{ "__type": "IngestedDoc", "__tag": 4010, "_content": { "Notes": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "By convention, Pxy is computed with the conjugate FFT of X multiplied by the FFT of Y." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "If the input series differ in length, the shorter series will be zero-padded to match." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "An appropriate amount of overlap will depend on the choice of window and on your requirements. For the default Hann window an overlap of 50% is a reasonable trade-off between accurately estimating the signal power, while not over counting any of the data. Narrower windows may require a larger overlap." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The ratio of the cross spectrum (" }, { "__type": "InlineCode", "__tag": 4051, "value": "scaling='spectrum'" }, { "__type": "Text", "__tag": 4046, "value": ") divided by the cross spectral density (" }, { "__type": "InlineCode", "__tag": 4051, "value": "scaling='density'" }, { "__type": "Text", "__tag": 4046, "value": ") is the constant factor of " }, { "__type": "InlineCode", "__tag": 4051, "value": "sum(abs(window)**2)*fs / abs(sum(window))**2" }, { "__type": "Text", "__tag": 4046, "value": ". If " }, { "__type": "ParamRef", "__tag": 4071, "name": "return_onesided" }, { "__type": "Text", "__tag": 4046, "value": " is " }, { "__type": "InlineCode", "__tag": 4051, "value": "True" }, { "__type": "Text", "__tag": 4046, "value": ", the values of the negative frequencies are added to values of the corresponding positive ones." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Consult the " }, { "__type": "InlineRole", "__tag": 4003, "value": "tutorial_SpectralAnalysis", "domain": null, "role": "ref", "inventory": null }, { "__type": "Text", "__tag": 4046, "value": " section of the " }, { "__type": "InlineRole", "__tag": 4003, "value": "user_guide", "domain": null, "role": "ref", "inventory": null }, { "__type": "Text", "__tag": 4046, "value": " for a discussion of the scalings of a spectral density and an (amplitude) spectrum." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Welch's method may be interpreted as taking the average over the time slices of a (cross-) spectrogram. Internally, this function utilizes the " }, { "__type": "CrossRef", "__tag": 4002, "value": "ShortTimeFFT", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.signal._short_time_fft:ShortTimeFFT" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " to determine the required (cross-) spectrogram. An example below illustrates that it is straightforward to calculate " }, { "__type": "CrossRef", "__tag": 4002, "value": "Pxy", "reference": { "__type": "RefInfo", "__tag": 4000, "module": null, "version": null, "kind": "local", "path": "Pxy" }, "kind": "local" }, { "__type": "Text", "__tag": 4046, "value": " directly with the " }, { "__type": "CrossRef", "__tag": 4002, "value": "ShortTimeFFT", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.signal._short_time_fft:ShortTimeFFT" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": ". However, there are some notable differences in the behavior of the " }, { "__type": "CrossRef", "__tag": 4002, "value": "ShortTimeFFT", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.signal._short_time_fft:ShortTimeFFT" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": ":" } ] }, { "__type": "BulletList", "__tag": 4053, "ordered": false, "start": 1, "children": [ { "__type": "ListItem", "__tag": 4054, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "There is no direct " }, { "__type": "CrossRef", "__tag": 4002, "value": "ShortTimeFFT", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.signal._short_time_fft:ShortTimeFFT" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " equivalent for the " }, { "__type": "CrossRef", "__tag": 4002, "value": "csd", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.signal._spectral_py:csd" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " parameter combination " }, { "__type": "InlineCode", "__tag": 4051, "value": "return_onesided=True, scaling='density'" }, { "__type": "Text", "__tag": 4046, "value": ", since " }, { "__type": "InlineCode", "__tag": 4051, "value": "fft_mode='onesided2X'" }, { "__type": "Text", "__tag": 4046, "value": " requires " }, { "__type": "InlineCode", "__tag": 4051, "value": "'psd'" }, { "__type": "Text", "__tag": 4046, "value": " scaling. The is due to " }, { "__type": "CrossRef", "__tag": 4002, "value": "csd", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.signal._spectral_py:csd" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " returning the doubled squared magnitude in this case, which does not have a sensible interpretation." } ] } ] }, { "__type": "ListItem", "__tag": 4054, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "CrossRef", "__tag": 4002, "value": "ShortTimeFFT", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.signal._short_time_fft:ShortTimeFFT" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " uses " }, { "__type": "InlineRole", "__tag": 4003, "value": "float64", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": " / " }, { "__type": "InlineRole", "__tag": 4003, "value": "complex128", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": " internally, which is due to the behavior of the utilized " }, { "__type": "CrossRef", "__tag": 