Interpolation Of Noisy Measurements In A Coarse Grid: Creating Waveforms For Intermediate Points On "747" Curves

In some situations, only a limited number of measurements under a limited number of conditions may be available for analysis. This paper describes an approach for creating additional interpolated measurements in which both measurement noise as well as signal have appropriate values. This is important, for example, when evaluating the behavior of advanced readback channels where quantities, such as sector failure rate (SFR), change very abruptly from 0% to 100% in response to relatively small parameter changes. This means that a smooth interpolation of SFR between coarse measurement points is little help in determining the actual boundary of good performance. If, instead, interpolated waveforms are fed into the channel, the boundary of the region of good performance can be clearly identified. This paper formulates a solution for the general problem of noisy measurement (waveform) interpolation and then applies this approach specifically to the situation, where a series of spin-stand waveforms were captured at various reader positions and with various written track squeeze positions (i.e., a set of "747s"). Using this approach, realistic waveforms can now be created and the SFR evaluated at any arbitrary intermediate reader and writer positions.