FFT

Although there are many frequency domain techniques which provide an orthogonal expansion of the time series data, all but the DFT are rarely used. The Discrete Fourier Transform (DFT) is one of the most commonly used techniques in the digital signal processing of EEG data. The DFT (the FFT is an efficient method of calculating the DFT) is used to determine the frequency content of the time domain data. As such, the DFT is not a data reduction technique as the DFT yields as many data points as existed in the time domain data.

The most common technique for reducing the frequency domain data is to focus on the amplitudes of the sinusoidal components and to ignore (discard) the phase information. To further reduce the data, the power of the various components is summarized into frequency bins. The power is analyzed because, although summing the amplitudes of the various frequency components does not yield a meaningful component, the sum of the magnitudes of the amplitudes of each frequency component squared does yield a meaningful measure (because of a characteristic of sinusoidal waveforms known as “orthogonality”). The magnitude squared of a sinusoidal voltage is proportional to the power in the voltage. For simplicity (as opposed to accuracy) I refer to any data derived from the DFT as FFT data and any data derived directly from the data as TDA data.