cupyx.scipy.signal.morlet2#

cupyx.scipy.signal.morlet2(M, s, w=5)[source]#

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

Return type:

(M,) ndarray

See also

morlet: Implementation of Morlet wavelet, incompatible with cwt

Notes

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 cupyx.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 cupyx.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()