Sample-By-Sample Linear Prediction

1. What is linear prediction method?
2. How do you write a linear prediction rule?
3. How do you find the best linear predictor?
4. What is linear prediction error?

What is linear prediction method?

Linear prediction is a mathematical operation where future values of a discrete-time signal are 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.

How do you write a linear prediction rule?

A particularly simple and popular type of rule is a linear prediction rule: yx ≡ a + xb for two numbers a and b. Remember that a is called the intercept of the line and b is called the slope. Slope is often thought of as “rise over run”.

How do you find the best linear predictor?

A linear predictor has the form g(x) = β0 + β1x(1) + β2x(2) + ··· + βdx(d). g(x) = βT x. Again, let β∗ minimize R(β) = E(Y − XT β)2. We call l∗(x) = xT β∗ the best linear predictor.

What is linear prediction error?

The prediction error, e(n), can be viewed as the output of the prediction error filter A(z), where. H(z) is the optimal linear predictor. x(n) is the input signal. x ^ ( n ) is the predicted signal.