Adaptive Filtering by Paulo S. R. Diniz

Author:Paulo S. R. Diniz
Language: eng
Format: epub
ISBN: 9783030290573
Publisher: Springer International Publishing

7.2.1 Forward Prediction Problem

The objective of the forward prediction is to predict a future sample of a given input sequence using the currently available information of the sequence. For example, one can try to predict the value of x(k) using past samples , through an FIR prediction filter with coefficients as

(7.1)

where is the predictor output signal,

is the FIR forward prediction coefficient vector, and

is the available input signal vector. The second variable included in the vectors of (7.1) is to indicate the vector dimension, since it is required in the order-updating equations of the LRLS algorithm. This second variable will be included where needed in the present chapter.

The instantaneous a posteriori forward prediction error is given by

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