morlet_func

ketos.utils.morlet_func(time, frequency, width, displacement, norm=True, dfdt=0)

Compute Morlet wavelet function

The function is implemented as in Eq. (15) in John Ashmead, “Morlet Wavelets in Quantum Mechanics”, Quanta 2012; 1: 58-70, with the replacement f -> 2*pi*f*s, to allow f to be identified with the physical frequency.

Args:

time: float or numpy array

Time in seconds at which the function is to be evaluated

frequency: float

Wavelet frequency in Hz

width: float

Wavelet width in seconds (1-sigma width of the Gaussian envelope function)

displacement: float

Wavelet centroid in seconds

norm: bool

Include [pi^1/4*sqrt(sigma)]^-1 normalization factor

dfdt: float

Rate of change in frequency as a function of time in Hz per second. If dfdt is non-zero, the frequency is computed as

f = frequency + (time - displacement) * dfdt

Returns:

y: float or numpy array

Value of Morlet wavelet function at time t

Example:

>>> from ketos.utils import morlet_func
>>> 
>>> time = np.array([-1., 0., 0.5])
>>> f = morlet_func(time=time, frequency=10, width=3, displacement=0)
>>> print(f)
[0.41022718 0.43366254 0.42768108]