A simple notebook to explore Morlet Wavelets in Time and in Frequency

MorletWavelets.lgt.py

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# # Morlet Wavelets in Time and in Frequency
#
# https://www.youtube.com/watch?v=wgRgodvU_Ms

# +
import numpy as np
from plotly import tools
import plotly.offline as py
import plotly.graph_objs as go


srate = 1000
time = np.linspace(-2,2,srate)
frex = 6.5

def morlet_wavelet(srate=1000, time=np.linspace(-2,2,1000),frex=6.5, S=7):
    """
    A function to make a morlet wavelet that can be explored with ipywidgets
    returns: a tuple of (morlet wavelet, guassian, sine wave)
    """
    sine_wave = np.exp(1j*2*np.pi*frex*time)
    s = S / (2*np.pi*frex)
    guas_win = np.exp( (-time**2) / (2*s**2))
    cmw = sine_wave * guas_win
    
    return cmw, guas_win, sine_wave



def MorletPlots(frex, S):
    """
    plotting function to plot a 23d Morlet Wavelet for exploration
    """
    srate = 500
    time=np.linspace(-2,2,srate)
    cmw, guas_win, sine_wave = morlet_wavelet(srate, time, frex, S)
    
    cmw_data = go.Scatter(
        x=time,
        y=cmw.real
    )

    
    sine = go.Scatter(
        x=time, 
        y=sine_wave.imag,
        
    )

    guas = go.Scatter(
        x=time,
        y=guas_win
    )
    
    fig = tools.make_subplots(rows=2, cols=2, specs=[[{}, {}], [{'colspan': 2}, None]],
                          subplot_titles=('Sine Wave','Guassian', 'Real Wavelet'))

    fig.append_trace(sine, 1, 1)
    fig.append_trace(guas, 1, 2)
    fig.append_trace(cmw_data, 2,1)


#     fig = go.Figure(data=data, layout=layout)
    fig['layout'].update(showlegend=False, title='Morlet Wavelet Function')

    py.iplot(fig, filename='custom-sized-subplot-with-subplot-titles')

# +
from IPython.display import display
from ipywidgets import interact, interactive, fixed, interact_manual
import ipywidgets as widgets


P = interactive(MorletPlots,frex=(1,10), S=30)
display(P)
# -