Notice that the rectangular taper looks like a rectangle (red trace in the figure above). The rectangular taper makes explicit our knowledge about the observed data (in this case, the 1 s interval of ECoG) and our ignorance about the unobserved data, which are assigned the value zero. We can think of the value 1 as representing the time period when our recording device is operational activating the ECoG recording device opens the rectangular taper (value 1), and deactivating the ECoG recording device closes the rectangular taper (value 0). A rectangular taper multiplies the observed data by 1 and the unobserved data by 0. Performing this finite observation (lasting 1 s) on a long duration (i.e., 90-year) time series can be understood as a rectangular taper. In the example here, we consider 1 s of ECoG data. However, ECoG recordings are finite, limited by convenience, technology, or other factors. For example, an individual’s brain voltage activity may persist for over 90 years, from birth until death. ¶ĮCoG time series continue for long durations. xlabel ( 'Frequency ' ) # Label the axes ylabel ( 'Power ' ) show ()īy Doing Nothing, We’re Doing Something: The Rectangular Taper. semilogx ( faxis, 10 * log10 ( Sxx )) # Plot spectrum vs frequency, xlim (, 100 ]) # Select frequency range, ylim () #. faxis = arange ( 0, fNQ, df ) # Construct a frequency axis. fNQ = 1 / dt / 2 # Determine the Nyquist frequency. max () # Determine the frequency resolution. Sxx = 2 * dt ** 2 / T * ( xf * conj ( xf )) # Compute the spectrum, Sxx = real ( Sxx ) #. mean ()) # Compute Fourier transform of x. x = hanning ( N ) * x # Apply the Hanning taper to the data. T = N * dt # Define the total duration of the data. shape # Define the total number of data points. and the t variable dt = t - t # Define the sampling interval. reshape ( - 1 ) # Extract the ECoG variable, t = data #. loadmat ( 'matfiles/04_ECoG-1.mat' ) # Load the ECoG data.
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