librosa.filters.wavelet_lengths

librosa.filters.wavelet_lengths(*, freqs, sr=22050, window='hann', filter_scale=1, gamma=0, alpha=None)[source]

Return length of each filter in a wavelet basis.

Parameters:
freqsnp.ndarray (positive)

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

srnumber > 0 [scalar]

Audio sampling rate

windowstr or callable

Window function to use on filters

filter_scalefloat > 0 [scalar]

Resolution of filter windows. Larger values use longer windows.

gammanumber >= 0 [scalar, optional]

Bandwidth offset for determining filter lengths, as used in Variable-Q transforms.

Bandwidth for the k’th filter is determined by:

```B[k] = alpha[k] * freqs[k] + gamma
```

`alpha[k]` is twice the relative difference between `freqs[k+1]` and `freqs[k-1]`:

```alpha[k] = (freqs[k+1]-freqs[k-1]) / (freqs[k+1]+freqs[k-1])
```

If `freqs` follows a geometric progression (as in CQT and VQT), the vector `alpha` is constant and such that:

```(1 + alpha) * freqs[k-1] = (1 - alpha) * freqs[k+1]
```

Furthermore, if `gamma=0` (default), `alpha` is such that even-`k` and odd-`k` filters are interleaved:

```freqs[k-1] + B[k-1] = freqs[k+1] - B[k+1]
```

If `gamma=None` is specified, then `gamma` is computed such that each filter has bandwidth proportional to the equivalent rectangular bandwidth (ERB) at frequency `freqs[k]`:

```gamma[k] = 24.7 * alpha[k] / 0.108
```

as derived by [1].

alphanumber > 0 [optional]

Optional pre-computed relative bandwidth parameter. Note that this must be provided if `len(freqs)==1` because bandwidth cannot be inferred from a single frequency. Otherwise, if left unspecified, it will be automatically derived by the rules specified above.

Returns:
lengthsnp.ndarray

The length of each filter.

f_cutofffloat

The lowest frequency at which all filters’ main lobes have decayed by at least 3dB.

This second output serves in cqt and vqt to ensure that all wavelet bands remain below the Nyquist frequency.

Raises:
ParameterError
• If `filter_scale` is not strictly positive

• If `gamma` is a negative number

• If any frequencies are <= 0

• If the frequency array is not sorted in ascending order

Notes

This function caches at level 10.