# scipy.signal.morlet2¶

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
Mint

Length of the wavelet.

sfloat

Width parameter of the wavelet.

wfloat, optional

Omega0. Default is 5

Returns
morlet(M,) ndarray

`morlet`

Implementation of Morlet wavelet, incompatible with `cwt`

Notes

New in version 1.4.0.

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 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()
``` 