A disk drive is disclosed comprising a disk including a plurality of servo tracks defined by servo sectors, wherein each servo sector comprises a servo preamble. A head is actuated over the disk, wherein the head is operable to generate a read signal. The disk drive further comprises control circuitry including an analog cutoff filter operable to filter the read signal to generate a filtered read signal. The filtered read signal is sampled to generate read samples. During a normal operating mode, the analog cutoff filter is configured to have a first bandwidth. During a measurement mode, the analog cutoff filter is configured to have a second bandwidth greater than the first bandwidth, and the read samples representing at least part of the servo preamble are processed to measure a signal-to-noise ratio (SNR) and/or a fly height of the head.