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numpy as np\nfrom scipy import signal\nimport matplotlib.pyplot as plt\nrng = np.random.default_rng()\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nGenerate a test signal, a 2 Vrms sine wave at 50Hz corrupted by\n0.001 V**2/Hz of white noise sampled at 1024 Hz.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "fs = 1024\nN = 10*fs\nnperseg = 512\namp = 2 * np.sqrt(2)\nnoise_power = 0.001 * fs / 2\ntime = np.arange(N) / float(fs)\ncarrier = amp * np.sin(2*np.pi*50*time)\nnoise = rng.normal(scale=np.sqrt(noise_power),\n size=time.shape)\nx = carrier + noise\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nCompute the STFT, and plot its magnitude\n\n" }, { "__type": "Code", "__tag": 4050, "value": "f, t, Zxx = signal.stft(x, fs=fs, nperseg=nperseg)\n", "execution_status": "success" }, { "__type": "Code", "__tag": 4050, "value": "plt.figure()\nplt.pcolormesh(t, f, np.abs(Zxx), vmin=0, vmax=amp, shading='gouraud')\nplt.ylim([f[1], f[-1]])\nplt.title('STFT Magnitude')\nplt.ylabel('Frequency [Hz]')\nplt.xlabel('Time [sec]')\n", "execution_status": "failure" }, { "__type": "Code", "__tag": 4050, "value": "plt.yscale('log')\nplt.show()\n", "execution_status": "success" }, { "__type": "Figure", "__tag": 4024, "value": { "__type": "RefInfo", "__tag": 4000, "module": "scipy", "version": "1.17.1", "kind": "assets", "path": "fig-ca46f7b556c7d449.png" } }, { "__type": "Text", "__tag": 4046, "value": "\nZero the components that are 10% or less of the carrier magnitude,\nthen convert back to a time series via inverse STFT\n\n" }, { "__type": "Code", "__tag": 4050, "value": "Zxx = np.where(np.abs(Zxx) >= amp/10, Zxx, 0)\n_, xrec = signal.istft(Zxx, fs)\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nCompare the cleaned signal with the original and true carrier signals.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "plt.figure()\nplt.plot(time, x, 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[1] Oppenheim, Alan V., Ronald W. Schafer, John R. Buck", " \"Discrete-Time Signal Processing\", Prentice Hall, 1999.", ".. [2] Daniel W. Griffin, Jae S. Lim \"Signal Estimation from", " Modified Short-Time Fourier Transform\", IEEE 1984,", " 10.1109/TASSP.1984.1164317" ], "qa": "scipy.signal._spectral_py:istft", "arbitrary": [], "local_refs": [ "'psd'}", "Zxx", "boundary", "freq_axis", "fs", "input_onesided", "nfft", "noverlap", "nperseg", "scaling: {'spectrum'", "t", "time_axis", "window", "x" ] }