Field of the Invention
This invention relates to a time-continous FIR filter for implementing
a Hilbert transform.
The invention also relates to a method of filtering signals whose
spectra are unknown a priori.
In particular, the invention relates to a circuit structure for programmable
time-continous analog filters specifically intended for read/write operations from/into
magnetic storage media.
One general aspect of the invention is a method of improving a circuit
structure -- which structure would implement a Hilbert transform and incorporate
a FIR filter -- particularly where the transform is to process input signals whose
spectra are unknown a priori. The description which follows only covers this field
of application for the sake of simplicity.
As is well known in this technical field, a circuit structure designed
to implement a Hilbert transform has a time-continous FIR (Finite Impulse Response)
filter for its basic component.
More particularly, a Hilbert transform is essentially a constant module
90° phase shifter, and this characteristic can be implemented by an impulsive
response FIR filter in the way shown in Figure 5, for example.
The frequency response of such a FIR filter can better approach an
ideal response, the greater is the filter length provided.
The accompanying Figure 1 shows schematically a conventional FIR
filter which includes a plurality of delay cells cascade connected together between
an input terminal and an output terminal.
A distinguishing feature of the cells is that they carry the same
amount of time delay, designated Td. The signal output from each cell is then
multiplied by a predetermined coefficient c0,...,cn.
The summation of all the signals, each multiplied by a respective
one of the coefficients c0,...,cn, gives a value Y representing the impulsive
response of the filter.
The performance of a time-continous FIR filter is also linked to another
parameter, that is, the band of the signal being input to the chain of delay cells.
The greater the band width, the larger becomes the number of the FIR filter coefficients
required for a closer approach to the ideal Hilbert transform.
It is a recognized fact that the frequency response of an amplified
signal amplitude is related to the frequency response of the signal phase. As
the input signal band grows wider, the phase frequency response becomes smaller,
and the so-called group delay is reduced. In fact group delay is the derivative
of phase with respect to frequency.
In other words, with an input signal having a broad band, a FIR filter
with a very large number of coefficients must be used in order to obtain a desired
frequency response. However, this requires fairly complicated and expensive circuit
structures, and demanding ones in terms of circuit area.
Furthermore, where the input signal has different spectrum forms,
there are no circuit structures available which can handle the frequency response
in an optimum manner. It is customary in such cases to adopt either of two different
A first approach consists in employing a FIR filter which has a fixed
number of coefficients c0,...,cn, so that the filter performances are those as
desired for all the spectra inputs.
A second approach consists in using a filter having coefficients c0,...,cn
which can be programmed to fit the spectrum of the input signal.
The first solution obviously involves a larger number of elements
than the second.
However, the basic element in the first approach is bound to be of
simpler construction on account of the coefficients being non-programmable.
While being advantageous from several aspects and substantially meeting
current requirements, neither the first nor the second of the above solutions fill
all the demands of processing input signals whose spectrum is unknown a priori.
The technical problem underlying the present invention is to provide
a FIR filter design for implementing a Hilbert transform, which has appropriate
structural and functional features to enable processing of signals whose spectra
are unknown beforehand, thereby overcoming the limitations and drawbacks of prior
Summary of the Invention
The principle behind this invention is one of using a FIR filter with
constant coefficients, and optimizing the filter response for the input signal
spectrum by modifying the time delay of the cells.
Based on this principle, the technical problem is solved by a filter
as previously indicated and defined in Claims 1 and following.
The technical problem is further solved by a filtering method for
processing signals having spectra unknown beforehand, as defined in Claims 5 and
The features and advantages of a filter and filtering method according
to the invention will be apparent from the following description of preferred
embodiments thereof, given by way of non-limitative example with reference to the
Brief Description of the Drawings
In the drawings:
- Figure 1 shows schematically a conventional FIR filter structure;
- Figure 2 is a block diagram of a PRLM decoding arrangement according to the
- Figure 3 is a block diagram of a PRLM decoding arrangement according to the
- Figure 4 shows comparative plots of response vs. time, respectively for longitudinal
recording and perpendicular recording signals, relating to the reading of data
from magnetic storage media;
- Figure 5 is a plot of response vs. time for a Hilbert FIR filter;
- Figures 6A and 6B are respective plots of frequency response for components
of the decoding arrangement shown in Figure 4;
- Figures 7A, 7B and 7C are respective plots of frequency response for the Hilbert
FIR filter of this invention.
