{ "__type": "IngestedDoc", "__tag": 4010, "_content": { "Notes": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "In order to enable inversion of an STFT via the inverse STFT in " }, { "__type": "InlineRole", "__tag": 4003, "value": "istft", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": ", the signal windowing must obey the constraint of \"Nonzero OverLap Add\" (NOLA), and the input signal must have complete windowing coverage (i.e. " }, { "__type": "InlineCode", "__tag": 4051, "value": "(x.shape[axis] - nperseg) % (nperseg-noverlap) == 0" }, { "__type": "Text", "__tag": 4046, "value": "). The " }, { "__type": "ParamRef", "__tag": 4071, "name": "padded" }, { "__type": "Text", "__tag": 4046, "value": " argument may be used to accomplish this." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Given a time-domain signal " }, { "__type": "InlineMath", "__tag": 4057, "value": "x[n]" }, { "__type": "Text", "__tag": 4046, "value": ", a window " }, { "__type": "InlineMath", "__tag": 4057, "value": "w[n]" }, { "__type": "Text", "__tag": 4046, "value": ", and a hop size " }, { "__type": "InlineMath", "__tag": 4057, "value": "H" }, { "__type": "Text", "__tag": 4046, "value": " = " }, { "__type": "InlineRole", "__tag": 4003, "value": "nperseg - noverlap", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": ", the windowed frame at time index " }, { "__type": "InlineMath", "__tag": 4057, "value": "t" }, { "__type": "Text", "__tag": 4046, "value": " is given by" } ] }, { "__type": "Math", "__tag": 4058, "value": "x_{t}[n]=x[n]w[n-tH]" }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The overlap-add (OLA) reconstruction equation is given by" } ] }, { "__type": "Math", "__tag": 4058, "value": "x[n]=\\frac{\\sum_{t}x_{t}[n]w[n-tH]}{\\sum_{t}w^{2}[n-tH]}" }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The NOLA constraint ensures that every normalization term that appears in the denominator of the OLA reconstruction equation is nonzero. Whether a choice of " }, { "__type": "ParamRef", "__tag": 4071, "name": "window" }, { "__type": "Text", "__tag": 4046, "value": ", " }, { "__type": "ParamRef", "__tag": 4071, "name": "nperseg" }, { "__type": "Text", "__tag": 4046, "value": ", and " }, { "__type": "ParamRef", "__tag": 4071, "name": "noverlap" }, { "__type": "Text", "__tag": 4046, "value": " satisfy this constraint can be tested with " }, { "__type": "CrossRef", "__tag": 4002, "value": "check_NOLA", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.signal._spectral_py:check_NOLA" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": "." } ] }, { "__type": "Admonition", "__tag": 4056, "kind": "versionadded", "base_type": "neutral", "children": [ { "__type": "AdmonitionTitle", "__tag": 4055, "children": [ { "__type": "Text", "__tag": 4046, "value": "versionadded 0.19.0" } ] } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Strong", "__tag": 4048, "children": [ { "__type": "Text", "__tag": 4046, "value": "Array API Standard Support" } ] } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "InlineRole", "__tag": 4003, "value": "stft", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": " is not in-scope for support of Python Array API Standard compatible backends other than NumPy." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "See " }, { "__type": "InlineRole", "__tag": 4003, "value": "dev-arrayapi", "domain": null, "role": "ref", "inventory": null }, { "__type": "Text", "__tag": 4046, "value": " for more information." } ] } ], "title": [], "level": 0, "target": null }, "Warns": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Raises": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Yields": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Methods": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Returns": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Parameters", "__tag": 4026, "children": [ { "__type": "DocParam", "__tag": 4016, "name": "f", "annotation": "ndarray", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Array of sample frequencies." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "t", "annotation": "ndarray", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Array of segment times." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "Zxx", "annotation": "ndarray", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "STFT of " }, { "__type": "ParamRef", "__tag": 4071, "name": "x" }, { "__type": "Text", "__tag": 4046, "value": ". By default, the last axis of " }, { "__type": "CrossRef", "__tag": 4002, "value": "Zxx", "reference": { "__type": "RefInfo", "__tag": 4000, "module": null, "version": null, "kind": "local", "path": "Zxx" }, "kind": "local" }, { "__type": "Text", "__tag": 4046, "value": " corresponds to the segment times." } ] } ] } ] } ], "title": [], "level": 0, "target": null }, "Summary": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Compute the Short Time Fourier Transform (legacy function)." } ] } ], "title": [], "level": 0, "target": null }, "Receives": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Warnings": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Attributes": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Parameters": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Parameters", "__tag": 4026, "children": [ { "__type": "DocParam", "__tag": 4016, "name": "x", "annotation": "array_like", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Time series of measurement values" } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "fs", "annotation": "float, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Sampling frequency of the " }, { "__type": "ParamRef", "__tag": 4071, "name": "x" }, { "__type": "Text", "__tag": 4046, "value": " time series. Defaults to 1.0." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "window", "annotation": "str or tuple or array_like, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Desired window to use. If " }, { "__type": "ParamRef", "__tag": 4071, "name": "window" }, { "__type": "Text", "__tag": 4046, "value": " is a string or tuple, it is passed to " }, { "__type": "CrossRef", "__tag": 4002, "value": "get_window", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.signal.windows._windows:get_window" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " to generate the window values, which are DFT-even by default. See " }, { "__type": "CrossRef", "__tag": 4002, "value": "get_window", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.signal.windows._windows:get_window" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " for a list of windows and required parameters. If " }, { "__type": "ParamRef", "__tag": 4071, "name": "window" }, { "__type": "Text", "__tag": 4046, "value": " is array_like it will be used directly as the window and its length must be nperseg. Defaults to a periodic Hann window." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "nperseg", "annotation": "int, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Length of each segment. Defaults to 256." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "noverlap", "annotation": "int, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Number of points to overlap between segments. If " }, { "__type": "InlineRole", "__tag": 4003, "value": "None", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": ", " }, { "__type": "InlineCode", "__tag": 4051, "value": "noverlap = nperseg // 2" }, { "__type": "Text", "__tag": 4046, "value": ". Defaults to " }, { "__type": "InlineRole", "__tag": 4003, "value": "None", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": ". When specified, the COLA constraint must be met (see Notes below)." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "nfft", "annotation": "int, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Length of the FFT used, if a zero padded FFT is desired. If " }, { "__type": "InlineRole", "__tag": 4003, "value": "None", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": ", the FFT length is " }, { "__type": "ParamRef", "__tag": 4071, "name": "nperseg" }, { "__type": "Text", "__tag": 4046, "value": ". Defaults to " }, { "__type": "InlineRole", "__tag": 4003, "value": "None", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": "." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "detrend", "annotation": "str or function or `False`, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Specifies how to detrend each segment. If " }, { "__type": "ParamRef", "__tag": 4071, "name": "detrend" }, { "__type": "Text", "__tag": 4046, "value": " is a string, it is passed as the " }, { "__type": "InlineRole", "__tag": 4003, "value": "type", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": " argument to the " }, { "__type": "ParamRef", "__tag": 4071, "name": "detrend" }, { "__type": "Text", "__tag": 4046, "value": " function. If it is a function, it takes a segment and returns a detrended segment. If " }, { "__type": "ParamRef", "__tag": 4071, "name": "detrend" }, { "__type": "Text", "__tag": 4046, "value": " is " }, { "__type": "InlineRole", "__tag": 4003, "value": "False", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": ", no detrending is done. Defaults to " }, { "__type": "InlineRole", "__tag": 4003, "value": "False", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": "." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "return_onesided", "annotation": "bool, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "If " }, { "__type": "InlineRole", "__tag": 4003, "value": "True", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": ", return a one-sided spectrum for real data. If " }, { "__type": "InlineRole", "__tag": 4003, "value": "False", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": " return a two-sided spectrum. Defaults to " }, { "__type": "InlineRole", "__tag": 4003, "value": "True", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": ", but for complex data, a two-sided spectrum is always returned." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "boundary", "annotation": "str or None, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Specifies whether the input signal is extended at both ends, and how to generate the new values, in order to center the first windowed segment on the first input point. This has the benefit of enabling reconstruction of the first input point when the employed window function starts at zero. Valid options are " }, { "__type": "InlineCode", "__tag": 4051, "value": "['even', 'odd', 'constant', 'zeros', None]" }, { "__type": "Text", "__tag": 4046, "value": ". Defaults to 'zeros', for zero padding extension. I.e. " }, { "__type": "InlineCode", "__tag": 4051, "value": "[1, 2, 3, 4]" }, { "__type": "Text", "__tag": 4046, "value": " is extended to " }, { "__type": "InlineCode", "__tag": 4051, "value": "[0, 1, 2, 3, 4, 0]" }, { "__type": "Text", "__tag": 4046, "value": " for " }, { "__type": "InlineCode", "__tag": 4051, "value": "nperseg=3" }, { "__type": "Text", "__tag": 4046, "value": "." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "padded", "annotation": "bool, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Specifies whether the input signal is zero-padded at the end to make the signal fit exactly into an integer number of window segments, so that all of the signal is included in the output. Defaults to " }, { "__type": "InlineRole", "__tag": 4003, "value": "True", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": ". Padding occurs after boundary extension, if " }, { "__type": "ParamRef", "__tag": 4071, "name": "boundary" }, { "__type": "Text", "__tag": 4046, "value": " is not " }, { "__type": "InlineRole", "__tag": 4003, "value": "None", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": ", and " }, { "__type": "ParamRef", "__tag": 4071, "name": "padded" }, { "__type": "Text", "__tag": 4046, "value": " is " }, { "__type": "InlineRole", "__tag": 4003, "value": "True", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": ", as is the default." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "axis", "annotation": "int, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Axis along which the STFT is computed; the default is over the last axis (i.e. " }, { "__type": "InlineCode", "__tag": 4051, "value": "axis=-1" }, { "__type": "Text", "__tag": 4046, "value": ")." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "scaling: {'spectrum', 'psd'}", "annotation": "", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The default 'spectrum' scaling allows each frequency line of " }, { "__type": "CrossRef", "__tag": 4002, "value": "Zxx", "reference": { "__type": "RefInfo", "__tag": 4000, "module": null, "version": null, "kind": "local", "path": "Zxx" }, "kind": "local" }, { "__type": "Text", "__tag": 4046, "value": " to be interpreted as a magnitude spectrum. The 'psd' option scales each line to a power spectral density - it allows to calculate the signal's energy by numerically integrating over " }, { "__type": "InlineCode", "__tag": 4051, "value": "abs(Zxx)**2" }, { "__type": "Text", "__tag": 4046, "value": "." } ] }, { "__type": "Admonition", "__tag": 4056, "kind": "versionadded", "base_type": "neutral", "children": [ { "__type": "AdmonitionTitle", "__tag": 4055, "children": [ { "__type": "Text", "__tag": 4046, "value": "versionadded 1.9.0" } ] } ] } ] } ] } ], "title": [], "level": 0, "target": null }, "Extended Summary": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "STFTs can be used as a way of quantifying the change of a nonstationary signal's frequency and phase content over time." } ] } ], "title": [], "level": 0, "target": null }, "Other Parameters": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null } }, "_ordered_sections": [ "Summary", "Extended Summary", "Parameters", "Attributes", "Methods", "Returns", "Yields", "Receives", "Other Parameters", "Raises", "Warns", "Warnings", "Notes" ], "item_file": "/scipy/signal/_spectral_py.py", "item_line": 1431, "item_type": "function", "aliases": [ "scipy.signal.stft" ], "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 whose frequency is slowly\nmodulated around 3kHz, corrupted by white noise of exponentially\ndecreasing magnitude sampled at 10 kHz.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "fs = 10e3\nN = 1e5\namp = 2 * np.sqrt(2)\nnoise_power = 0.01 * fs / 2\ntime = np.arange(N) / float(fs)\nmod = 500*np.cos(2*np.pi*0.25*time)\ncarrier = amp * np.sin(2*np.pi*3e3*time + mod)\nnoise = rng.normal(scale=np.sqrt(noise_power),\n size=time.shape)\nnoise *= np.exp(-time/5)\nx = carrier + noise\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nCompute and plot the STFT's magnitude.