Loading doc/source/tutorials/tutorial11.rst 0 → 100644 +160 −0 Original line number Diff line number Diff line Tutorial 11 - Morlet Wavelet Decomposition ======================================================= In this tutorial, we will look at describing time-frequency dynamics in a signal using a Morlet Wavelet decomposition. For this tutorial, we will use the same MEG example data which we have used in previous tutorials. We start by importing our modules and finding and loading the example data. .. code-block:: python import os from os.path import join import h5py import numpy as np import matplotlib.pyplot as plt import sails plt.style.use('ggplot') SAILS will automatically detect the example data if downloaded into your home directory. If you've used a different location, you can specify this in an environment variable named ``SAILS_EXAMPLE_DATA``. .. code-block:: python # Specify environment variable with example data location # This is only necessary if you have not checked out the # example data into $HOME/sails-example-data #os.environ['SAILS_EXAMPLE_DATA'] = '/path/to/sails-example-data' # Locate and validate example data directory example_path = sails.find_example_path() # Load data using h5py data_path = os.path.join(sails.find_example_path(), 'meg_occipital_ve.hdf5') X = h5py.File(data_path, 'r')['X'][:, 122500:130000, 0] sample_rate = 250 time_vect = np.linspace(0, X.shape[1] // sample_rate, X.shape[1]) The Morlet Wavelet transform first defines a set of wavelet functions to use as am adaptive basis set. These wavelets are simple burst-like oscillations created to a pre-defined set of parameters. .. code-block:: python # Wavelet frequencies in Hz freqs = [10] # Number of cycles within the oscillatory event ncycles = 5 # Length of window in seconds win_len = 10 # Compute wavelets mlt = sails.wavelet.get_morlet_basis(freqs, ncycles, win_len, sample_rate, normalise=False) ``mlt`` is now a list of wavelet basis functions. In this case, we have a single 10Hz basis. This wavelet is a complex-valued array (in the same way that a Fourier transform returns a complex valued result). To visualise the wavelet, we can plot the real and imaginary parts of the complex function. .. code-block:: python plt.figure() plt.plot(mlt[0].real) plt.plot(mlt[0].imag) plt.legend(['Real', 'Imag']) Note that the real and imaginary components are the same apart from a 90 degree phase shift in the time-series. This shift allow the wavelet transform to estimate the full amplitude envelope and phase of the underlying signal. The ``ncycles`` parameter is critical for defining the time-frequency resolution of the wavelet transform. A small value (typically less than 5) will lead to high temporal resolution but low frequency resolution whilst a large value (typically greater than 7) will have a low temporal resolutoin and a high frequency resolution. We will look into this in more detail later - for now, we can see that this parameter simply changes the number of cycles of oscillation present in our basis wavelets. .. code-block:: python # Compute wavelets mlt3 = sails.wavelet.get_morlet_basis(freqs, 3, win_len, sample_rate, normalise=False) mlt5 = sails.wavelet.get_morlet_basis(freqs, 5, win_len, sample_rate, normalise=False) mlt7 = sails.wavelet.get_morlet_basis(freqs, 7, win_len, sample_rate, normalise=False) plt.figure() for idx, mlt in enumerate([mlt3, mlt5, mlt7]): y = mlt[0].real t = np.arange((len(y))) - len(y)/2 # zero-centre the wavelet plt.plot(t, y + idx*2) plt.legend(['3-cycles', '5-cycles', '7-cycles']) We can see that the frequency of the oscillation in each wavelet is unchanged whilst the number of cycles is modified by changing ``ncycles``. We will often compute wavelets for a range of frequencies rather than just one. Here we pass in an array of frequency values to compute wavelets for. .. code-block:: python freqs = [3, 6, 9, 12, 15] # Compute wavelets mlt = sails.wavelet.get_morlet_basis(freqs, ncycles, win_len, sample_rate, normalise=False) plt.figure() for ii in range(len(freqs)): y = mlt[ii].real t = np.arange((len(y))) - len(y)/2 # zero-centre the wavelet