4002, "value": "fft", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.fft" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " module. Thus, those are the dtypes being returned. The " }, { "__type": "CrossRef", "__tag": 4002, "value": "csd", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.signal._spectral_py:csd" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " function casts the return values to " }, { "__type": "InlineRole", "__tag": 4003, "value": "float32", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": " / " }, { "__type": "InlineRole", "__tag": 4003, "value": "complex64", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": " if the input is " }, { "__type": "InlineRole", "__tag": 4003, "value": "float32", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": " / " }, { "__type": "InlineRole", "__tag": 4003, "value": "complex64", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": " as well." } ] } ] }, { "__type": "ListItem", "__tag": 4054, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The " }, { "__type": "CrossRef", "__tag": 4002, "value": "csd", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.signal._spectral_py:csd" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " function calculates " }, { "__type": "InlineCode", "__tag": 4051, "value": "np.conj(Sx[q,p]) * Sy[q,p]" }, { "__type": "Text", "__tag": 4046, "value": ", whereas " }, { "__type": "InlineRole", "__tag": 4003, "value": "~ShortTimeFFT.spectrogram", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": " calculates " }, { "__type": "InlineCode", "__tag": 4051, "value": "Sx[q,p] * np.conj(Sy[q,p])" }, { "__type": "Text", "__tag": 4046, "value": " where " }, { "__type": "InlineCode", "__tag": 4051, "value": "Sx[q,p]" }, { "__type": "Text", "__tag": 4046, "value": ", " }, { "__type": "InlineCode", "__tag": 4051, "value": "Sy[q,p]" }, { "__type": "Text", "__tag": 4046, "value": " are the STFTs of " }, { "__type": "ParamRef", "__tag": 4071, "name": "x" }, { "__type": "Text", "__tag": 4046, "value": " and " }, { "__type": "ParamRef", "__tag": 4071, "name": "y" }, { "__type": "Text", "__tag": 4046, "value": ". Also, the window positioning is different." } ] } ] } ] }, { "__type": "Admonition", "__tag": 4056, "kind": "versionadded", "base_type": "neutral", "children": [ { "__type": "AdmonitionTitle", "__tag": 4055, "children": [ { "__type": "Text", "__tag": 4046, "value": "versionadded 0.16.0" } ] } ] }, { "__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": "CrossRef", "__tag": 4002, "value": "csd", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.signal._spectral_py:csd" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable " }, { "__type": "InlineCode", "__tag": 4051, "value": "SCIPY_ARRAY_API=1" }, { "__type": "Text", "__tag": 4046, "value": " and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported." } ] }, { "__type": "Code", "__tag": 4050, "value": "==================== ==================== ====================\nLibrary CPU GPU\n==================== ==================== ====================\nNumPy ✅ n/a \nCuPy n/a ⛔ \nPyTorch ⛔ ⛔ \nJAX ⛔ ⛔ \nDask ⛔ n/a \n==================== ==================== ====================", "execution_status": null }, { "__type": "Blockquote", "__tag": 4059, "children": [ { "__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": "Pxy", "annotation": "ndarray", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Cross spectral density or cross power spectrum of x,y." } ] } ] } ] } ], "title": [], "level": 0, "target": null }, "Summary": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Estimate the cross power spectral density, Pxy, using Welch's method." } ] } ], "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": "y", "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": " and " }, { "__type": "ParamRef", "__tag": 4071, "name": "y" }, { "__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 None, but if window is str or tuple, is set to 256, and if window is array_like, is set to the length of the window." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "noverlap: int, optional", "annotation": "", "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": " and may not be greater than " }, { "__type": "ParamRef", "__tag": 4071, "name": "nperseg" }, { "__type": "Text", "__tag": 4046, "value": "." } ] } ] }, { "__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 'constant'." } ] } ] }, { "__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": "scaling", "annotation": "{ 'density', 'spectrum' }, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Selects between computing the cross spectral density ('density') where " }, { "__type": "CrossRef", "__tag": 4002, "value": "Pxy", "reference": { "__type": "RefInfo", "__tag": 4000, "module": null, "version": null, "kind": "local", "path": "Pxy" }, "kind": "local" }, { "__type": "Text", "__tag": 4046, "value": " has units of V**2/Hz and computing the cross spectrum ('spectrum') where " }, { "__type": "CrossRef", "__tag": 4002, "value": "Pxy", "reference": { "__type": "RefInfo", "__tag": 4000, "module": null, "version": null, "kind": "local", "path": "Pxy" }, "kind": "local" }, { "__type": "Text", "__tag": 4046, "value": " has units of V**2, if " }, { "__type": "ParamRef", "__tag": 4071, "name": "x" }, { "__type": "Text", "__tag": 4046, "value": " and " }, { "__type": "ParamRef", "__tag": 4071, "name": "y" }, { "__type": "Text", "__tag": 