Servo writing a disk drive by overwriting a harmonic frequency fill pattern in the servo burst area

1. A disk drive comprising:

(a) a disk comprising a plurality of tracks, wherein:

each track comprises a plurality of data sectors and a plurality of servo sectors;

each servo sector comprises a plurality of servo bursts written using perpendicular magnetic recording;

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 in a read signal at the transition between the servo burst and the fill pattern;

(b) a head actuated over the disk for generating the read signal;

(c) a sampling device for sampling the read signal to generate a sequence of read signal sample values; and

(d) control circuitry for demodulating 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.

2. The disk drive as recited in claim 1 , wherein the servo bursts are written over the fill pattern.

3. The disk drive as recited in claim 1 , wherein the control circuitry computes the single-point DFT by:

(a) summing four of the read signal sample values multiplied by respective cosine coefficients {+1, +1, −1, −1} to generate a cosine term;

(b) summing the four read signal sample values multiplied by respective sine coefficients {+1, −1, −1, +1} to generate a sine term;

(c) summing a plurality of the cosine terms into a summed cosine term denoted Σcos;

(d) summing a plurality of the sine terms into a summed sine term denoted Σsin; and

(e) computing the square root of ((Σcos) 2 +(Σsin) 2 ).

4. A method of servo writing servo sectors onto the disk of a disk drive, the disk drive comprising the disk, and a head actuated over the disk, the method comprising the steps of:

(a) using perpendicular magnetic recording to write a fill pattern at a first frequency in a servo burst area of a servo sector; and

(b) using perpendicular magnetic recording to write a plurality of servo bursts over the fill pattern at a servo burst frequency, wherein the first frequency is substantially equal to an even harmonic of the servo burst frequency.

5. The method as recited in claim 4 , wherein a phase shift occurs at the transition between the servo burst and the fill pattern.