@ -368,7 +368,7 @@
},
{
"cell_type": "code",
"execution_count": 8 ,
"execution_count": 1 ,
"metadata": {},
"outputs": [],
"source": [
@ -493,6 +493,237 @@
"\n",
" return signal_noisy, params, bounds, seeds, metadata"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Estimador de orden"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"from scipy.optimize import minimize\n",
"import matplotlib.pyplot as plt\n",
"\n",
"def estimar_parametros(y, t, N, rangos_freq):\n",
" \"\"\"\n",
" Estima parámetros de una suma de N cosenos:\n",
" y(t) = sum A_k cos(2π f_k t + φ_k)\n",
"\n",
" Estrategia:\n",
" - No lineal: optimiza solo las frecuencias.\n",
" - Lineal: estima amplitudes y fases para cada conjunto de frecuencias.\n",
"\n",
" Parámetros\n",
" ----------\n",
" y : array_like\n",
" Señal observada (vector de tamaño M).\n",
" t : array_like\n",
" Vector de tiempos (tamaño M).\n",
" N : int\n",
" Número de cosenos a estimar.\n",
" rangos_freq : list of tuples\n",
" Lista [(fmin1,fmax1), (fmin2,fmax2), ...] con los rangos válidos\n",
" para cada frecuencia.\n",
"\n",
" Retorna\n",
" -------\n",
" params : list of tuples\n",
" Lista [(A1,f1,phi1), ..., (AN,fN,phiN)].\n",
" \"\"\"\n",
"\n",
" M = len(y)\n",
"\n",
" # --- Función de coste: dado un vector de frecuencias, ajusta amplitudes/fases y calcula error ---\n",
" def coste(frecuencias):\n",
" # Matriz de diseño con cosenos y senos\n",
" X = []\n",
" for f in frecuencias:\n",
" X.append(np.cos(2*np.pi*f*t))\n",
" X.append(np.sin(2*np.pi*f*t))\n",
" X = np.column_stack(X) # M x (2N)\n",
"\n",
" # Resolver mínimos cuadrados lineales\n",
" coef, _, _, _ = np.linalg.lstsq(X, y, rcond=None)\n",
" y_hat = X @ coef\n",
" resid = y - y_hat\n",
" return np.sum(resid**2)\n",
"\n",
" # --- Inicialización aleatoria dentro de los rangos ---\n",
" f0 = np.array([np.random.uniform(low, high) for (low, high) in rangos_freq])\n",
"\n",
" # --- Restricciones de cada frecuencia ---\n",
" bounds = rangos_freq\n",
"\n",
" # --- Optimización no lineal en frecuencias ---\n",
" res = minimize(coste, f0, bounds=bounds, method=\"L-BFGS-B\")\n",
"\n",
" f_est = res.x\n",
"\n",
" # --- Una vez obtenidas las frecuencias, estimar amplitudes y fases ---\n",
" X = []\n",
" for f in f_est:\n",
" X.append(np.cos(2*np.pi*f*t))\n",
" X.append(np.sin(2*np.pi*f*t))\n",
" X = np.column_stack(X)\n",
"\n",
" coef, _, _, _ = np.linalg.lstsq(X, y, rcond=None)\n",
"\n",
" params = []\n",
" for k in range(N):\n",
" a = coef[2*k]\n",
" b = coef[2*k + 1]\n",
" A = np.sqrt(a**2 + b**2)\n",
" phi = np.arctan2(-b, a)\n",
" params.append((A, f_est[k], phi))\n",
"\n",
" return params\n",
"\n",
"\n",
"def estimar_orden(y, t, N_max, C, rangos_freq, eps=1e-8):\n",
" \"\"\"\n",
" Estima el orden de la señal (cantidad de cosenos) probando N=1..N_max\n",
" con el criterio penalizado.\n",
" \"\"\"\n",
"\n",
" M = len(y)\n",
" criterios = []\n",
"\n",
" for N in range(1, N_max+1):\n",
" # Usamos solo los primeros N rangos\n",
" params = estimar_parametros(y, t, N, rangos_freq[:N])\n",
"\n",
" # Reconstrucción\n",
" y_hat = np.zeros_like(y)\n",
" for A, f, phi in params:\n",
" y_hat += A * np.cos(2*np.pi*f*t + phi)\n",
"\n",
" # Varianza del error\n",
" resid = y - y_hat\n",
" sigma2 = np.mean(resid**2)\n",
"\n",
" # Criterio penalizado (según tu pedido)\n",
" J = M * np.log(sigma2 + eps) + C * N\n",
" criterios.append(J)\n",
"\n",
" criterios = np.array(criterios)\n",
" N_hat = np.argmin(criterios) + 1\n",
"\n",
