In Process1, select the simulated signal.
#Mashinsky signal tutorial code
Ntime= 6000, Sampling frequency= 1000Hz (signal duration = 6000/1000 = 6 seconds).Ĭopy-paste the few lines of code above to generate the sum of three sinusoids.ĭouble-click on the new file to look at the simulated signal. Run process: Simulate > Simulate generic signals. The 50Hz and noise are present everywhere, the 2Hz and 20Hz start only after two seconds.ĭata(1,i) = sin(f1*2*pi*t(i)) + 0.4 * cos(f2*2*pi*t(i)) ĭata = Data + 0.2 * sin(f3*2*pi*t) + 0.4 * rand(1,6000) Įmpty the Process1 list (right-click > Clear list) then click on.
The following code generates a sum of three sinusoids (2Hz, 20Hz, 50Hz) with random white noise. We will illustrate the time-frequency decomposition process with a simulated signal. To evaluate the duration of these edge effects for a given frequency band, use the interface of the process "Pre-process > Band-pass filter" or refer to the filters specifications ( tutorial #10). The band-pass filters used before extracting the signal envelope are relatively narrow and may cause long transients. We also need to consider these edge effects when using the Hilbert transform approach. Examples of such transients are given in the figures below. More precisely, if f is your frequency of interest, you can expect the edge effects to span over FWHM_t seconds: FWHM_t = FWHM_tc * fc / f / 2. In such case, the edge effects are roughly half these times: 300ms in 5Hz and 150ms in 10Hz.
#Mashinsky signal tutorial series
Similarly to any convolution of signals, there is zero padding at the edges of the time series and therefore the wavelet coefficients are weaker at the beginning and end of the time series.įrom the figure above, which designs the Morlet wavelet, we can see that the default wavelet (central frequency fc=1Hz, FWHM_tc=3sec) has temporal resolution 0.6sec at 5Hz and 0.3sec at 10Hz. Wavelet coefficients are computed by convolving the wavelet kernel with the time series. Users should pay attention to edge effects when applying wavelet analysis.
#Mashinsky signal tutorial full
Resolution is given in units of Full Width Half Maximum of the Gaussian kernel, both in time and frequency. These two parameters, uniquely define the temporal and spectral resolution of the wavelet for all other frequencies, as shown in the plots below. For example, we may wish to have a temporal resolution of 3 seconds at frequency 1 Hz (default parameters). Then, the desirable time resolution for the central frequency should be defined. Unless interested in designing the wavelet at a particular frequency band, the default 1Hz should be fine. All other wavelets will be scaled and shifted versions of the mother wavelet. the frequency where we will define the mother wavelet. To design the wavelet, we first need to choose a central frequency, ie. When designing the wavelet, we basically decide a trade-off between temporal and spectral resolution. For low frequencies, the frequency resolution is high but the time resolution is low. An example of this wavelet is shown below, where the blue and red curves represent the real and imaginary part, respectively.Ĭontrary to the standard short-time Fourier transform, wavelets have variable resolution in time and frequency. They have the shape of a sinusoid, weighted by a Gaussian kernel, and they can therefore capture local oscillatory components in the time series. In Brainstorm we offer two approaches for computing time-frequency decomposition (TF): the first one is based on the convolution of the signal with series of complex Morlet wavelets, the second filters the signal in different frequency bands and extracts the envelope of the filtered signals using the Hilbert transform.Ĭomplex Morlet wavelets are very popular in EEG/MEG data analysis for time-frequency decomposition. For a better understanding of this topic, we recommend the lecture of the following article: Bertrand O, Tallon-Baudry C (2000), Oscillatory gamma activity in humans: a possible role for object representation. Averaging trials in time-frequency domain allows to extract the power of the oscillation regardless of the phase shifts. The averaging in time domain may also lead to a cancellation of these oscillations when they are not strictly locked in phase across trials. A lot of the information of interest is carried by oscillations at certain frequencies, but the amplitude of these oscillations is sometimes a lot lower than the amplitude of the slower components of the signal, making them difficult to observe. Some of the MEG/EEG signal properties are difficult to access in time domain (graphs time/amplitude).
Display: Power spectrum and time series.
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