clouddrift.wavelet.morse_wavelet

clouddrift.wavelet.morse_wavelet(length: int, gamma: float, beta: float, radian_frequency: ndarray, order: int | None = 1, normalization: str | None = 'bandpass') → tuple[ndarray, ndarray]

Compute the generalized Morse wavelets of Olhede and Walden (2002), doi: 10.1109/TSP.2002.804066.

Parameters

lengthint

Length of the wavelets.

gammafloat

Gamma parameter of the wavelets.

betafloat

Beta parameter of the wavelets.

radian_frequencynp.ndarray

The radian frequencies at which the Fourier transform of the wavelets reach their maximum amplitudes. radian_frequency is between 0 and 2 * np.pi * 0.5, the normalized Nyquist radian frequency.

orderint, optional

Order of wavelets, default is 1.

normalizationstr, optional

Normalization for the wavelet output. By default it is assumed to be "bandpass" which uses a bandpass normalization, meaning that the FFT of the wavelets have peak value of 2 for all central frequencies radian_frequency. The other option is "energy"``which uses the unit energy normalization. In this last case, the time-domain wavelet energies ``np.sum(np.abs(wave)**2) are always unity.

Returns

waveletnp.ndarray

Time-domain wavelets with shape (order, radian_frequency, length).

wavelet_fft: np.ndarray

Frequency-domain wavelets with shape (order, radian_frequency, length).

Examples

Compute a Morse wavelet with gamma parameter 3, beta parameter 4, at radian frequency 0.2 cycles per unit time:

>>> wavelet, wavelet_fft = morse_wavelet(1024, 3, 4, np.array([2*np.pi*0.2]))
>>> np.shape(wavelet)
(1, 1, 1024)

Compute a suite of Morse wavelets with gamma parameter 3, beta parameter 4, up to order 3, at radian frequencies 0.2 and 0.3 cycles per unit time:

>>> wavelet, wavelet_fft = morse_wavelet(1024, 3, 4, np.array([2*np.pi*0.2, 2*np.pi*0.3]), order=3)
>>> np.shape(wavelet)
(3, 2, 1024)

Compute a Morse wavelet specifying an energy normalization : >>> wavelet, wavelet_fft = morse_wavelet(1024, 3, 4, np.array([2*np.pi*0.2]), normalization=”energy”)

Raises

ValueError

If normalization optional argument is not in [“bandpass”, “energy”]``.

See Also

wavelet_transform(), morse_wavelet_transform(), morse_freq(), morse_logspace_freq(), morse_amplitude(), morse_properties()