Referring to the drawing views, and in particular to the example of
Figure 3, the block structure of a Hilbert transform according to this invention
is generally shown at 1 in schematic form.
One possible application of the invention concerns the method of
recording logic information in magnetic storage media, e.g. hard disks. In particular,
an object of this invention is to have storage density increased by allowing the
logic information to be recorded in the magnetic storage medium along a vertical
This recording method is known as "perpendicular recording" and affords
increased storage density for a given area of the magnetic storage medium over
"longitudinal recording", the latter being the type of magnetization currently
in use. It effectively enhances the storage density of information in magnetic
media, such as hard disks.
To decode a signal from longitudinal recording, a decoding arrangement
of the Partial Response with Maximum Likelyhood type, shown schematically in Figure
2, is usually employed.
A first block VGA is a voltage gain amplifier which is input a signal
from a device arranged to read data from a magnetic storage medium, not shown
Connected to the output of the block VGA is a low-pass filter LPF
having an analog-to-digital converter ADC placed downstream of it.
An equalizer eqFIR is connected to the output of the converter ADC.
Advantageously in this invention, the arrangement shown in Figure
2 can be modified for processing and decoding signals from perpendicular recording.
On account of the properties of Hilbert transform, in fact, the output
signal from a Hilbert filter FIR is quite similar to the input signal to the low-pass
filter LPF of Figure 2. Accordingly, the same decoding arrangement as is used for
longitudinal recording can be used for perpendicular recording if a Hilbert filter
FIR is connected in the block chain.
More particularly, as shown in the example of Figure 3, the Hilbert
filter FIR is connected between the block VGA and the low-pass filter LPF.
Plotted in Figure 4 is an impulsive response relating to two different
magnetizations originating from a positive isolated transition, a double transition
(d-pulse), and a negative isolated transition.
With the decoding arrangement of this invention shown in Figure 3,
the signal indicated by a full line in Figure 4, relating to perpendicular recording,
can be converted to a signal like that indicated by a dash line, representative
of longitudinal recording.
The transfer function provided by the invention is aimed at minimizing
the number of coefficients of the Hilbert FIR by imposing a 90-degree phase shift
in the range of interest but accepting a substantially non-constant module.
In essence, to recover a gain variation, particularly a gain attenuation,
it was considered of obtaining an increase in gain from another portion of the
decoding arrangement. For the purpose, the designs of the low-pass filter LPF and
the equalizer eqFIR of Figure 3 have been altered, with respect to an ideal Hilbert
filter, to compensate for the less-than-ideal performance of the near-Hilbert filter.
Reference can be made to the graph in Figure 6A, which shows a curve
3 relating to the transfer function of the low-pass filter, a curve 4 for the
equalizer function, and a curve 5 for the Hilbert filter FIR.
With this solution, the value of the coefficients of the filter FIR
which reproduce the Hilbert tranform becomes a function of the input signal spectrum,
which spectrum is dependent on the stored data packing density.
Thus, the values of FIR would have to be modified according to the
more or less inwardly located track of the magnetic storage medium which contains
the information to be read, since the density of the stored information, and with
it the signal spectrum, is dependent on which track is being read.
Advantageously, this invention provides instead for a modification
of the delay value Td of the cells which comprise the filter.
Td is the value of the delay element of each cell in the time-continous
filter FIR. As can be appreciated from Figures 7B and 7C, to program the delay
value Td is to program the values of the coefficients c0,...,cn of the time-continous
filter FIR. In these figures, Tc is the inverse channel period of the working frequency
fc, which changes with the position of the read/write head on the magnetic storage
Thus, according to the invention, a FIR with fixed coefficients can
be used, and use can be made of the programmed delay Td=k*Tc to obtain
a desired frequency response according to the different storage densities.
Plotted in Figure 7A is the transfer function of a Hilbert transform
approximated for three different storage densities.
It will be appreciated from the foregoing that the filter and filtering
method of this invention have a major advantage in that they allow data to be
read from magnetic storage media used in the perpendicular recording mode, at the
expense of only minor modifications in current apparatus for reading information
from such magnetic storage media.