plt.plot(t, y + ii*2) plt.legend(freqs) This time, we see that changing frequency keeps a consistent number of cycles in each wavelet but modifies the oscillatory period. To compute the wavelet transform itself, each wavelet basis function is convolved across the dataset. In this instance (as the wavelet function is symmetric and the input time-series are real values) this convolution is similar to computing the correlation between the basis function and the time-series at each point in time. Let's compute the wavelet transform at 10Hz on our real data. .. code-block:: python freqs = [10] cwt = sails.wavelet.morlet(X[0, :], freqs, sample_rate) plt.figure() plt.subplot(211) plt.plot(X.T) plt.subplot(212) plt.plot(cwt.T) We can see that the wavelet power tracks the amplitude of the oscillations visible in the original time-series. Finally, let's compute a full wavelet transform across a wider range of frequencies .. code-block:: python freqs = np.linspace(1, 20, 38) cwt = sails.wavelet.morlet(X[0, :], freqs, sample_rate, normalise='tallon') plt.figure() plt.subplot(211) plt.plot(time_vect, X.T) plt.xlim(time_vect[0], time_vect[-1]) plt.subplot(212) plt.pcolormesh(time_vect, freqs, cwt) sails/tests/test_wavelet.py +3 −2 Original line number Diff line number Diff line Loading @@ -13,10 +13,11 @@ class MorletBasisTests(unittest.TestCase): sample_rate = 128 freqs = np.linspace(1, 50, 49) ncycles = 5 win_len = 5 from ..wavelet import get_morlet_basis mlt = get_morlet_basis(freqs, ncycles, sample_rate) mlt = get_morlet_basis(freqs, ncycles, win_len, sample_rate) # Check we have same number of morlet basis waves as input freqs assert(len(mlt) == freqs.shape[0]) Loading @@ -26,7 +27,7 @@ class MorletBasisTests(unittest.TestCase): assert(np.all(np.diff([len(m) for m in mlt]) <= 0)) # Example with faster sample_rate mlt2 = get_morlet_basis(freqs, ncycles, sample_rate*2) mlt2 = get_morlet_basis(freqs, ncycles, win_len, sample_rate*2) check = np.c_[[len(m) for m in mlt], [len(m) for m in mlt2]] # Morlets from double sample rate should be twice as long (or off-by-one) Loading sails/wavelet.py +106 −17 Original line number Diff line number Diff line from scipy import signal #!/usr/bin/python # vim: set expandtab ts=4 sw=4: import numpy as np from scipy import signal def morlet(x, freqs, sample_rate, window_len=4, ncycles=5, ret_basis=False, ret_mode='power', normalise=False): def morlet(x, freqs, sample_rate, win_len=4, ncycles=5, ret_basis=False, ret_mode='power', normalise='wikipedia'): """Compute a morlet wavelet time-frequency transform on a univariate dataset. Parameters Loading @@ -14,7 +17,7 @@ def morlet(x, freqs, sample_rate, window_len=4, ncycles=5, ret_basis=False, Array of frequency values in Hz sample_rate : scalar Sampling frequency of data in Hz window_len : scalar win_len : scalar Length of wavelet window ncycles : int Width of wavelets in number of cycles Loading @@ -22,22 +25,34 @@ def morlet(x, freqs, sample_rate, window_len=4, ncycles=5, ret_basis=False, Boolean flag indicating whether to return the basis set alongside the transform. ret_mode : {'power', 'amplitude', 'complex'} Flag indicating whether which form of the wavelet transform to return. normalise : {None, 'simple', 'tallon', 'wikipedia', 'mne'} Flag indicating which normalisation factor to apply to the wavelet basis. See `sails.wavelet.get_morlet_basis` for details. Default = 'wikipedia'. Returns ------- 2D array Array containing morlet wavelet transformed data [nfreqs x nsamples] """ orig_dim = x.ndim if orig_dim == 1: x = x[np.newaxis, :] cwt = np.zeros((len(freqs), *x.shape[:]), dtype=complex) if 0 in freqs: raise ValueError("0 cannot be in freqs.") cwt = np.zeros((x.shape[0], len(freqs), x.shape[1]), dtype=complex) # Get morlet basis mlt = get_morlet_basis(freqs, ncycles, sample_rate, normalise=normalise) mlt = get_morlet_basis(freqs, ncycles, win_len, sample_rate, normalise) for jj in range(x.shape[0]): for ii in range(len(freqs)): a = signal.convolve(x, mlt[ii].real, mode='same', method='fft') b = signal.convolve(x, mlt[ii].imag, mode='same', method='fft') cwt[ii, ...] = a+1j*b a = signal.convolve(x[jj, :], mlt[ii].real, mode='same', method='fft') b = signal.convolve(x[jj, :], mlt[ii].imag, mode='same', method='fft') cwt[jj, ii, :] = a+1j*b if ret_mode == 'power': cwt = np.power(np.abs(cwt), 2) Loading @@ -46,13 +61,68 @@ def morlet(x, freqs, sample_rate, window_len=4, ncycles=5, ret_basis=False, elif ret_mode != 'complex': raise ValueError("'ret_mode not recognised, please use one of {'power','amplitude','complex'}") if orig_dim == 1: cwt = cwt[0, ...] if ret_basis: return cwt, mlt else: return cwt def get_morlet_basis(freq, ncycles, sample_rate, normalise=False, win_len=5): def cross_morlet(x, freqs, sample_rate, win_len=4, ncycles=5, ret_mode='power', normalise='wikipedia'): """Compute a morlet cross wavelet time-frequency transform on a multivariate dataset. Parameters ---------- x : vector array_like Time-series to compute cross wavelet transform from. freqs : array_like Array of frequency values in Hz. sample_rate : scalar Sampling frequency of data in Hz. win_len : scalar Length of wavelet window. ncycles : int Width of wavelets in number of cycles. ret_mode : {'power', 'amplitude', 'complex'} Flag indicating whether which form of the wavelet transform to return. normalise : {None, 'simple', 'tallon', 'wikipedia', 'mne'} Flag indicating which normalisation factor to apply to the wavelet basis. See `sails.wavelet.get_morlet_basis` for details. Default = 'wikipedia'. Returns ------- 4D array Array containing morlet cross wavelet transformed data [nfreqs x nsamples x nchannels x nchannels]. """ if ret_mode not in ['power', 'amplitude', 'complex']: raise ValueError("'ret_mode not recognised, please use one of {'power','amplitude','complex'}") # Run standard wavelet decomposition return complex values wt = morlet(x, freqs, sample_rate, win_len=win_len, ncycles=ncycles, ret_mode='complex', normalise=normalise) # Preallocate output array [nchannels x nchannels x nfreqs x ntimes] S = np.empty((wt.shape[0], wt.shape[0], wt.shape[1], wt.shape[2]), dtype=complex) # Main loop for ii in range(wt.shape[1]): for jj in range(wt.shape[2]): S[:, :, ii, jj] = np.dot(wt[:, ii, jj, np.newaxis], wt[np.newaxis, :, ii, jj].conj()) if ret_mode == 'power': S = np.power(np.abs(S), 2) elif ret_mode == 'amplitude': S = np.abs(S) elif ret_mode != 'complex': raise ValueError("'ret_mode not recognised, please use one of {'power', 'amplitude', 'complex'}") return S def get_morlet_basis(freq, ncycles, win_len, sample_rate, normalise='wikipedia'): """Compute a morlet wavelet basis set based on specified parameters. Parameters Loading @@ -61,20 +131,38 @@ def get_morlet_basis(freq, ncycles, sample_rate, normalise=False, win_len=5): Array of frequency values in Hz ncycles : int Width of wavelets in number of cycles win_len : scalar Length of wavelet window sample_rate : scalar Sampling frequency of data in Hz normalise : {None, 'simple', 'tallon', 'wikipedia', 'mne'} Flag indicating which normalisation factor to apply to the wavelet basis. win_len : float Window length duration factor Flag indicating which normalisation factor to apply to the wavelet basis (default is 'wikipedia') - can be one of: * None - no normalisation is applied * 'simple' - wavelet is normalised by its own sum * 'tallon' - normalisation from Tallon-Baudry et al 1997 * 'wikipedia' normalisation from https://en.wikipedia.org/wiki/Morlet_wavelet * 'mne' - normalisation used in MNE-Python Returns ------- list of vector arrays Complex valued arrays containing morlet wavelets """ References ---------- .. [1] Tallon-Baudry, C., Bertrand, O., Delpuech, C., & Pernier, J. (1997). Oscillatory γ-Band (30–70 Hz) Activity Induced by a Visual Search Task in Humans. In The Journal of Neuroscience (Vol. 17, Issue 2, pp. 722–734). Society for Neuroscience. https://doi.org/10.1523/jneurosci.17-02-00722.1997 """ m = [] for ii in range(len(freq)): # Sigma controls the width of the gaussians applied to each wavelet. This Loading Loading @@ -112,4 +200,5 @@ def get_morlet_basis(freq, ncycles, sample_rate, normalise=False, win_len=5): mlt = mlt / (np.sqrt(0.5) * np.linalg.norm(mlt.ravel())) m.append(mlt) return m Loading
