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
[sin(ρωkT S )sin(ωkT S +θ)] = 0;
[sin(ρωkT S )cos(ωkT S +θ)] = 0; ∀ρ=3, 5, 7, ...
Moreover, if the noise n(k) is zero-mean AWGN then the following ensemble
averages are also equal to zero,
[n(k)sin(ωkT S )] = 0,
[n(k)cos(ωkT S )] = 0.
A s =
[a 1 sin(ωkT S )sin(ωkT S +θ)] = a 1 cos(θ),
A c =
[a 1 sin(ωkT S )cos(ωkT S +θ)] = a 1 sin(θ).
The estimated ampl itude of the burst waveform of fundamental frequency ω
rad/s is A df t =
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  and , 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.