Hardware Reference

In-Depth Information

where, θ represents the synchronization error due to clock jitter, and n(k)is

additive white Gaussian noise (AWGN). The number N is chosen such that

integer number of full cycles of the fundamental frequency are sampled. Then

it can be easily proven that

N−1

X

[sin(ρωkT
S
)sin(ωkT
S
+θ)] = 0;

k=0

N−1

X

[sin(ρωkT
S
)cos(ωkT
S
+θ)] = 0; ∀ρ=3, 5, 7, ...

(2.27)

k=0

Moreover, if the noise n(k) is zero-mean AWGN then the following ensemble

averages are also equal to zero,

N−1

X

E

[n(k)sin(ωkT
S
)] = 0,

k=0

N−1

X

E

[n(k)cos(ωkT
S
)] = 0.

(2.28)

k=0

So,

N−1

X

A
s
=

[a
1
sin(ωkT
S
)sin(ωkT
S
+θ)] = a
1
cos(θ),

k=0

N−1

X

A
c
=

[a
1
sin(ωkT
S
)cos(ωkT
S
+θ)] = a
1
sin(θ).

(2.29)

k=0

The estimated ampl
itude of
the burst waveform of fundamental frequency ω

rad/s is A
df t
=

p

A
s
+ A
c
. This method can be applied to estimate the

amplitudes of both frequency components of the dual-frequency burst.

Estimating Head Position from Data Block Signal

When the head reads information from the data blocks, the readback signal is

converted into a sequence of '0's and '1's by the partial response maximum like-

lihood or PRML read channel. The operation of the PRML channel generates

mean squared error (MSE) between the readback signal and the most likely

candidate signal. This MSE is representative of absolute value of the position

offset of the read head from the track-center. An inverse mapping of the MSE

gives rise to two possible values of PES. An algorithm, referred to as ACORN

estimator in [95] and [96], uses the MSE from the PRML channel together

with the PES reading from the servo channel to provide accurate estimates of

position error at high sampling frequency.