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# scipy.signal.morlet

`scipy.signal.``morlet`(M, w=5.0, s=1.0, complete=True)

  Complex Morlet wavelet.

  Parameters:

  M : int

  > Length of the wavelet.

  w : float, optional

  > Omega0. Default is 5

  s : float, optional

  > Scaling factor, windowed from `-s*2*pi` to `+s*2*pi`. Default is 1.

  complete : bool, optional

  > Whether to use the complete or the standard version.

  Returns: | morlet : (M,) ndarray

  See also

  `scipy.signal.gausspulse`

  Notes

  The standard version:

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

  This commonly used wavelet is often referred to simply as the Morlet wavelet. Note that this simplified version can cause admissibility problems at low values of w.

  The complete version:

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

  This version has a correction term to improve admissibility. For w greater than 5, the correction term is negligible.

  Note that the energy of the return wavelet is not normalised according to `s`.

  The fundamental frequency of this wavelet in Hz is given by `f = 2*s*w*r / M` where r is the sampling rate.

  Note: This function was created before `cwt` and is not compatible with it.