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librosa.filters.wavelet(*, freqs, sr=22050, window='hann', filter_scale=1, pad_fft=True, norm=1, dtype=<class 'numpy.complex64'>, gamma=0, alpha=None, **kwargs)[source]

Construct a wavelet basis using windowed complex sinusoids.

This function constructs a wavelet filterbank at a specified set of center frequencies.

freqsnp.ndarray (positive)

Center frequencies of the filters (in Hz). Must be in ascending order.

srnumber > 0 [scalar]

Audio sampling rate

windowstring, tuple, number, or function

Windowing function to apply to filters.

filter_scalefloat > 0 [scalar]

Scale of filter windows. Small values (<1) use shorter windows for higher temporal resolution.


Center-pad all filters up to the nearest integral power of 2.

By default, padding is done with zeros, but this can be overridden by setting the mode= field in kwargs.

norm{inf, -inf, 0, float > 0}

Type of norm to use for basis function normalization. See librosa.util.normalize

gammanumber >= 0

Bandwidth offset for variable-Q transforms.


The data type of the output basis. By default, uses 64-bit (single precision) complex floating point.

alphanumber > 0 [optional]

If only one frequency is provided (len(freqs)==1), then filter bandwidth cannot be computed. In that case, the alpha parameter described above can be explicitly specified here.

If two or more frequencies are provided, this parameter is ignored.

**kwargsadditional keyword arguments

Arguments to np.pad() when pad==True.

filtersnp.ndarray, len(filters) == n_bins

each filters[i] is a (complex) time-domain filter

lengthsnp.ndarray, len(lengths) == n_bins

The (fractional) length of each filter in samples


This function caches at level 10.


Create a constant-Q basis

>>> freqs = librosa.cqt_frequencies(n_bins=84, fmin=librosa.note_to_hz('C1'))
>>> basis, lengths = librosa.filters.wavelet(freqs=freqs, sr=22050)

Plot one octave of filters in time and frequency

>>> import matplotlib.pyplot as plt
>>> basis, lengths = librosa.filters.wavelet(freqs=freqs, sr=22050)
>>> fig, ax = plt.subplots(nrows=2, figsize=(10, 6))
>>> notes = librosa.midi_to_note(np.arange(24, 24 + len(basis)))
>>> for i, (f, n) in enumerate(zip(basis, notes[:12])):
...     f_scale = librosa.util.normalize(f) / 2
...     ax[0].plot(i + f_scale.real)
...     ax[0].plot(i + f_scale.imag, linestyle=':')
>>> ax[0].set(yticks=np.arange(len(notes[:12])), yticklabels=notes[:12],
...           ylabel='CQ filters',
...           title='CQ filters (one octave, time domain)',
...           xlabel='Time (samples at 22050 Hz)')
>>> ax[0].legend(['Real', 'Imaginary'])
>>> F = np.abs(np.fft.fftn(basis, axes=[-1]))
>>> # Keep only the positive frequencies
>>> F = F[:, :(1 + F.shape[1] // 2)]
>>> librosa.display.specshow(F, x_axis='linear', y_axis='cqt_note', ax=ax[1])
>>> ax[1].set(ylabel='CQ filters', title='CQ filter magnitudes (frequency domain)')