Most present disk drives are based on magnetic recording technology. Magnetic recording technology may be described by two distinct processes: writing onto the magnetic storage media and reading from the magnetic storage media. The whole phenomena of writing on the surface of a magnetic storage media consists of changing the magnetic polarity from north to south or from south to north.
FIG. 1a illustrates a change in the orientation of the magnetic field 110. While writing on the magnetic surface, the magnetic storage media which is typically a disk, continues to rotate under the recording head. The change in magnetic polarity (also referred to as change in magnetization) creates a transition in the write data signal which is used to record data onto the magnetic storage media. Because it is impossible to instantaneously build up a current, the transition in the write data signal has a finite rise time. FIG. 1 illustrates the transition of the write data signal 120 as the magnetic field 110 changes magnetization.
In order to read back data from the magnetic storage media, the transitions are detected by the read head. The read head may be the same head as the recording head and is therefore referred to as the R/W head. The readback signal is typically a voltage signal representing the non-linear response of the write data signal. The readback 130 illustrates the readback signal for the transition in the write data signal 120 shown in FIG. 1a.
FIG. 1b illustrates a write data signal 140 having multiple transitions. The readback signal 160 illustrates the non-linear transform of the write data signal 140. According to FIG. 1b, the magnetic recording media and the R/W head creates the non-linear system 150.
All magnetic recorders produce unwanted signals in the form of noise, which impose limitations on the achievable performance of the magnetic recorder. Two of the major sources of noise is the medium noise and the head noise. The medium noise arises from the fact that no medium is magnetically homogeneous. In other words, the recording medium noise is due to the uncertainty or randomness of some property of the medium and any variation from point to point will produce medium noise. The major head noise arises from the fact that any head possess an impedance, and the real part of this impedance gives rise to noise of thermal origin. Other forms of head noise are associated with magnetic domain changes or magnetostriction effects such as the Barkhausen noise.
Noise renders the output signal an imperfect replica of the non-linear transform of the input signal. In other words, the noise causes the readback signals to deviate from an ideal readback signal. Therefore, one of the tasks of the recording system designer is reduce the noise to a tolerable level so that some predetermined criteria of performance are met. A common criteria for performance is the signal-to-noise ratio ("SNR").
Currently, several techniques are available for measuring the distortion of the readback signal caused by noise. The distortion in the readback signal is typically caused by multiple factors. Among these factors are: amplitude loss due to linear superposition of crowded transitions, pattern induced bit-shift, isolated pulse distortion, over-write of a previously written signal, partial erasure of data, and other forms of noise.
Dipulse Extraction using Pseudo-random Sequences proposed by IBM in 1987 is a well know method of measuring different nonlinear distortions in the readback signal. Alexander Taratorin, PRML: A Practical Approach, Guzik Technical Enterprises. The Dipulse Extraction is based on the "shift" and "add" properties of a pseudo-random sequence. A Pseudo-Random Sequence is generated by a polynomial (e.g., x.sup.7 +X.sup.3 +1) which possess "shift" and "add" properties. The shift and add properties means that the exclusive OR (a product of two NRZ bits) of the initial sequence is the same sequence shifted by some number of bits. If the pseudo-random sequence is written on the disk, different non-linear distortions create specific terms in the readback signal. More specifically, the readback signal is described by the main or "zero" term and one or several "copies" or "echoes" caused by non-linearities. The shift and add properties allow one to predict where the echoes will be found.
The method of dipulse extraction provides a method for selecting these echoes. The advantage of the dipulse extraction method is that it provides a separation of different non-linear effects into different echoes of pseudo-random sequence and some approximate estimates of these non-linearities. The amount of distortion can be determined by the size of the echo. The dipulse extraction method of testing requires the measurement of the dipulse shape or an idealized dipulse shape. However, this method is complicated and requires sophisticated hardware and software.
FIG. 1c illustrates an extracted dipulse with echoes which characterize non-linearities. The waveform 170 is the result of complex computations based on the pseudo-random sequence. According to FIG. 1c, there is a main pulse referred to as the main term 180 and four smaller pulses referred to as echoes 190a, 190b, 190c, and 190d. The echoes may correspond to various non-linearities such as an over-write of a previously written signal, a hard/easy transition shift or a nonlinear transistion shift.
Under certain circumstances, it may be useful to measure the distortion on an isolated pulse without measuring the other distortion variables. Therefore, it is desirable to provide a simple and accurate method of measuring the distortion of an isolated pulse without using the complex method of dipulse extraction. Furthermore, it is desirable to measure distortion of an isolated pulse without the interference between two adjacent pulses forming a dipulse.