{ "__type": "IngestedDoc", "__tag": 4010, "_content": { "Notes": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Admonition", "__tag": 4056, "kind": "warning", "base_type": "warning", "children": [ { "__type": "AdmonitionTitle", "__tag": 4055, "children": [ { "__type": "Text", "__tag": 4046, "value": "warning " } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "For " }, { "__type": "InlineCode", "__tag": 4051, "value": "type in {2, 3}" }, { "__type": "Text", "__tag": 4046, "value": ", " }, { "__type": "InlineCode", "__tag": 4051, "value": "norm=\"ortho\"" }, { "__type": "Text", "__tag": 4046, "value": " breaks the direct correspondence with the inverse direct Fourier transform." } ] } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "For " }, { "__type": "InlineCode", "__tag": 4051, "value": "norm=\"ortho\"" }, { "__type": "Text", "__tag": 4046, "value": " both the " }, { "__type": "CrossRef", "__tag": 4002, "value": "dst", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.fft._realtransforms:dst" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " and " }, { "__type": "CrossRef", "__tag": 4002, "value": "idst", "reference": { "__type": "RefInfo", "__tag": 4000, "module": null, "version": null, "kind": "local", "path": "idst" }, "kind": "local" }, { "__type": "Text", "__tag": 4046, "value": " are scaled by the same overall factor in both directions. By default, the transform is also orthogonalized which for types 2 and 3 means the transform definition is modified to give orthogonality of the DST matrix (see " }, { "__type": "CrossRef", "__tag": 4002, "value": "dst", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.fft._realtransforms:dst" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " for the full definitions)." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "'The' IDST is the IDST-II, which is the same as the normalized DST-III." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The IDST is equivalent to a normal DST except for the normalization and type. DST type 1 and 4 are their own inverse and DSTs 2 and 3 are each other's inverses. For an example that demonstrates the relation between the DST and ISDT, consult the " }, { "__type": "CrossRef", "__tag": 4002, "value": "DST and IDST", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "docs", "path": "tutorial:fft" }, "kind": "exists" }, { "__type": "Text", "__tag": 4046, "value": " section of the " }, { "__type": "CrossRef", "__tag": 4002, "value": "user_guide", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "docs", "path": "tutorial:index" }, "kind": "exists" }, { "__type": "Text", "__tag": 4046, "value": "." } ] } ], "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": "idst", "annotation": "ndarray of real", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The transformed input array." } ] } ] } ] } ], "title": [], "level": 0, "target": null }, "Summary": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Return the Inverse Discrete Sine Transform of an arbitrary type sequence." } ] } ], "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": "The input array." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "type", "annotation": "{1, 2, 3, 4}, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Type of the DST (see Notes). Default type is 2." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "n", "annotation": "int, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Length of the transform. If " }, { "__type": "InlineCode", "__tag": 4051, "value": "n < x.shape[axis]" }, { "__type": "Text", "__tag": 4046, "value": ", " }, { "__type": "ParamRef", "__tag": 4071, "name": "x" }, { "__type": "Text", "__tag": 4046, "value": " is truncated. If " }, { "__type": "InlineCode", "__tag": 4051, "value": "n > x.shape[axis]" }, { "__type": "Text", "__tag": 4046, "value": ", " }, { "__type": "ParamRef", "__tag": 4071, "name": "x" }, { "__type": "Text", "__tag": 4046, "value": " is zero-padded. The default results in " }, { "__type": "InlineCode", "__tag": 4051, "value": "n = x.shape[axis]" }, { "__type": "Text", "__tag": 4046, "value": "." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "axis", "annotation": "int, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Axis along which the idst 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": "norm", "annotation": "{\"backward\", \"ortho\", \"forward\"}, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Normalization mode (see Notes). Default is \"backward\"." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "overwrite_x", "annotation": "bool, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "If True, the contents of " }, { "__type": "ParamRef", "__tag": 4071, "name": "x" }, { "__type": "Text", "__tag": 4046, "value": " can be destroyed; the default is False." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "workers", "annotation": "int, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Maximum number of workers to use for parallel computation. If negative, the value wraps around from " }, { "__type": "InlineCode", "__tag": 4051, "value": "os.cpu_count()" }, { "__type": "Text", "__tag": 4046, "value": ". See " }, { "__type": "CrossRef", "__tag": 4002, "value": "fft", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "scipy", "version": "?", "kind": "module", "path": "scipy.fft._basic:fft" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " for more details." