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"Summary", "Extended Summary", "Parameters", "Attributes", "Methods", "Returns", "Yields", "Receives", "Other Parameters", "Raises", "Warns", "Warnings", "Notes" ], "item_file": "/scipy/signal/_spectral_py.py", "item_line": 515, "item_type": "function", "aliases": [ "scipy.signal.welch" ], "example_section_data": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Code", "__tag": 4050, "value": "import 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 1234 Hz, corrupted by\n0.001 V**2/Hz of white noise sampled at 10 kHz.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "fs = 10e3\nN = 1e5\namp = 2*np.sqrt(2)\nfreq = 1234.0\nnoise_power = 0.001 * fs / 2\ntime = np.arange(N) / fs\nx = amp*np.sin(2*np.pi*freq*time)\nx += rng.normal(scale=np.sqrt(noise_power), size=time.shape)\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nCompute and plot the power spectral density.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "f, Pxx_den = signal.welch(x, fs, nperseg=1024)\n", "execution_status": "success" }, { "__type": "Code", "__tag": 4050, "value": "plt.semilogy(f, Pxx_den)\nplt.ylim([0.5e-3, 1])\nplt.xlabel('frequency [Hz]')\nplt.ylabel('PSD [V**2/Hz]')\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-34c2e297ec6ef3d0.png" } }, { "__type": "Text", "__tag": 4046, "value": "\nIf we average the last half of the spectral density, to exclude the\npeak, we can recover the noise power on the signal.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "np.mean(Pxx_den[256:])\n", "execution_status": "failure" }, { "__type": "Text", "__tag": 4046, "value": "\nNow compute and plot the power spectrum.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "f, Pxx_spec = signal.welch(x, fs, 'flattop', 1024, scaling='spectrum')\n", "execution_status": "success" }, { "__type": "Code", "__tag": 4050, "value": "plt.figure()\nplt.semilogy(f, np.sqrt(Pxx_spec))\nplt.xlabel('frequency [Hz]')\nplt.ylabel('Linear spectrum [V RMS]')\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-7fadd3dc1fa1d7c6.png" } }, { "__type": "Text", "__tag": 4046, "value": "\nThe peak height in the power spectrum is an estimate of the RMS\namplitude.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "np.sqrt(Pxx_spec.max())\n", "execution_status": "failure" }, { "__type": "Text", "__tag": 4046, "value": "\nIf we now introduce a discontinuity in the signal, by increasing the\namplitude of a small portion of the signal by 50, we can see the\ncorruption of the mean average power spectral density, but using a\nmedian average better estimates the normal behaviour.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "x[int(N//2):int(N//2)+10] *= 50.\nf, Pxx_den = signal.welch(x, fs, nperseg=1024)\nf_med, Pxx_den_med = signal.welch(x, fs, nperseg=1024, average='median')\n", "execution_status": "success" }, { "__type": "Code", "__tag": 4050, "value": "plt.semilogy(f, Pxx_den, label='mean')\nplt.semilogy(f_med, Pxx_den_med, label='median')\nplt.ylim([0.5e-3, 1])\nplt.xlabel('frequency [Hz]')\nplt.ylabel('PSD [V**2/Hz]')\nplt.legend()\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", 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[1] P. Welch, \"The use of the fast Fourier transform for the", " estimation of power spectra: A method based on time averaging", " over short, modified periodograms\", IEEE Trans. Audio", " Electroacoust. vol. 15, pp. 70-73, 1967.", ".. [2] M.S. Bartlett, \"Periodogram Analysis and Continuous Spectra\",", " Biometrika, vol. 37, pp. 1-16, 1950." ], "qa": "scipy.signal._spectral_py:welch", "arbitrary": [], "local_refs": [ "Pxx", "average", "axis", "detrend", "f", "fs", "nfft", "noverlap", "nperseg", "return_onesided", "scaling", "window", "x" ] }