A microphone assembly includes an acoustic sensor and a voice activity detector on an integrated circuit coupled to an external-device interface. The acoustic sensor produces an electrical signal representative of acoustic energy detected by the sensor. A filter bank separates data representative of the acoustic energy into a plurality of frequency bands. A power tracker obtains a power estimate for at least one band, including a first estimate based on relatively fast changes in a power metric of the data and a second estimate based on relatively slow changes in a power metric of the data. The presence of voice activity in the electrical signal is based upon the power estimate.