Filters

Let us return to the RC circuit and apply a voltage square wave pulse (Fig. 3B). At the outset, the voltage change is seen across the resistor, but there is a lag in the appearance of voltage across the capacitor. At steady state (with no current flow after the capacitor is fully charged), there is no measurable voltage drop across the resistor and there is maximal voltage across the capacitor. The sum of the voltages across these elements always equals the input voltage. Thus, the voltage output across the resistor is very sensitive to sudden changes in input voltage (high frequencies) but insensitive to relatively unchanging voltage (low frequencies); the opposite is true of the capacitor. Therefore, these circuit elements form the basis of high- and low-frequency electronic filters of variable input waveforms (as we record in EMG and EEG). That is, the resistive element serves as a low-frequency filter, and the capacitive element serves as a high-frequency filter.

The low-frequency (or high-pass) filter is helpful in EEG, for instance, in blunting slow DC potentials that are of lesser interest. A shorter time constant makes for a more stringent low-frequency filter (higher cutoff frequency). The relationship between t and the low-frequency filter is given by:

Fcutoff = 1/(2nT) = 0.16/T, where Fcutoff is that frequency above which greater than 70% of the input amplitudes will pass.

The high-frequency (low-pass) filter is based on the capacitive element and is useful in EEG, to attenuate undesired frequencies that may stem from muscle activity near the scalp leads. The cutoff frequency is defined similarly as in the low-frequency filter. The combination of the low- and high-frequency filters defines the operative bandwidth in use. This is the range of input frequencies that will be allowed through for further analysis.

With such RC circuit-based filters (e.g., as in older analog EEG machines), input data is not filtered in an all-or-none fashion, but rather there is a roll-off in the restriction of input frequencies above and below the low- and high-frequency filter settings (Fig. 4). By combining such circuits, one can obtain filters that are more specific, such as the 60-Hz "notch" filter, which more dramatically blunts 60-Hz inputs, a common source of artifact in typical recording environments because of ambient electrical noise. This discussion notwithstanding, modern digital EEGs filter input data using different methodologies than described, with much steeper frequency response characteristics than available with simple RC circuits. It is important to note that overly stringent filtering can distort the output data, for instance, making waveforms seem less sharp than in reality. This can become clinically relevant to the interpretation of the data, for instance, in the recognition of subtle notched morphologies on EEG.

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