Linear predictive analysis
Encyclopedia
Linear predictive analysis can be thought of as a simple form of first-order extrapolation
: 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
to the graph and extending the line.
One use of this is in Linear predictive coding
which can be used as a method of reducing the amount of data needed to approximately encode
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.
Extrapolation
In mathematics, extrapolation is the process of constructing new data points. It is similar to the process of interpolation, which constructs new points between known points, but the results of extrapolations are often less meaningful, and are subject to greater uncertainty. It may also mean...
: 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
Tangent
In geometry, the tangent line to a plane curve at a given point is the straight line that "just touches" the curve at that point. More precisely, a straight line is said to be a tangent of a curve at a point on the curve if the line passes through the point on the curve and has slope where f...
to the graph and extending the line.
One use of this is in Linear predictive coding
Linear predictive coding
Linear predictive coding is a tool 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
Encode
Encode may refer to:* Can be related to "Code"* Encode ApS, a Danish software company* Encode SA, a Greek information security company* ENCODE, the ENCyclopedia Of DNA Elements...
a series. Suppose it is desired to store or transmit a series of values representing voice. The value at each sampling
Sampling (signal processing)
In signal processing, sampling is the reduction of a continuous signal to a discrete signal. A common example is the conversion of a sound wave to a sequence of samples ....
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.