Linear predictive analysis is a simple form of first-order

extrapolation In mathematics, extrapolation is a type of estimation, beyond the original observation range, of the value of a variable on the basis of its relationship with another variable. It is similar to interpolation, which produces estimates between know ...

: if it has been changing at this rate then it will probably continue to change at approximately the same rate, at least in the short term. This is equivalent to fitting a

tangent In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve. More ...

to the graph and extending the line. One use of this is in

Linear predictive coding Linear predictive coding (LPC) is a method used mostly in audio signal processing and speech processing for representing the spectral envelope of a digital signal of speech in compressed form, using the information of a linear predictive model. ...

which can be used as a method of reducing the amount of data needed to approximately

encode The Encyclopedia of DNA Elements (ENCODE) is a public research project which aims to identify functional elements in the human genome. ENCODE also supports further biomedical research by "generating community resources of genomics data, software ...

a series. Suppose it is desired to store or transmit a series of values representing voice. The value at each sampling point could be transmitted (if 256 values are possible then 8 bits of data for each point are required, if the precision of 65536 levels are desired then 16 bits per sample are required). If it is known that the value rarely changes more than +/- 15 values between successive samples (-15 to +15 is 31 steps, counting the zero) then we could encode the change in 5 bits. As long as the change is less than +/- 15 values in successive steps the value will exactly reproduce the desired sequence. When the rate of change exceeds +/-15 then the reconstructed values will temporarily differ from the desired value; provided fast changes that exceed the limit are rare it may be acceptable to use the approximation in order to attain the improved coding density.

See also