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "orthogonalize", "annotation": "bool, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Whether to use the orthogonalized IDST variant (see Notes). Defaults to " }, { "__type": "InlineCode", "__tag": 4051, "value": "True" }, { "__type": "Text", "__tag": 4046, "value": " when " }, { "__type": "InlineCode", "__tag": 4051, "value": "norm=\"ortho\"" }, { "__type": "Text", "__tag": 4046, "value": " and " }, { "__type": "InlineCode", "__tag": 4051, "value": "False" }, { "__type": "Text", "__tag": 4046, "value": " otherwise." } ] }, { "__type": "Admonition", "__tag": 4056, "kind": "versionadded", "base_type": "neutral", "children": [ { "__type": "AdmonitionTitle", "__tag": 4055, "children": [ { "__type": "Text", "__tag": 4046, "value": "versionadded 1.8.0" } ] } ] } ] } ] } ], "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": "build-install/usr/lib/python3.14/site-packages/scipy/fft/_realtransforms.py", "item_line": 656, "item_type": "_Function", "aliases": [ "scipy.fft.idst" ], "example_section_data": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Text", "__tag": 4046, "value": "The following example calculates the signal from a spectrum `X` where only the first\nbin has a non-zero value. The signal for all four DST types is plotted:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "import numpy as np\nimport matplotlib.pyplot as plt\nfrom scipy.fft import idst\nN = 15\nX = np.array([0, N]) # the last `N-2` bin zero-valued bins are not needed\n_, ax = plt.subplots()\n", "execution_status": "success", "out": "" }, { "__type": "Code", "__tag": 4050, "value": "ax.set(title=f\"Inverse of one component DST ({N} samples)\",\n xlim=(0, N), xlabel=\"k\", ylabel=\"x[k]\")\nfor t_ in range(1, 5):\n x = idst(X, type=t_, n=N) # parameter `n` pads `X` to length `N`.\n ax.plot(x, '.-', alpha=0.5, label=f\"Type {t_}\")\n", "execution_status": "failure", "out": "[]\n[]\n[]\n[]\n" }, { "__type": "Code", "__tag": 4050, "value": "ax.grid(True)\n", "execution_status": "success", "out": "" }, { "__type": "Code", "__tag": 4050, "value": "ax.legend()\n", "execution_status": "failure", "out": "\n" }, { "__type": "Code", "__tag": 4050, "value": "plt.show()\n", "execution_status": "success", "out": "" }, { "__type": "Figure", "__tag": 4024, "value": { "__type": "RefInfo", "__tag": 4000, "module": "scipy", "version": "2.0.0.dev0+git20260907.41eeb59", "kind": "assets", "path": "fig-74ea999d03c327e7.png" } }, { "__type": "Text", "__tag": 4046, "value": "\nThe resulting signals are sines with their period and their phase determined by the\nused DST type. The following table shows those, with `N` being the number of signal\nsamples and `n` is the index of the non-zero bin (here: ``N, n = 15, 1``):\n\n+------+------------------------------+------------------------+\n| Type | period in samples | phase shift in samples |\n+======+==============================+========================+\n| 1 | :math:`2 (N+1) / (n+1) = 16` | :math:`-1` |\n+------+------------------------------+------------------------+\n| 2 | :math:`2 N / (n+1) = 15` | :math:`-1/2` |\n+------+------------------------------+------------------------+\n| 3 | :math:`2 N / (n+1/2) = 20` | :math:`-1` |\n+------+------------------------------+------------------------+\n| 4 | :math:`2 N / (n+1/2) = 20` | :math:`-1/2` |\n+------+------------------------------+------------------------+" } ], "title": [], "level": 0, "target": null }, "see_also": [ { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "dst", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.fft._realtransforms:dst" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Forward DST" } ] } ], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "irfft", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "current-module", "version": "current-version", "kind": "to-resolve", "path": "irfft" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Inverse FFT for real input" } ] } ], "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": "type", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "2" }, { "__type": "SigParam", "__tag": 4030, "name": "n", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "axis", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "-1" }, { "__type": "SigParam", "__tag": 4030, "name": "norm", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "overwrite_x", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "False" }, { "__type": "SigParam", "__tag": 4030, "name": "workers", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "orthogonalize", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" } ], "return_annotation": { "__type": "Empty", "__tag": 4031 }, "target_name": "idst" }, "references": null, "qa": "scipy.fft._realtransforms:idst", "arbitrary": [], "local_refs": [ "axis", "idst", "n", "norm", "orthogonalize", "overwrite_x", "type", "workers", "x" ] }