A disk drive is disclosed comprising a disk having a plurality of servo bursts written using perpendicular magnetic recording, wherein each servo burst is written at a servo burst frequency. A fill pattern is written between the servo bursts using perpendicular magnetic recording at a frequency substantially equal to an even harmonic of the servo burst frequency, and a phase shift occurs at the transition between the servo burst and the fill pattern. A head is actuated over the disk, and a sampling device samples a read signal emanating from the head to generate a sequence of read signal sample values. Control circuitry demodulates the servo bursts from the sequence of read signal sample values by computing a single-point Discrete Fourier Transform (DFT) at the servo burst frequency.