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 measurement-noise as well as signal both have appropriate values. A simple example of how not to do this would be to average two waveforms captured from a Hard-Disk-Drive at different readback positions and expect this to behave like a waveform captured at the midpoint between the two positions. A waveform created in this manner would yield a reasonable interpolation of the signals from the disk (including media noise), but the noise from the read-head and preamplifier would not be representative since it gets reduced 3 dB by the averaging. Using such a waveform to evaluate sector-failure rate in an experimental software readback channel would give a hugely optimistic result! This paper formulates a better solution for the general problem 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').