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name: discrete-transforms description: "Routes PyWavelets users through DWT, IDWT, multilevel transforms, SWT, MRA, coefficient packing, thresholding, padding, and fully separable transforms." disable-model-invocation: true metadata: disco-role: operating license: MIT

Discrete Transforms

Use this sub-skill for the core pywt transform stack: decimated DWT/IDWT, 2D and ND transforms, coefficient packing, stationary wavelets, multiresolution analysis, thresholding, signal-extension modes, padding, and fully separable transforms.

Route here when the task asks for

• dwt, idwt, wavedec, waverec, dwt2, idwt2, wavedec2, waverec2
• dwtn, idwtn, wavedecn, waverecn
• swt, iswt, swt2, iswt2, swtn, iswtn
• mra, mra2, mran, imra, imra2, imran
• coeffs_to_array, array_to_coeffs, ravel_coeffs, unravel_coeffs, wavedecn_size, wavedecn_shapes
• threshold, threshold_firm, pad, Modes.modes, dwt_coeff_len, dwt_max_level, dwtn_max_level
• fswavedecn, fswaverecn, or FswavedecnResult

Route elsewhere when the task is about

• wavelet catalogs, custom wavelets, wavefun, central_frequency, scale2frequency, or cwt: go to ../wavelets-and-cwt/SKILL.md
• packet trees, node paths, packet reconstruction, or WaveletPacket*: go to ../wavelet-packets/SKILL.md

Start here

• Read references/workflows.md for concrete transform recipes.
• Read references/api-reference.md when you need the verified signatures or result-shape rules.
• Read references/troubleshooting.md when modes, axes, coefficient shapes, or SWT/MRA constraints fail.
• Run ../../scripts/check_pywavelets_install.py when you want a quick smoke check that covers the core transform stack.

Common workflow anchors

• Use pywt.Modes.modes to confirm supported extension modes before choosing mode=.
• For 1D smoke checks, db1 and symmetric are the safest defaults.
• For SWT and SWT-based MRA, prefer mode='periodization' and a signal length that is a multiple of 2**level.
• For waverec and waverecn, zero arrays are the safe way to omit coefficients; None is not the general replacement mechanism.
• For coefficient packing, prefer coeffs_to_array / array_to_coeffs when you need a shaped array and ravel_coeffs / unravel_coeffs when you need a flat vector.
• For fully separable transforms, inspect the returned FswavedecnResult object instead of treating it as a raw coefficient list.

Useful bundled data

• pywt.data.ecg() is a compact 1D signal for DWT, SWT, and thresholding examples.
• pywt.data.camera() is a compact 2D image for dwt2, wavedec2, dwtn, wavedecn, swt2, and packet-adjacent smoke checks.
• pywt.data.nino() is useful when a transform recipe needs a small real-valued signal with a time axis.

What to expect from the references

• references/workflows.md gives copyable recipes for 1D, 2D, ND, SWT, MRA, coefficient packing, thresholding, padding, and fully separable transforms.
• references/api-reference.md lists the verified function signatures and the major return-shape conventions.
• references/troubleshooting.md explains the common error fragments and recovery steps for transform and coefficient workflows.