What determines the sharpness of the frequency response curve in a filter?

The sharpness of the frequency response curve in a filter is determined by the rolloff. Rolloff refers to how quickly the filter attenuates signals outside its passband, which indicates the steepness of the frequency response curve. A sharper rolloff means that the filter distinguishes more effectively between the frequencies it allows to pass and those it suppresses, resulting in a more selective filtering process.

When the rolloff is steep, the transition from the passband to the stopband is abrupt, leading to a clearer delineation between what frequencies are passed and what frequencies are blocked. This is desirable in many applications where precise frequency selection is critical.

The other options, while related to the operation of filters, do not directly determine the sharpness of the frequency response. Bandwidth relates to the range of frequencies that the filter can pass, a notch relates to a specific rejection band in the filter but does not describe the overall frequency response curve, and capacitance primarily affects the reactive properties of the filter circuit rather than its frequency response sharpness.