An fir predictor interpretation of LS estimation of sinusoidal amplitudes followed by extrapolation

Prediction of time series consisting of a weighted sum of complex sinusoids corrupted by additive noise can be used for e.g. mobile radio channels. Least squares estimation of the complex amplitudes of sinusoids with known frequencies followed by extrapolation to the desired prediction range, is here interpreted as a linear FIR predictor using a sinusoidal filter. This interpretation enables an analysis of the properties of the predictor. An improved method utilizing a Wiener predictor, designed under the assumption that all the complex sinusoids have equal magnitudes, is proposed. The performance of the different prediction methods are evaluated in simulations and the proposed predictor is seen to have a performance close to the optimal Wiener predictor.