Module « scipy.signal »

Fonction cwt - module scipy.signal

Signature de la fonction cwt

def cwt(data, wavelet, widths, dtype=None, **kwargs) 

Description

cwt.__doc__

    Continuous wavelet transform.

    Performs a continuous wavelet transform on `data`,
    using the `wavelet` function. A CWT performs a convolution
    with `data` using the `wavelet` function, which is characterized
    by a width parameter and length parameter. The `wavelet` function
    is allowed to be complex.

    Parameters
    ----------
    data : (N,) ndarray
        data on which to perform the transform.
    wavelet : function
        Wavelet function, which should take 2 arguments.
        The first argument is the number of points that the returned vector
        will have (len(wavelet(length,width)) == length).
        The second is a width parameter, defining the size of the wavelet
        (e.g. standard deviation of a gaussian). See `ricker`, which
        satisfies these requirements.
    widths : (M,) sequence
        Widths to use for transform.
    dtype : data-type, optional
        The desired data type of output. Defaults to ``float64`` if the
        output of `wavelet` is real and ``complex128`` if it is complex.

        .. versionadded:: 1.4.0

    kwargs
        Keyword arguments passed to wavelet function.

        .. versionadded:: 1.4.0

    Returns
    -------
    cwt: (M, N) ndarray
        Will have shape of (len(widths), len(data)).

    Notes
    -----

    .. versionadded:: 1.4.0

    For non-symmetric, complex-valued wavelets, the input signal is convolved
    with the time-reversed complex-conjugate of the wavelet data [1].

    ::

        length = min(10 * width[ii], len(data))
        cwt[ii,:] = signal.convolve(data, np.conj(wavelet(length, width[ii],
                                        **kwargs))[::-1], mode='same')

    References
    ----------
    .. [1] S. Mallat, "A Wavelet Tour of Signal Processing (3rd Edition)",
        Academic Press, 2009.

    Examples
    --------
    >>> from scipy import signal
    >>> import matplotlib.pyplot as plt
    >>> t = np.linspace(-1, 1, 200, endpoint=False)
    >>> sig  = np.cos(2 * np.pi * 7 * t) + signal.gausspulse(t - 0.4, fc=2)
    >>> widths = np.arange(1, 31)
    >>> cwtmatr = signal.cwt(sig, signal.ricker, widths)
    >>> plt.imshow(cwtmatr, extent=[-1, 1, 1, 31], cmap='PRGn', aspect='auto',
    ...            vmax=abs(cwtmatr).max(), vmin=-abs(cwtmatr).max())
    >>> plt.show()