Describe › Signal & numerical

Interpolation (spline / linear)

Interpolation resamples an (X, Y) curve on a uniform grid using a natural cubic spline or linear segments.

What is Interpolation (spline / linear)?

Interpolation estimates values between measured points. Linear interpolation connects points with straight segments — simple and monotone-preserving but kinked. A natural cubic spline fits piecewise cubics with matched first and second derivatives, giving a smooth curve through every point (curvature zero at the ends).

Common uses: putting irregularly-spaced data on an even grid, upsampling for a smoother plot, or aligning two series to a common X. Unlike regression, interpolation passes exactly through the data — it does not smooth noise, so interpolate clean data.

When should I use Interpolation (spline / linear)?

  • Evenly spacing or upsampling an (X, Y) curve.
  • Reading off Y at X values between measured points.

What data does it need?

An X column and a Y column (numeric) + method (spline or linear) + number of output points.

What does it report?

The interpolated curve on the uniform grid, overlaid on the original data points.

What does it assume?

  • X values are distinct (duplicate X breaks interpolation).
  • The data is essentially noise-free — interpolation reproduces noise faithfully; smooth first if needed.

How do I interpret the result?

A spline can overshoot between widely-spaced points; if that produces implausible wiggles, use linear.

See also

References

  • de Boor (1978). A Practical Guide to Splines.