" return N_hat, criterios\n"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"ename": "IndexError",
"evalue": "index 10 is out of bounds for axis 0 with size 10",
"output_type": "error",
"traceback": [
"\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[1;31mIndexError\u001b[0m Traceback (most recent call last)",
"Cell \u001b[1;32mIn[6], line 38\u001b[0m\n\u001b[0;32m 33\u001b[0m params_est \u001b[38;5;241m=\u001b[39m estimar_parametros(signal_noisy, t, N_true, rangos_freq)\n\u001b[0;32m 35\u001b[0m \u001b[38;5;66;03m# ============================\u001b[39;00m\n\u001b[0;32m 36\u001b[0m \u001b[38;5;66;03m# 3. Estimar orden\u001b[39;00m\n\u001b[0;32m 37\u001b[0m \u001b[38;5;66;03m# ============================\u001b[39;00m\n\u001b[1;32m---> 38\u001b[0m N_hat, criterios \u001b[38;5;241m=\u001b[39m \u001b[43mestimar_orden\u001b[49m\u001b[43m(\u001b[49m\u001b[43msignal_noisy\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mt\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mN_max\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mN_max\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mC\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mC\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mrangos_freq\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mrangos_freq\u001b[49m\u001b[43m)\u001b[49m\n\u001b[0;32m 40\u001b[0m \u001b[38;5;66;03m# ============================\u001b[39;00m\n\u001b[0;32m 41\u001b[0m \u001b[38;5;66;03m# 4. Reconstrucción de la señal\u001b[39;00m\n\u001b[0;32m 42\u001b[0m \u001b[38;5;66;03m# ============================\u001b[39;00m\n\u001b[0;32m 43\u001b[0m y_hat \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mzeros_like(signal_noisy)\n",
"Cell \u001b[1;32mIn[4], line 91\u001b[0m, in \u001b[0;36mestimar_orden\u001b[1;34m(y, t, N_max, C, rangos_freq, eps)\u001b[0m\n\u001b[0;32m 87\u001b[0m criterios \u001b[38;5;241m=\u001b[39m []\n\u001b[0;32m 89\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m N \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mrange\u001b[39m(\u001b[38;5;241m1\u001b[39m, N_max\u001b[38;5;241m+\u001b[39m\u001b[38;5;241m1\u001b[39m):\n\u001b[0;32m 90\u001b[0m \u001b[38;5;66;03m# Usamos solo los primeros N rangos\u001b[39;00m\n\u001b[1;32m---> 91\u001b[0m params \u001b[38;5;241m=\u001b[39m \u001b[43mestimar_parametros\u001b[49m\u001b[43m(\u001b[49m\u001b[43my\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mt\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mN\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mrangos_freq\u001b[49m\u001b[43m[\u001b[49m\u001b[43m:\u001b[49m\u001b[43mN\u001b[49m\u001b[43m]\u001b[49m\u001b[43m)\u001b[49m\n\u001b[0;32m 93\u001b[0m \u001b[38;5;66;03m# Reconstrucción\u001b[39;00m\n\u001b[0;32m 94\u001b[0m y_hat \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mzeros_like(y)\n",
"Cell \u001b[1;32mIn[4], line 71\u001b[0m, in \u001b[0;36mestimar_parametros\u001b[1;34m(y, t, N, rangos_freq)\u001b[0m\n\u001b[0;32m 69\u001b[0m params \u001b[38;5;241m=\u001b[39m []\n\u001b[0;32m 70\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m k \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mrange\u001b[39m(N):\n\u001b[1;32m---> 71\u001b[0m a \u001b[38;5;241m=\u001b[39m \u001b[43mcoef\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;241;43m2\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mk\u001b[49m\u001b[43m]\u001b[49m\n\u001b[0;32m 72\u001b[0m b \u001b[38;5;241m=\u001b[39m coef[\u001b[38;5;241m2\u001b[39m\u001b[38;5;241m*\u001b[39mk \u001b[38;5;241m+\u001b[39m \u001b[38;5;241m1\u001b[39m]\n\u001b[0;32m 73\u001b[0m A \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39msqrt(a\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m2\u001b[39m \u001b[38;5;241m+\u001b[39m b\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m2\u001b[39m)\n",
