The sharpness of the frequency response curve is determined by which filter characteristic?

The sharpness of the frequency response curve is indeed determined by the rolloff characteristic of a filter. Rolloff refers to the rate at which the filter attenuates frequencies beyond the cutoff point. A steep rolloff indicates that the transition from passband to stopband is quick, leading to a sharper frequency response. This is important in EEG technology because it affects how well the filter can differentiate between desired signals (such as brain waves) and unwanted noise.

In contrast, gain refers to the amplification level of the signals that pass through the filter but does not directly assess the sharpness of frequency response. Cutoff frequency identifies the point at which the filter begins to attenuate the signal, but it does not indicate how quickly or sharply this transition occurs. Bandwidth defines the range of frequencies that can pass through the filter but is a broader measure and does not specifically pinpoint the sharpness of the filtering effect. Thus, the rolloff characteristic is the key determinant of how sharply a filter can delineate between different frequency ranges within the context of EEG signal processing.