Hardware Reference
In-Depth Information
patterns simultaneously, that is when the head is at or around the junction
of these patterns, the readback waveform y
dual
(t) is the superposition of the
burst waveforms y
1
(t)andy
2
(t)oftwodifferent frequencies:
y
dual
(t)=m
1
y
1
(t)+m
2
y
2
(t).
(2.24)
The amplitudes m
1
(x)andm
2
(x) of the individual burst waveforms vary lin-
early as a function of the off-track displacement x of the read head from the
center of the track.
The area detection method can not be applied directly for estimating the
amplitude from the dual-frequency burst waveform. One possible solution is
to use two band-pass filters to separate the two frequencies, and then applying
area detection method to the samples at the outputs of two filters. Maximum
likelihood detection and coherent detection using selective harmonics can be
used to estimate individual amplitude from the samples of the dual-frequency
burst waveform. Both of these methods are sensitive to jitter in sampling
clock. If the clock is not synchronized, the phase error between the sampled
signal and model signal contributes to error in the estimate of amplitude. Such
error can be eliminated if both sine and cosine are used in the model signal.
The Coherent Detection using DFT of estimated amplitude of a periodic signal
with fundamental frequency ω from its samples is given by
m
s
(k)=sin(ωkT
S
);
m
c
(k)=cos(ωkT
S
);
A
s
= y
T
m
s
; A
c
= y
T
m
c
;
A
df t
=
p
A
s
+ A
c
.
(2.25)
This method, which extracts the amplitude of the fundamental frequency of the
burst signal, is equivalent to discrete Fourier Transform (DFT) with interest in
one frequency only. The burst signal is superposition of two periodic signals of
two different fundamental frequencies, ω
1
andω
1
. The coherent detection using
DFT can be employed to estimate the amplitude of each of these frequencies
present in the burst signal. However, in reality, the servo burst signals y
1
and
y
2
contain not only the fundamental frequencies but also other odd harmonics
and noise [202]. It should be noted that the burst signals are odd signals and
therefore contain sine waves only. Applying the above mentioned method for
estimating amplitude of the fundamental frequencies, we get
N−1
X
A
s
=
[a
1
sin(ωkT
S
)+a
3
sin(ω3kT
S
)+a
5
sin(ω5kT
S
)
k=0
+ .... + n(k)] sin(ωkT
S
+θ);
N−1
X
A
c
=
[a
1
sin(ωkT
S
)+a
3
sin(ω3kT
S
)+a
5
sin(ω5kT
S
)
k=0
+ .... + n(k)] cos(ωkT
S
+θ);
(2.26)
