diff --git a/pywt/_cwt.py b/pywt/_cwt.py index 58d1aceb7..45b9b0838 100644 --- a/pywt/_cwt.py +++ b/pywt/_cwt.py @@ -62,6 +62,7 @@ def cwt(data, scales, wavelet, sampling_period=1., method='conv'): - ``fft`` uses frequency domain convolution. - ``auto`` uses automatic selection based on an estimate of the computational complexity at each scale. + The ``conv`` method complexity is ``O(len(scale) * len(data))``. The ``fft`` method is ``O(N * log2(N))`` with ``N = len(scale) + len(data) - 1``. It is well suited for large size diff --git a/pywt/_swt.py b/pywt/_swt.py index 2600b169c..575c4e803 100644 --- a/pywt/_swt.py +++ b/pywt/_swt.py @@ -86,16 +86,17 @@ def swt(data, wavelet, level=None, start_level=0, axis=-1, at cost of redundancy in the transform (the size of the output coefficients is larger than the input). - When the following three conditions are true:: + When the following three conditions are true: - 1.) The wavelet is orthogonal - 2.) ``swt`` is called with ``norm=True`` - 3.) ``swt`` is called with ``trim_approx=True`` + 1. The wavelet is orthogonal + 2. ``swt`` is called with ``norm=True`` + 3. ``swt`` is called with ``trim_approx=True`` the transform has the following additional properties that may be desirable in applications: - 1.) energy is conserved - 2.) variance is partitioned across scales + + 1. energy is conserved + 2. variance is partitioned across scales When used with ``norm=True``, this transform is closely related to the multiple-overlap DWT (MODWT) as popularized for time-series analysis, @@ -106,7 +107,7 @@ def swt(data, wavelet, level=None, start_level=0, axis=-1, References ---------- .. [1] DB Percival and AT Walden. Wavelet Methods for Time Series Analysis. - Cambridge University Press, 2000. + Cambridge University Press, 2000. """ if not _have_c99_complex and np.iscomplexobj(data): @@ -328,16 +329,18 @@ def swt2(data, wavelet, level, start_level=0, axes=(-2, -1), at cost of redundancy in the transform (the size of the output coefficients is larger than the input). - When the following three conditions are true:: + When the following three conditions are true: - 1.) The wavelet is orthogonal - 2.) ``swt2`` is called with ``norm=True`` - 3.) ``swt2`` is called with ``trim_approx=True`` + 1. The wavelet is orthogonal + 2. ``swt2`` is called with ``norm=True`` + 3. ``swt2`` is called with ``trim_approx=True`` the transform has the following additional properties that may be desirable in applications: - 1.) energy is conserved - 2.) variance is partitioned across scales + + 1. energy is conserved + 2. variance is partitioned across scales + """ axes = tuple(axes) data = np.asarray(data) @@ -562,16 +565,18 @@ def swtn(data, wavelet, level, start_level=0, axes=None, trim_approx=False, at cost of redundancy in the transform (the size of the output coefficients is larger than the input). - When the following three conditions are true:: + When the following three conditions are true: - 1.) The wavelet is orthogonal - 2.) ``swtn`` is called with ``norm=True`` - 3.) ``swtn`` is called with ``trim_approx=True`` + 1. The wavelet is orthogonal + 2. ``swtn`` is called with ``norm=True`` + 3. ``swtn`` is called with ``trim_approx=True`` the transform has the following additional properties that may be desirable in applications: - 1.) energy is conserved - 2.) variance is partitioned across scales + + 1. energy is conserved + 2. variance is partitioned across scales + """ data = np.asarray(data) if not _have_c99_complex and np.iscomplexobj(data):