morlet2(M, s, w=5)
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)
This function was designed to work with cwt
. Because morlet2
returns an array of complex numbers, the :None:None:`dtype` argument of cwt
should be set to :None:None:`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)
Length of the wavelet.
Width parameter of the wavelet.
Omega0. Default is 5
Complex Morlet wavelet, designed to work with cwt
.
morlet
Implementation of Morlet wavelet, incompatible with :None:None:`cwt`
>>> 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()
The following pages refer to to this document either explicitly or contain code examples using this.
scipy.signal._wavelets.morlet
scipy.signal._wavelets.morlet2
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