finiteimpulseresponseinterpolation

Finite impulse response interpolation uses finite-length impulse response filters to estimate samples between known discrete samples or to reconstruct a signal at a different sampling rate. It is a common method for resampling, time alignment, or up/down-sampling, offering controlled distortion and predictable delay by convolving the input with a fixed interpolation kernel.

An FIR interpolation filter produces y[n] = sum_{k=0}^{N-1} h[k] x[n - k], where the coefficients h[k] are chosen to realize a desired fractional delay d and, if needed, a specific phase response. In practice, d is implemented via parametric designs (such as Farrow) or polyphase decompositions to handle multiple interpolation phases efficiently. The filter length N trades off accuracy and cost.

Common approaches include windowed-sinc interpolation, where an ideal sinc kernel is truncated by a window, and explicit fractional-delay filters that approximate non-integer delays. Polyphase and Farrow architectures enable efficient rate conversion by sharing computations across phases.

Applications include audio and image resampling, video frame-rate conversion, and sensor data interpolation. FIR interpolation provides linear-phase options, robust control of aliasing, and a predictable delay, at the expense of interpolation error if the kernel length is too short or the input spectrum is poorly bandlimited.

Limitations include the need to select length and window to meet accuracy and real-time constraints. Modern designs often use polyphase or multi-tap structures to optimize performance.