The magnetic tape includes a non-magnetic support; and a magnetic layer, in which the magnetic layer has a timing-based servo pattern, an edge shape of the timing-based servo pattern, specified by magnetic force microscopy is a shape in which a difference L.sub.99.9−L.sub.0.1 between a value L.sub.99.9 of a cumulative distribution function of 99.9% and a value L.sub.0.1 of a cumulative distribution function of 0.1% in a position deviation width from an ideal shape of the magnetic tape in a longitudinal direction is 180 nm or less, and an absolute value ΔN of a difference between a refractive index Nxy of the magnetic layer, measured in an in-plane direction and a refractive index Nz of the magnetic layer, measured in a thickness direction is 0.25 or more and 0.40 or less.

A data storage device is disclosed comprising at least one head configured to access a magnetic tape comprising a plurality of servo frames each comprising an A servo burst, a B servo burst, a C servo burst, and a D servo burst. The A servo burst in a first servo frame is read using the head to generate a first read signal which is sampled to generate first signal samples. A first matched filter matched to the A servo burst filters the first signal samples to generate first filtered samples within a first burst window, and the first burst window is updated based on the first filtered samples. The first filtered samples within the first burst window are processed to generate a position error signal (PES), and a position of the head is controlled relative to the magnetic tape based on the PES.

A receiver is configured to detect, at a communication interface, a received signal that suffers from degradations incurred over a communication channel. The receiver applies an adaptive filter to a series of received blocks of a digital representation of the received signal, thereby generating respective filtered blocks, where each received block represents 2N frequency bins, and where N is a positive integer. The receiver calculates coefficients for use by the adaptive filter on a j.sup.th received block as a function of (i) error estimates associated with an (j−D−1).sup.th filtered block, where D is a positive integer representing a number of blocks, and where j is a positive integer greater than (D−1); and (ii) an inverse of an approximate covariance matrix associated with the (j−D−1).sup.th received block, where the approximate covariance matrix is a diagonal matrix of size L×L, and where L is a positive integer lower than 2N.

The invention provides a method and apparatus for filtering a temporal signal. A target magnitude frequency response H.sub.T(f) is specified (101,201) of frequency f in terms of a column vector l of K weights l.sub.k where log H.sub.T(f)=l.sup.TW(f) and W(f) is a column vector of K magnitude basis functions W.sub.k(f). A constrained frequency response H.sub.c(f) is computed (102,214) defined by log H.sub.c(f)=g.sup.TV(f) , where V(f) is a column vector of N constrained basis functions V.sub.n(f) for which each exp g.sub.nV.sub.n(f) satisfies a constraint preserved by concatenation, and g is a column vector of N coefficients satisfying a matching criterion between l.sup.TW(f) and g.sup.TV(f). An input temporal signal is received (103,212) and filtered (104,210) with the constrained frequency response H.sub.c(f) to form a filtered temporal signal; and the filtered temporal signal is output (105,211).

Systems and methods for adaptation of a two-dimensional magnetic recording (TDMR) channel are provided. Read-back signals from respective read sensors of a TDMR channel are received at an equalizer, the read-back signals corresponding to a digital signal value. A log-likelihood ratio (LLR) signal is generated based at least in part on the read-back signals. A cross-entropy value is generated indicative of a mismatch between a probability of detected bit and a probability of the true recorded bit. The equalizer is adapted by setting an equalizer parameter to a value that corresponds to a minimum cross-entropy value from among the computed cross-entropy value and one or more previously computed cross-entropy values, to decrease a read-back bit error rate for the TDMR channel.

The magnetic tape includes a non-magnetic support and a magnetic layer including ferromagnetic powder and a binding agent, in which the magnetic layer has a timing-based servo pattern, an edge shape of the timing-based servo pattern, specified by magnetic force microscopy is a shape in which a difference (L.sub.99.9−L.sub.0.1) between a value L.sub.99.9 of a cumulative distribution function of 99.9% and a value L.sub.0.1 of a cumulative distribution function of 0.1% in a position deviation width from an ideal shape of the magnetic tape in a longitudinal direction is 180 nm or less, and an isoelectric point of a surface zeta potential of the magnetic layer is 3.8 or less.

Deterioration of convergence performance or operational stability due to an increase in constraint length is suppressed when coefficients are updated, so that decoding performance is improved. A decoding device according to the present technology includes an adaptive equalization unit that performs adaptive equalization, an adaptive maximum likelihood decoding unit that causes an identification point of maximum likelihood decoding to adaptively follow a characteristic of an input signal, a target waveform generation unit that, by convoluting a partial response coefficient into a decoded value, generates an equalization target waveform of the adaptive equalization which is performed by the adaptive equalization unit, an error signal generation unit that generates, as an equalization error signal, an error signal between the equalization target waveform and an equalized signal, and a coefficient updating unit that, through least-square-method computation for minimizing a correlation between the decoded value and the equalization error signal, updates the partial response coefficient which is used by the target waveform generation unit to generate the equalization target waveform.

The magnetic tape includes a non-magnetic support; and a magnetic layer, in which the magnetic layer has a timing-based servo pattern, an edge shape of the timing-based servo pattern, specified by magnetic force microscopy is a shape in which a difference L.sub.99.9−L.sub.0.1 between a value L.sub.99.9 of a cumulative distribution function of 99.9% and a value L.sub.0.1 of a cumulative distribution function of 0.1% in a position deviation width from an ideal shape of the magnetic tape in a longitudinal direction is 180 nm or less, and an absolute value ΔN of a difference between a refractive index Nxy of the magnetic layer, measured in an in-plane direction and a refractive index Nz of the magnetic layer, measured in a thickness direction is 0.25 or more and 0.40 or less.

The invention provides a method and apparatus for filtering a temporal signal. A target magnitude frequency response H.sub.T(f) is specified (101,201) of frequency f in terms of a column vector l of K weights l.sub.k where log H.sub.T(f)=l.sup.TW(f) and W(f) is a column vector of K magnitude basis functions W.sub.k(f). A constrained frequency response H.sub.c(f) is computed (102,214) defined by log H.sub.c(f)=g.sup.TV(f) , where V(f) is a column vector of N constrained basis functions V.sub.n(f) for which each exp g.sub.nV.sub.n(f) satisfies a constraint preserved by concatenation, and g is a column vector of N coefficients satisfying a matching criterion between l.sup.TW(f) and g.sup.TV(f). An input temporal signal is received (103,212) and filtered (104,210) with the constrained frequency response H.sub.c(f) to form a filtered temporal signal; and the filtered temporal signal is output (105,211).

At least some aspects of the present disclosure provide for a method. In at least one example, the method includes applying first equalization to a received data signal to generate an equalizer signal and comparing the equalized signal to each of a plurality of reference voltages for a predetermined period of time per respective reference voltage to generate a comparison result. The method further includes determining a plurality of counts with each count of the plurality of counts uniquely corresponding to a number of rising edges in the comparison result for each of the plurality of reference voltages. The method further includes comparing at least one of the plurality of counts to at least another of the plurality of counts to determine a relationship among the plurality of counts and applying second equalization to the received data signal based on the determined relationship among the plurality of counts.