Frequency-Based Measures

 

The power spectrum is a basic tool of time series analysis in the frequency domain. It is defined as the square of the amplitude of the Fourier transform of the time series and estimates how the total variance of the signal (time series) is distributed in the spectrum of frequencies. Among different power spectrum estimates we use here the standard periodogram estimate. The frequency ranges from 0 to 1/2 since an implicit sampling time of one is assumed for all time series. The power spectrum is a function of frequency and thus it does not constitute a measure, but measures can be derived from this function. In some applications, such as EEG analysis, the interest is in the energy at specific frequency bands. Here up to five frequency bands can be specified. The default frequency limits for the five bands correspond to the theta (è), alpha (á), beta (â), gamma (ã) and delta (ä) bands. Also, the median frequency can be computed giving the frequency at which the energy is halved.
 

Energy Band A (EnergyBndA)

Energy Band A is the energy in a given frequency band. The band is specified by the lower and upper frequency limits. The standard periodogram is called to compute the power spectrum assuming  frequency=1, so that the largest frequency the power spectrum is computed  for is 0.5. The frequency  resolution is given by the length of the time series. The energy in the given frequency band is simply the fraction of the sum of the values of the power spectrum at the discrete frequencies within the band to the energy over the entire frequency range.

The following parameters can be specified:

- lower band frequency (l) : the lower frequency limit for the frequency band. A single value for l should be given and it should hold 0 < l < 0.5. 

- upper band frequency (u) : the upper frequency limit for the frequency band. A single value for u should be given and it should hold l < u < 0.5.

Example: If the user selects this measure by activating the check box in the beginning of the measure line and sets for lower band frequency (l) '0.003' and for the upper band frequency (u) '0.05', then Energy Band A is computed for the specified frequency interval [l, u] in the measure list the following measure name will appear (the frequency values are multiplied by 1000 and rounded)

EnergyBndAl3u50

 

Energy Band B (EnergyBndB)

The same as for Energy Band A (EnergyBndA) holds for another selection of frequency band.
 

Energy Band C (EnergyBndC)

The same as for Energy Band A (EnergyBndA) holds for another selection of frequency band.
 

Energy Band D (EnergyBndD)

The same as for Energy Band A (EnergyBndA) holds for another selection of frequency band.
 

Energy Band E (EnergyBndE)

The same as for Energy Band A (EnergyBndA) holds for another selection of frequency band.
 

Median Frequency (MedianFreq)

Median Frequency is the frequency at which the energy is halved, i.e. the frequency f* for which the fraction of the sum of the values of the power spectrum at the discrete frequencies in [0,f*] to the energy over the entire frequency range is 1/2. The rest is as described for the Energy Band A (EnergyBndA).
 

OK

By pressing this button the window of "Frequency-based Measures" will disappear and the user will be moved to the "Select / run measures" window. Any changes in the measures and parameter values will be stored.
 

Cancel

Quit without doing anything and return to the "Select / run measures" window. Any changes in the measures and parameter values will be ignored.
 

Help

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