INTERPOLATION Introduction Polynomial Interpolation Model-Based Interpolation Summary ? ? ? I nterpolation 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 continuoustime 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. | Advanced Digital Signal Processing and Noise Reduction Second Edition. Saeed V. Vaseghi Copyright 2000 John Wiley Sons Ltd ISBNs 0-471-62692-9 Hardback 0-470-84162-1 Electronic 10 INTERPOLATION Introduction Polynomial Interpolation Model-Based Interpolation 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. 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 continuoustime 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. The classical approach to interpolation is to construct a polynomial that passes through the known samples. In Section 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 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. 298 Interpolation Introduction The objective of interpolation is to obtain a high-fidelity reconstruction of the unknown or the missing samples of a signal. The emphasis