doc/source/tutorials/tutorial11.rst 0 → 100644 +160 −0 Original line number Diff line number Diff line Tutorial 11 - Morlet Wavelet Decomposition ======================================================= In this tutorial, we will look at describing time-frequency dynamics in a signal using a Morlet Wavelet decomposition. For this tutorial, we will use the same MEG example data which we have used in previous tutorials. We start by importing our modules and finding and loading the example data. .. code-block:: python import os from os.path import join import h5py import numpy as np import matplotlib.pyplot as plt import sails plt.style.use('ggplot') SAILS will automatically detect the example data if downloaded into your home directory. If you've used a different location, you can specify this in an environment variable named ``SAILS_EXAMPLE_DATA``. .. code-block:: python # Specify environment variable with example data location # This is only necessary if you have not checked out the # example data into $HOME/sails-example-data #os.environ['SAILS_EXAMPLE_DATA'] = '/path/to/sails-example-data' # Locate and validate example data directory example_path = sails.find_example_path() # Load data using h5py data_path = os.path.join(sails.find_example_path(), 'meg_occipital_ve.hdf5') X = h5py.File(data_path, 'r')['X'][:, 122500:130000, 0] sample_rate = 250 time_vect = np.linspace(0, X.shape[1] // sample_rate, X.shape[1]) The Morlet Wavelet transform first defines a set of wavelet functions to use as am adaptive basis set. These wavelets are simple burst-like oscillations created to a pre-defined set of parameters. .. code-block:: python # Wavelet frequencies in Hz freqs = [10] # Number of cycles within the oscillatory event ncycles = 5 # Length of window in seconds win_len = 10 # Compute wavelets mlt = sails.wavelet.get_morlet_basis(freqs, ncycles, win_len, sample_rate, normalise=False) ``mlt`` is now a list of wavelet basis functions. In this case, we have a single 10Hz basis. This wavelet is a complex-valued array (in the same way that a Fourier transform returns a complex valued result). To visualise the wavelet, we can plot the real and imaginary parts of the complex function. .. code-block:: python plt.figure() plt.plot(mlt[0].real) plt.plot(mlt[0].imag) plt.legend(['Real', 'Imag']) Note that the real and imaginary components are the same apart from a 90 degree phase shift in the time-series. This shift allow the wavelet transform to estimate the full amplitude envelope and phase of the underlying signal. The ``ncycles`` parameter is critical for defining the time-frequency resolution of the wavelet transform. A small value (typically less than 5) will lead to high temporal resolution but low frequency resolution whilst a large value (typically greater than 7) will have a low temporal resolutoin and a high frequency resolution. We will look into this in more detail later - for now, we can see that this parameter simply changes the number of cycles of oscillation present in our basis wavelets. .. code-block:: python # Compute wavelets mlt3 = sails.wavelet.get_morlet_basis(freqs, 3, win_len, sample_rate, normalise=False) mlt5 = sails.wavelet.get_morlet_basis(freqs, 5, win_len, sample_rate, normalise=False) mlt7 = sails.wavelet.get_morlet_basis(freqs, 7, win_len, sample_rate, normalise=False) plt.figure() for idx, mlt in enumerate([mlt3, mlt5, mlt7]): y = mlt[0].real t = np.arange((len(y))) - len(y)/2 # zero-centre the wavelet plt.plot(t, y + idx*2) plt.legend(['3-cycles', '5-cycles', '7-cycles']) We can see that the frequency of the oscillation in each wavelet is unchanged whilst the number of cycles is modified by changing ``ncycles``. We will often compute wavelets for a range of frequencies rather than just one. Here we pass in an array of frequency values to compute wavelets for. .. code-block:: python freqs = [3, 6, 9, 12, 15] # Compute wavelets mlt = sails.wavelet.get_morlet_basis(freqs, ncycles, win_len, sample_rate, normalise=False) plt.figure() for ii in range(len(freqs)): y = mlt[ii].real t = np.arange((len(y))) - len(y)/2 # zero-centre the wavelet