Module « scipy.signal »

Fonction morlet2 - module scipy.signal

Signature de la fonction morlet2

def morlet2(M, s, w=5) 

Description

morlet2.__doc__

    Complex Morlet wavelet, designed to work with `cwt`.

    Returns the complete version of morlet wavelet, normalised
    according to `s`::

        exp(1j*w*x/s) * exp(-0.5*(x/s)**2) * pi**(-0.25) * sqrt(1/s)

    Parameters
    ----------
    M : int
        Length of the wavelet.
    s : float
        Width parameter of the wavelet.
    w : float, optional
        Omega0. Default is 5

    Returns
    -------
    morlet : (M,) ndarray

    See Also
    --------
    morlet : Implementation of Morlet wavelet, incompatible with `cwt`

    Notes
    -----

    .. versionadded:: 1.4.0

    This function was designed to work with `cwt`. Because `morlet2`
    returns an array of complex numbers, the `dtype` argument of `cwt`
    should be set to `complex128` for best results.

    Note the difference in implementation with `morlet`.
    The fundamental frequency of this wavelet in Hz is given by::

        f = w*fs / (2*s*np.pi)

    where ``fs`` is the sampling rate and `s` is the wavelet width parameter.
    Similarly we can get the wavelet width parameter at ``f``::

        s = w*fs / (2*f*np.pi)

    Examples
    --------
    >>> from scipy import signal
    >>> import matplotlib.pyplot as plt

    >>> M = 100
    >>> s = 4.0
    >>> w = 2.0
    >>> wavelet = signal.morlet2(M, s, w)
    >>> plt.plot(abs(wavelet))
    >>> plt.show()

    This example shows basic use of `morlet2` with `cwt` in time-frequency
    analysis:

    >>> from scipy import signal
    >>> import matplotlib.pyplot as plt
    >>> t, dt = np.linspace(0, 1, 200, retstep=True)
    >>> fs = 1/dt
    >>> w = 6.
    >>> sig = np.cos(2*np.pi*(50 + 10*t)*t) + np.sin(40*np.pi*t)
    >>> freq = np.linspace(1, fs/2, 100)
    >>> widths = w*fs / (2*freq*np.pi)
    >>> cwtm = signal.cwt(sig, signal.morlet2, widths, w=w)
    >>> plt.pcolormesh(t, freq, np.abs(cwtm), cmap='viridis', shading='gouraud')
    >>> plt.show()