interpolation

interpolation is a specific kind of estimation — estimating within the known range of data points. Specific→general per Law 9.

interpolation is a specific technique within data-analysis: approximating values between known discrete data points. Specific→general per Law 9.

Which-came-first: interpolation (estimating within known range) is the older, more fundamental concept; extrapolation (estimating beyond range) extends it. Interpolation fed into extrapolation as the conceptual starting point.

Which-came-first test: the mathematical concept of interpolation (estimating values between known data points, formalized since Newton/Lagrange) predates zero-padding as a signal-processing technique (developed with the FFT era, 1960s). The interpolation theory fed into zero-padding: the technique works precisely because DFT of a zero-padded signal produces interpolated spectral samples. Y (interpolation) existed first and fed into X (zero-padding).

Pinned sense (Law 11d): an interpolation method is a specific interpolation procedure — the from-definition carves 'a human-made procedure that estimates unknown values within the range of a discrete set of known data points', a specific case of the target's carved sense ('a mathematical procedure for estimating unknown values that fall within the range of a discrete set of known data points'). Is-a holds, specific→general (Law 9). This is the missing middle rung: with windowed-sinc-interpolation→interpolation method in the queue, filing the general rung directly was refused as a leap; completing the ladder here lets the general rung be reached derivably.

Sample-rate conversion requires interpolation to estimate signal values at new sample positions that fall between original samples. Remove interpolation and the converter cannot reconstruct the resampled waveform. The removal test passes: interpolation is the mathematical mechanism that enables resampling.