Linear prediction

Linear prediction is a mathematical operation where future values of a digital signal is estimated as a linear function of previous samples.

In digital signal processing linear prediction is often called linear predictive coding (LPC) and can thus be viewed as a subset of filter theory. In system analysis (a subfield of mathematics), linear prediction can be viewed as a part of mathematical modelling or optimization.

The most common representation is

x'(n) = sum_i=1^p a_i x(n-i)

where x'(n) is the estimated signal value, x(n) the previous values, and a_i the predictor coefficients. The error generated by this estimate is

e(n) = x(n) - x'(n)

where x(n) is the true signal value and x'(n) the estimated value.

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