## Abstract

Interpolation is the estimation of the unknown, or the lost, samples of a signal using a weighted average of a number of known samples at the neighbourhood points. Interpolators are used in various forms in most signal processing and decision making systems. Applications of interpolators include conversion of a discrete-time signal to a continuous-time signal, sampling rate conversion in multi-rate systems, low bit rate speech coding, upsampling of a signal for improved graphical representation, and restoration of a sequence of samples irrevocably distorted by transmission errors, impulsive noise, drop outs etc.

This chapter begins with a study of the ideal interpolation of a band limited signal, a simple model for the effects of a number of missing samples, and the factors that affect interpolation. The classical approach to interpolation is to construct a polynomial that passes through the known samples. In Section 10.2 a general form of polynomial interpolation, and its special forms Lagrange, Newton, Hermite, and cubic spline interpolators are considered. Optimal interpolators utilise predictive and statistical models of the signal process. In Section 10.3 a number of model-based interpolation methods are considered. These methods include maximum a posterior interpolation and least squared error interpolation based on an autoregressive model. Finally we consider time-frequency interpolation, and interpolation through search of an adaptive codebook for the best signal.

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