# scipy.signal.cwt

scipy.signal.cwt(data, wavelet, widths, dtype=None, **kwargs)

  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.

      New in version 1.4.0.

    kwargs

      Keyword arguments passed to wavelet function.

      New in version 1.4.0.

  Returns:
    cwt: (M, N) ndarray

      Will have shape of (len(widths), len(data)).

  Notes

  New in version 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

      >>> import numpy as np
      >>> 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)

  Note

  For cwt matrix plotting it is advisable to flip the y-axis

      >>> cwtmatr_yflip = np.flipud(cwtmatr)
      >>> plt.imshow(cwtmatr_yflip, extent=[-1, 1, 1, 31], cmap='PRGn', aspect='auto',
      ...            vmax=abs(cwtmatr).max(), vmin=-abs(cwtmatr).max())
      >>> plt.show()