"\u001b[1;31mIndexError\u001b[0m: index 10 is out of bounds for axis 0 with size 10"
]
}
],
"source": [
"\n",
"# ============================\n",
"# Configuración del experimento\n",
"# ============================\n",
"fs = 200\n",
"T = 30\n",
"sigma2 = 0.01\n",
"N_card_true = 3\n",
"N_resp_true = 2\n",
"C = 10 # constante de penalización\n",
"N_max = 8 # orden máximo a probar\n",
"\n",
"# ============================\n",
"# 1. Generar señal sintética\n",
"# ============================\n",
"signal_noisy, params_true, bounds, seeds, metadata = generar_muestras_cardiorespiratorias(\n",
" N_card=N_card_true,\n",
" N_resp=N_resp_true,\n",
" fs=fs,\n",
" T=T,\n",
" sigma2=sigma2,\n",
" seed=42\n",
")\n",
"\n",
"t = np.arange(0, T, 1/fs)\n",
"\n",
"# ============================\n",
"# 2. Estimar parámetros para orden verdadero\n",
"# ============================\n",
"# Aquí se asume que ya tenés `estimar_parametros` definida\n",
"N_true = N_card_true + N_resp_true\n",
"rangos_freq = [bounds['f_card']] * N_card_true + [bounds['f_resp']] * N_resp_true\n",
"\n",
"params_est = estimar_parametros(signal_noisy, t, N_true, rangos_freq)\n",
"\n",
"# ============================\n",
"# 3. Estimar orden\n",
"# ============================\n",
"N_hat, criterios = estimar_orden(signal_noisy, t, N_max=N_max, C=C, rangos_freq=rangos_freq)\n",
"\n",
"# ============================\n",
"# 4. Reconstrucción de la señal\n",
"# ============================\n",
"y_hat = np.zeros_like(signal_noisy)\n",
"for A, f, phi in params_est:\n",
" y_hat += A * np.cos(2*np.pi*f*t + phi)\n",
"\n",
"# ============================\n",
"# 5. Gráficos\n",
"# ============================\n",
"plt.figure(figsize=(12,5))\n",
"plt.plot(t, signal_noisy, label=\"Señal observada\", alpha=0.7)\n",
"plt.plot(t, y_hat, label=f\"Reconstrucción (N={N_true})\", linewidth=2)\n",
"plt.xlabel(\"Tiempo [s]\")\n",
"plt.ylabel(\"Amplitud\")\n",
"plt.legend()\n",
"plt.title(\"Señal sintética vs Reconstrucción\")\n",
"plt.show()\n",
"\n",
"plt.figure(figsize=(6,4))\n",
"plt.plot(range(1, len(criterios)+1), criterios, marker=\"o\")\n",
"plt.axvline(N_hat, color=\"r\", linestyle=\"--\", label=f\"Orden estimado = {N_hat}\")\n",
"plt.xlabel(\"Orden N\")\n",
"plt.ylabel(\"Criterio penalizado\")\n",
"plt.title(\"Selección de orden\")\n",
"plt.legend()\n",
"plt.show()\n",
"\n",
"# ============================\n",
"# 6. Resultados\n",
"# ============================\n",
"print(\"Parámetros verdaderos:\")\n",
"for i, (A,f,phi) in enumerate(zip(\n",
" np.concatenate([params_true['A_card'], params_true['A_resp']]),\n",
" np.concatenate([params_true['f_card'], params_true['f_resp']]),\n",
" np.concatenate([params_true['phase_card'], params_true['phase_resp']])\n",
" )):\n",
" print(f\"Componente {i+1}: A={A:.3f}, f={f:.3f}, phi={phi:.3f}\")\n",
"\n",
"print(\"\\nParámetros estimados:\")\n",
"for i, (A,f,phi) in enumerate(params_est):\n",
" print(f\"Componente {i+1}: A={A:.3f}, f={f:.3f}, phi={phi:.3f}\")\n",
"\n",
"print(f\"\\nOrden verdadero: {N_true}\")\n",
"print(f\"Orden estimado : {N_hat}\")"
]
}
],
"metadata": {
