Wavelet

Compare IDL code to python code for the wavelet transformation of a simple wave function.

IDL code: SPEDAS

The SPEDAS IDL code uses Complex Morlet wavelets internally, and computes the resulting power.

  ; Create a tplot variable that contains a wave.
  t =  FINDGEN(4000)
  time = time_double('2010-01-01') + 10*t  
  data = sin(2*!pi*t/32.) 
  data2 = sin(2*!pi*t/64.)
  data[1000:3000] = data2[1000:3000]  
  var = 'sin_wav'
  store_data, var, data={x:time, y:data}

  ; Apply wavelet transformation.
  wav_data, var 

  ; Plot the wave and the result of the transformation.
  pvar = 'sin_wav_wv_pow'
  tplot, [var, pvar]

Python code: pySPEDAS

Similar code in python uses the pywavelets library. This example uses the Complex Morlet wavelets.

import numpy as np
import pytplot
from pyspedas import time_float
from pyspedas.analysis.wavelet import wavelet

# Create a tplot variable that contains a wave.
t = np.arange(4000.)
y = np.sin(2*np.pi*t/32.) 
y2 = np.sin(2*np.pi*t/64.) 
y[1000:3000] = y2[1000:3000]
var = 'sin_wav'
time = time_float('2010-01-01') + 10*t
pytplot.store_data(var, data={'x':time, 'y':y})

# Complex Morlet wavelets transformation.
powervar = wavelet(var, wavename='cmorl0.5-1.0')
pvar = powervar[0]

# Define plotting parameters and plot. 
pytplot.options(pvar, 'colormap', 'jet')
pytplot.ylim(pvar, 0.001, 0.1)
pytplot.options(pvar, 'ylog', True)
pytplot.options(pvar, 'ytitle', pvar)
pytplot.tplot([var, pvar])

With a small change to the python code we can use a different wavelet, for example the Gaussian Derivative wavelet.

import numpy as np
import pytplot
from pyspedas import time_float
from pyspedas.analysis.wavelet import wavelet

# Create a tplot variable that contains a wave.
t = np.arange(4000.)
y = np.sin(2*np.pi*t/32.) 
y2 = np.sin(2*np.pi*t/64.) 
y[1000:3000] = y2[1000:3000]
var = 'sin_wav'
time = time_float('2010-01-01') + 10*t
pytplot.store_data(var, data={'x':time, 'y':y})

# Gaussian Derivative wavelets transformation.
powervar = wavelet(var, wavename='gaus1')
pvar = powervar[0]

# Define plotting parameters and plot. 
pytplot.options(pvar, 'colormap', 'jet')
pytplot.ylim(pvar, 0.001, 0.1)
pytplot.options(pvar, 'ylog', True)
pytplot.options(pvar, 'ytitle', pvar)
pytplot.tplot([var, pvar])