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The purpose of adaptive linear prediction is to use an adaptive filter to estimate the future values of a signal based on past values of the signal. Adaptive linear prediction also is useful in speech and image compression techniques, for example, in linear predictive coding (LPC).
The following figure shows a diagram of an adaptive linear prediction system.
In the previous figure, s(n) is a time series at time n and x(n) is a delayed version of s(n) that is the input signal to the adaptive filter. y(n) is the output of the adaptive filter. The adaptive linear prediction system calculates the difference between s(n) and y(n) and produces an error signal e(n). The system iteratively adjusts the coefficients of the adaptive filter to minimize the power of e(n). When the power of e(n) reaches the minimal value, the adaptive filter can predict the future values of the time series based on the past values.
Adaptive linear prediction is a method to estimate autoregressive (AR) models of an unknown plant. You can multiply the adaptive filter coefficients by –1 to obtain the AR coefficients of the unknown plant. The difference between adaptive linear prediction and other AR model estimation methods is that you can use adaptive linear prediction to perform AR model estimation in online mode. For example, you can use adaptive linear prediction to detect engine knocking that occurs due to an ignition-system malfunction. By performing adaptive linear prediction on the vibration signal of the engine, you can monitor the amplitude of the error signal in real time. If the amplitude of the error signal has transient changes, those transient changes indicate that engine knocking occurs.
Refer to the Use Adaptive Filter for Linear Prediction VI in the examples\Adaptive Filters\Getting Started directory for an example that uses the LabVIEW Adaptive Filter Toolkit to perform adaptive linear prediction.