c = DEPTH * t1000 * D0 * (L_T1K / r) ** p0
+        out.append(-20 * np.log10(max(1 - c, 1e-9)))
+    return np.array(out)
+
+
+def run():
+    meas = np.array(list(DUAL.ravel()) + list(T1KQ) + list(T1K))
+    x0 = [0.9, 4.24, 0.085, 0.003, 0.5, 1.454]
+    r = least_squares(lambda p: model(p) - meas, x0,
+                      bounds=([0.1, 0.5, 0.0, -0.01, 0.01, 0.3],
+                              [5, 12, 0.3, 0.02, 5, 5]),
+                      max_nfev=10000, xtol=1e-12, ftol=1e-12)
+    Q, gain, p0, p1, D0, t1000 = r.x
+    rmse = np.sqrt(np.mean((model(r.x) - meas) ** 2))
+    print(f'FIT rmse={rmse:.4f} dB  Q={Q:.3f} gain={gain:.3f} '
+          f'p(dB)={p0:.4f}{p1:+.4f}*dB  D0={D0:.3f} t1000={t1000:.3f}')
+    print('p при 0/-7/-18 dB:', p0, p0+p1*-7.142, p0+p1*-18.063)
+    pred = model(r.x)
+    n = 0
+    print('--- dual_b1q ---')
+    for i, q in enumerate(QS):
+        print(f'q={q:5.1f} {DUAL[i,0]:7.3f}/{pred[2*i]:7.3f}  '
+              f'{DUAL[i,1]:7.3f}/{pred[2*i+1]:7.3f}')
+    print('--- t1kq -18dB ---')
+    for i, fc in enumerate(FCS):
+        print(f'fc={fc:5.0f} {T1KQ[i]:6.3f}/{pred[22+i]:6.3f}')
+    print('--- t1k 0dB ---')
+    for i, fc in enumerate(FCS):
+        print(f'fc={fc:5.0f} {T1K[i]:6.3f}/{pred[29+i]:6.3f}')
+
+
+if __name__ == '__main__':
+    run()