Why is a filter used with derivative action and how is it configured?

Pure derivative amplifies high-frequency noise (derivative of noise is larger noise). Derivative filter (first-order lag) limits high-frequency gain: filtered derivative = Td*s/(alpha*Td*s + 1). Alpha (typically 0.1) sets filter time constant as fraction of Td. Smaller alpha = more filtering but less true derivative action; larger alpha = less filtering but more noise sensitivity. Some controllers use derivative on PV only (not error) to avoid derivative kick on setpoint changes. Filter configuration is critical for noisy processes like flow measurement.