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The filter should mostly\neliminate the 40 Hz and 80 Hz components, leaving just the 4 Hz signal.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "u = (np.cos(2*np.pi*4*t) + 0.6*np.sin(2*np.pi*40*t) +\n 0.5*np.cos(2*np.pi*80*t))\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nSimulate the filter with `lsim`.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "tout, yout, xout = lsim((b, a), U=u, T=t)\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nPlot the result.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "plt.plot(t, u, 'r', alpha=0.5, linewidth=1, label='input')\nplt.plot(tout, yout, 'k', linewidth=1.5, label='output')\nplt.legend(loc='best', shadow=True, framealpha=1)\n", "execution_status": "failure" }, { "__type": "Code", "__tag": 4050, "value": "plt.grid(alpha=0.3)\n", "execution_status": "success" }, { "__type": "Code", "__tag": 4050, "value": "plt.xlabel('t')\n", "execution_status": "failure" }, { "__type": "Code", "__tag": 4050, "value": "plt.show()\n", "execution_status": "success" }, { "__type": "Figure", "__tag": 4024, "value": { "__type": "RefInfo", "__tag": 4000, "module": "scipy", "version": "1.17.1", "kind": "assets", "path": "fig-3551d39a0709ecb2.png" } }, { "__type": "Text", "__tag": 4046, "value": "\nIn a second example, we simulate a double integrator ``y'' = u``, with\na constant input ``u = 1``. We'll use the state space representation\nof the integrator.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "from scipy.signal import lti\nA = np.array([[0.0, 1.0], [0.0, 0.0]])\nB = np.array([[0.0], [1.0]])\nC = np.array([[1.0, 0.0]])\nD = 0.0\nsystem = lti(A, B, C, D)\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\n`t` and `u` define the time and input signal for the system to\nbe simulated.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "t = np.linspace(0, 5, num=50)\nu = np.ones_like(t)\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nCompute the simulation, and then plot `y`. 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