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "f, t, Zxx = signal.stft(x, fs, nperseg=1000)\n", "execution_status": "success" }, { "__type": "Code", "__tag": 4050, "value": "plt.pcolormesh(t, f, np.abs(Zxx), vmin=0, vmax=amp, shading='gouraud')\nplt.title('STFT Magnitude')\nplt.ylabel('Frequency [Hz]')\nplt.xlabel('Time [sec]')\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-fa4ff677f983ebaf.png" } }, { "__type": "Text", "__tag": 4046, "value": "\nCompare the energy of the signal `x` with the energy of its STFT:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "E_x = sum(x**2) / fs # Energy of x\nf, t, Zxx = signal.stft(x, fs, nperseg=1000, return_onesided=False,\n scaling='psd')\ndf, dt = f[1] - f[0], t[1] - t[0]\nE_Zxx = sum(np.sum(Zxx.real**2 + Zxx.imag**2, axis=0) * df) * dt\n", "execution_status": "success" }, { "__type": "Code", "__tag": 4050, "value": "np.isclose(E_x, E_Zxx, rtol=1e-2)\n", "execution_status": "failure" } ], "title": [], "level": 0, "target": null }, "see_also": [ { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "ShortTimeFFT", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.signal._short_time_fft:ShortTimeFFT" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Newer STFT/ISTFT implementation providing more features." } ] } ], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "check_COLA", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.signal._spectral_py:check_COLA" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Check whether the Constant OverLap Add (COLA) constraint is met" } ] } ], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "check_NOLA", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.signal._spectral_py:check_NOLA" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Check whether the Nonzero Overlap Add (NOLA) constraint is met" } ] } ], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "csd", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.signal._spectral_py:csd" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Cross spectral density by Welch's method." } ] } ], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "istft", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "current-module", "version": "current-version", "kind": "to-resolve", "path": "istft" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Inverse Short Time Fourier Transform" } ] } ], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "lombscargle", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.signal._spectral_py:lombscargle" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Lomb-Scargle periodogram for unevenly sampled data" } ] } ], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "spectrogram", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "current-module", "version": "current-version", "kind": "to-resolve", "path": "spectrogram" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Spectrogram by Welch's method." } ] } ], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "welch", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.signal._spectral_py:welch" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Power spectral density by Welch's method." } ] } ], "type": "func" } ], "signature": { "__type": "SignatureNode", "__tag": 4029, "kind": "function", "parameters": [ { "__type": "SigParam", "__tag": 4030, "name": "x", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": { "__type": "Empty", "__tag": 4031 } }, { "__type": "SigParam", "__tag": 4030, "name": "fs", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "1.0" }, { "__type": "SigParam", "__tag": 4030, "name": "window", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "hann_periodic" }, { "__type": "SigParam", "__tag": 4030, "name": "nperseg", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "256" }, { "__type": "SigParam", "__tag": 4030, "name": "noverlap", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "nfft", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "detrend", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "False" }, { "__type": "SigParam", "__tag": 4030, "name": "return_onesided", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "True" }, { "__type": "SigParam", "__tag": 4030, "name": "boundary", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "zeros" }, { "__type": "SigParam", "__tag": 4030, "name": "padded", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "True" }, { "__type": "SigParam", "__tag": 4030, "name": "axis", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "-1" }, { "__type": "SigParam", "__tag": 4030, "name": "scaling", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "spectrum" } ], "return_annotation": { "__type": "Empty", "__tag": 4031 }, "target_name": "stft" }, "references": [ ".. [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:stft", "arbitrary": [], "local_refs": [ "'psd'}", "Zxx", "axis", "boundary", "detrend", "f", "fs", "nfft", "noverlap", "nperseg", "padded", "return_onesided", "scaling: {'spectrum'", "t", "window", "x" ] }