resamplinginterpolation

Resampling interpolation is a data processing technique used to estimate values at a new set of sampling points from a dataset measured on a different grid. It combines resampling—changing the sampling grid or sampling rate—with interpolation—the construction of intermediate values from known samples. The term is common in signal processing, image processing, and geographic information systems, where data must be transferred between coordinate systems, resolutions, or sampling schemes.

In practice, you map the original samples f(x_k) to a new grid x'_j and compute the resampled values f̂(x'_j) by applying an interpolation kernel h: f̂(x') ≈ sum_k f(x_k) h(x' - x_k). In one dimension, simple kernels include nearest neighbor, linear, and cubic polynomials; in two dimensions, the approach extends with separable or isotropic kernels such as bilinear, bicubic, or Lanczos (windowed sinc). Other methods, like Fourier-based resampling, treat the signal in the frequency domain.

Downsampling often requires prefiltering to reduce aliasing, while upsampling emphasizes reconstructing missing samples. The choice of kernel, its support, and boundary handling affect smoothness, accuracy, and artifacts such as blurring or ringing. Nonuniform sampling or irregular grids add additional complexity and may require generalized interpolation schemes.

Applications include image resizing and video scaling, audio sample-rate conversion, reprojecting raster or vector data in GIS, and aligning time-series observations from different sensors.

Limitations: resampling interpolation cannot create information beyond the original samples; accuracy depends on signal regularity and kernel properties.