Interpolation
Saeed V. Vaseghi · 2001
10.1 Introduction 10.2 Polynomial interpolation 10.3 Model-based interpolation 10.4 Summary 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. Applications of interpolators include conversion of a discrete-time signal to a continuous-time signal, sampling rate conversion in multirate communication systems, low-bit-rate speech coding, up-sampling of a signal for improved graphical representation, and restoration of a sequence of samples irrevocably distorted by transmission errors, impulsive noise, dropouts, etc. This chapter begins with a study of the basic concept of ideal interpolation of a band-limited signal, a simple model for the effects of a number of missing samples, and the factors that affect the interpolation process. In Section 10.2, 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 posteriori interpolation, and least square error interpolation based on an autoregressive model. Finally, we consider time–frequency interpolation, and interpolation through searching an adaptive signal codebook for the best-matching signal.