plt.plot(t, y + ii*2) plt.legend(freqs) This time, we see that changing frequency keeps a consistent number of cycles in each wavelet but modifies the oscillatory period. To compute the wavelet transform itself, each wavelet basis function is convolved across the dataset. In this instance (as the wavelet function is symmetric and the input time-series are real values) this convolution is similar to computing the correlation between the basis function and the time-series at each point in time. Let's compute the wavelet transform at 10Hz on our real data. .. code-block:: python freqs = [10] cwt = sails.wavelet.morlet(X[0, :], freqs, sample_rate) plt.figure() plt.subplot(211) plt.plot(X.T) plt.subplot(212) plt.plot(cwt.T) We can see that the wavelet power tracks the amplitude of the oscillations visible in the original time-series. Finally, let's compute a full wavelet transform across a wider range of frequencies .. code-block:: python freqs = np.linspace(1, 20, 38) cwt = sails.wavelet.morlet(X[0, :], freqs, sample_rate, normalise='tallon') plt.figure() plt.subplot(211) plt.plot(time_vect, X.T) plt.xlim(time_vect[0], time_vect[-1]) plt.subplot(212) plt.pcolormesh(time_vect, freqs, cwt)
sails/tests/test_wavelet.py +3 −2 Original line number Diff line number Diff line Loading @@ -13,10 +13,11 @@ class MorletBasisTests(unittest.TestCase): sample_rate = 128 freqs = np.linspace(1, 50, 49) ncycles = 5 win_len = 5 from ..wavelet import get_morlet_basis mlt = get_morlet_basis(freqs, ncycles, sample_rate) mlt = get_morlet_basis(freqs, ncycles, win_len, sample_rate) # Check we have same number of morlet basis waves as input freqs assert(len(mlt) == freqs.shape[0]) Loading @@ -26,7 +27,7 @@ class MorletBasisTests(unittest.TestCase): assert(np.all(np.diff([len(m) for m in mlt]) <= 0)) # Example with faster sample_rate mlt2 = get_morlet_basis(freqs, ncycles, sample_rate*2) mlt2 = get_morlet_basis(freqs, ncycles, win_len, sample_rate*2) check = np.c_[[len(m) for m in mlt], [len(m) for m in mlt2]] # Morlets from double sample rate should be twice as long (or off-by-one) Loading
sails/wavelet.py +106 −17 Original line number Diff line number Diff line from scipy import signal #!/usr/bin/python # vim: set expandtab ts=4 sw=4: import numpy as np from scipy import signal def morlet(x, freqs, sample_rate, window_len=4, ncycles=5, ret_basis=False, ret_mode='power', normalise=False): def morlet(x, freqs, sample_rate, win_len=4, ncycles=5, ret_basis=False, ret_mode='power', normalise='wikipedia'): """Compute a morlet wavelet time-frequency transform on a univariate dataset. Parameters Loading @@ -14,7 +17,7 @@ def morlet(x, freqs, sample_rate, window_len=4, ncycles=5, ret_basis=False, Array of frequency values in Hz sample_rate : scalar Sampling frequency of data in Hz window_len : scalar win_len : scalar Length of wavelet window ncycles : int Width of wavelets in number of cycles Loading @@ -22,22 +25,34 @@ def morlet(x, freqs, sample_rate, window_len=4, ncycles=5, ret_basis=False, Boolean flag indicating whether to return the basis set alongside the transform. ret_mode : {'power', 'amplitude', 'complex'} Flag indicating whether which form of the wavelet transform to return. normalise : {None, 'simple', 'tallon', 'wikipedia', 'mne'} Flag indicating which normalisation factor to apply to the wavelet basis. See `sails.wavelet.get_morlet_basis` for details. Default = 'wikipedia'. Returns ------- 2D array Array containing morlet wavelet transformed data [nfreqs x nsamples] """ orig_dim = x.ndim if orig_dim == 1: x = x[np.newaxis, :] cwt = np.zeros((len(freqs), *x.shape[:]), dtype=complex) if 0 in freqs: raise ValueError("0 cannot be in freqs.") cwt = np.zeros((x.shape[0], len(freqs), x.shape[1]), dtype=complex) # Get morlet basis mlt = get_morlet_basis(freqs, ncycles, sample_rate, normalise=normalise) mlt = get_morlet_basis(freqs, ncycles, win_len, sample_rate, normalise) for jj in range(x.shape[0]): for ii in range(len(freqs)): a = signal.convolve(x, mlt[ii].real, mode='same', method='fft') b = signal.convolve(x, mlt[ii].imag, mode='same', method='fft') cwt[ii, ...] = a+1j*b a = signal.convolve(x[jj, :], mlt[ii].real, mode='same', method='fft') b = signal.convolve(x[jj, :], mlt[ii].imag, mode='same', method='fft') cwt[jj, ii, :] = a+1j*b if ret_mode == 'power': cwt = np.power(np.abs(cwt), 2) Loading @@ -46,13 +61,68 @@ def morlet(x, freqs, sample_rate, window_len=4, ncycles=5, ret_basis=False, elif ret_mode != 'complex': raise ValueError("'ret_mode not recognised, please use one of {'power','amplitude','complex'}") if orig_dim == 1: cwt = cwt[0, ...] if ret_basis: return cwt, mlt else: return cwt def get_morlet_basis(freq, ncycles, sample_rate, normalise=False, win_len=5): def cross_morlet(x, freqs, sample_rate, win_len=4, ncycles=5, ret_mode='power', normalise='wikipedia'): """Compute a morlet cross wavelet time-frequency transform on a multivariate dataset. Parameters ---------- x : vector array_like Time-series to compute cross wavelet transform from. freqs : array_like Array of frequency values in Hz. sample_rate : scalar Sampling frequency of data in Hz. win_len : scalar Length of wavelet window. ncycles : int Width of wavelets in number of cycles. ret_mode : {'power', 'amplitude', 'complex'} Flag indicating whether which form of the wavelet transform to return. normalise : {None, 'simple', 'tallon', 'wikipedia', 'mne'} Flag indicating which normalisation factor to apply to the wavelet basis. See `sails.wavelet.get_morlet_basis` for details. Default = 'wikipedia'. Returns ------- 4D array Array containing morlet cross wavelet transformed data [nfreqs x nsamples x nchannels x nchannels]. """ if ret_mode not in ['power', 'amplitude', 'complex']: raise ValueError("'ret_mode not recognised, please use one of {'power','amplitude','complex'}") # Run standard wavelet decomposition return complex values wt = morlet(x, freqs, sample_rate, win_len=win_len, ncycles=ncycles, ret_mode='complex', normalise=normalise) # Preallocate output array [nchannels x nchannels x nfreqs x ntimes] S = np.empty((wt.shape[0], wt.shape[0], wt.shape[1], wt.shape[2]), dtype=complex) # Main loop for ii in range(wt.shape[1]): for jj in range(wt.shape[2]): S[:, :, ii, jj] = np.dot(wt[:, ii, jj, np.newaxis], wt[np.newaxis, :, ii, jj].conj()) if ret_mode == 'power': S = np.power(np.abs(S), 2) elif ret_mode == 'amplitude': S = np.abs(S) elif ret_mode != 'complex': raise ValueError("'ret_mode not recognised, please use one of {'power', 'amplitude', 'complex'}") return S def get_morlet_basis(freq, ncycles, win_len, sample_rate, normalise='wikipedia'): """Compute a morlet wavelet basis set based on specified parameters. Parameters Loading @@ -61,20 +131,38 @@ def get_morlet_basis(freq, ncycles, sample_rate, normalise=False, win_len=5): Array of frequency values in Hz ncycles : int Width of wavelets in number of cycles win_len : scalar Length of wavelet window sample_rate : scalar Sampling frequency of data in Hz normalise : {None, 'simple', 'tallon', 'wikipedia', 'mne'} Flag indicating which normalisation factor to apply to the wavelet basis. win_len : float Window length duration factor Flag indicating which normalisation factor to apply to the wavelet basis (default is 'wikipedia') - can be one of: * None - no normalisation is applied * 'simple' - wavelet is normalised by its own sum * 'tallon' - normalisation from Tallon-Baudry et al 1997 * 'wikipedia' normalisation from https://en.wikipedia.org/wiki/Morlet_wavelet * 'mne' - normalisation used in MNE-Python Returns ------- list of vector arrays Complex valued arrays containing morlet wavelets """ References ---------- .. [1] Tallon-Baudry, C., Bertrand, O., Delpuech, C., & Pernier, J. (1997). Oscillatory γ-Band (30–70 Hz) Activity Induced by a Visual Search Task in Humans. In The Journal of Neuroscience (Vol. 17, Issue 2, pp. 722–734). Society for Neuroscience. https://doi.org/10.1523/jneurosci.17-02-00722.1997 """ m = [] for ii in range(len(freq)): # Sigma controls the width of the gaussians applied to each wavelet. This Loading Loading @@ -112,4 +200,5 @@ def get_morlet_basis(freq, ncycles, sample_rate, normalise=False, win_len=5): mlt = mlt / (np.sqrt(0.5) * np.linalg.norm(mlt.ravel())) m.append(mlt) return m