4046, "value": " are measured in V and " }, { "__type": "ParamRef", "__tag": 4071, "name": "fs" }, { "__type": "Text", "__tag": 4046, "value": " is measured in Hz. Defaults to 'density'" } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "axis", "annotation": "int, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Axis along which the CSD is computed for both inputs; 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": "average", "annotation": "{ 'mean', 'median' }, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Method to use when averaging periodograms. If the spectrum is complex, the average is computed separately for the real and imaginary parts. Defaults to 'mean'." } ] }, { "__type": "Admonition", "__tag": 4056, "kind": "versionadded", "base_type": "neutral", "children": [ { "__type": "AdmonitionTitle", "__tag": 4055, "children": [ { "__type": "Text", "__tag": 4046, "value": "versionadded 1.2.0" } ] } ] } ] } ] } ], "title": [], "level": 0, "target": null }, "Extended Summary": { "__type": "Section", "__tag": 4015, "children": [], "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": 690, "item_type": "function", "aliases": [ "scipy.signal.csd" ], "example_section_data": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Text", "__tag": 4046, "value": "The following example plots the cross power spectral density of two signals with\nsome common features:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "import numpy as np\nfrom scipy import signal\nimport matplotlib.pyplot as plt\nrng = np.random.default_rng()\n\n# Generate two test signals with some common features:\nN, fs = 100_000, 10e3 # number of samples and sampling frequency\namp, freq = 20, 1234.0 # amplitude and frequency of utilized sine signal\nnoise_power = 0.001 * fs / 2\ntime = np.arange(N) / fs\nb, a = signal.butter(2, 0.25, 'low')\nx = rng.normal(scale=np.sqrt(noise_power), size=time.shape)\ny = signal.lfilter(b, a, x)\nx += amp*np.sin(2*np.pi*freq*time)\ny += rng.normal(scale=0.1*np.sqrt(noise_power), size=time.shape)\n\n# Compute and plot the magnitude of the cross spectral density:\nnperseg, noverlap, win = 1024, 512, 'hann'\nf, Pxy = signal.csd(x, y, fs, win, nperseg, noverlap)\nfig0, ax0 = plt.subplots(tight_layout=True)\n", "execution_status": "success" }, { "__type": "Code", "__tag": 4050, "value": "ax0.set_title(f\"CSD ({win.title()}-window, {nperseg=}, {noverlap=})\")\nax0.set(xlabel=\"Frequency $f$ in kHz\", ylabel=\"CSD Magnitude in V²/Hz\")\nax0.semilogy(f/1e3, np.abs(Pxy))\n", "execution_status": "failure" }, { "__type": "Code", "__tag": 4050, "value": "ax0.grid()\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-769169c5ff11c822.png" } }, { "__type": "Text", "__tag": 4046, "value": "\nThe cross spectral density is calculated by taking the average over the time slices\nof a spectrogram:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "SFT = signal.ShortTimeFFT.from_window('hann', fs, nperseg, noverlap,\n scale_to='psd', fft_mode='onesided2X',\n phase_shift=None)\nSxy1 = SFT.spectrogram(y, x, detr='constant', k_offset=nperseg//2,\n p0=0, p1=(N-noverlap) // SFT.hop)\nPxy1 = Sxy1.mean(axis=-1)\nnp.allclose(Pxy, Pxy1) # same result as with csd()\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nAs discussed in the Notes section, the results of using an approach analogous to\nthe code snippet above and the `csd` function may deviate due to implementation\ndetails.\n\nNote that the code snippet above can be easily adapted to determine other\nstatistical properties than the mean value." } ], "title": [], "level": 0, "target": null }, "see_also": [ { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "coherence", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.signal._spectral_py:coherence" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Magnitude squared coherence by Welch's method." } ] } ], "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": "periodogram", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.signal._spectral_py:periodogram" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Simple, optionally modified periodogram" } ] } ], "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. [Equivalent to csd(x,x)]" } ] } ], "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": "y", "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": "None" }, { "__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": "constant" }, { "__type": "SigParam", "__tag": 4030, "name": "return_onesided", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "True" }, { "__type": "SigParam", "__tag": 4030, "name": "scaling", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "density" }, { "__type": "SigParam", "__tag": 4030, "name": "axis", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "-1" }, { "__type": "SigParam", "__tag": 4030, "name": "average", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "mean" } ], "return_annotation": { "__type": "Empty", "__tag": 4031 }, "target_name": "csd" }, "references": [ ".. [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] Rabiner, Lawrence R., and B. Gold. \"Theory and Application of", " Digital Signal Processing\" Prentice-Hall, pp. 414-419, 1975" ], "qa": "scipy.signal._spectral_py:csd", "arbitrary": [], "local_refs": [ "Pxy", "average", "axis", "detrend", "f", "fs", "nfft", "noverlap: int", "nperseg", "optional", "return_onesided", "scaling", "window", "x", "y" ] }