Spectral Interpolation

Spectral interpolation is a mathematical technique used to estimate values of a function at specific points by analyzing its behavior across a broader spectrum. It involves transforming a set of discrete data points into a complete frequency or spectral representation, typically using tools like Fourier transforms. Once in this spectral domain, interpolation can be performed more smoothly and accurately, especially for functions that are smooth and periodic. After interpolating in the spectral domain, an inverse transform converts the data back to the original domain, providing precise estimates at desired points. This approach is powerful for high-accuracy signal processing, numerical analysis, and scientific computing.