D= 1+b 1 + b 2 ,
A= (1+a 1 + a2)/D,
B= (−2+2a 2 )/D,
C= (1−a 1 + a 2 )/D,
E= (−2+2b 2 )/D,
F= (1−b 1 + b 2 )/D
a 1 = πζ a f ∗ ,
a 2 = πf ∗ ) 2 ,
b 1 = πζ b f ∗ ,
b 2 =πf
) 2 ,
and f ∗ = f 0 /f s for sampling frequency f s .
Using the bias free structure, the internal AC and DC gains can both be
lower compared with those obtained direct form implementations .
The peak filter can be used for disturbances in the low frequency band such
as for runout compensation  or the disturbances in higher frequency
band similar to the phase stable design . It provides additional vibration
suppression of few dB for the sinusoidal disturbances of suﬃciently long time.
One drawback of this approach is the inferior transient response of the closed
loop system. With such a scheme in use, the transient response of the system
becomes oscillatory because of the phase distortion induced by the peak filter.
While responding to an external periodic disturbance, such as an RRO, it takes
few cycles before the filter can reproduce the disturbance internally so that it
can be cancelled. This is not what one would like to see when the system
is responding to the reference command. Time taken by the transient of the
peak filter's response to decay is the main factor contributing to the oscillatory
output. This can be reduced by letting the filter run even during the track
seek process; interested readers may refer to  for further explanation on
this solution. An alternative solution suggested in  selects filter zeros such
that the phase lag contributed by the peak filter is minimized.
3.2.6 Summary: Application of Different Filters
Over the years, the demand for higher bandwidth of the HDD servomechanism
continued. It was about 300 Hz in the middle of 1990s and increased to over
1 kHz by 2001 . This has been possible by multi-pronged developments
including better mechanics with higher bandwidth, faster microprocessor that
allows implementation of complex higher order controller with less computa-
tional delay, and better servo modeling and control designs. Higher bandwidth