SUNG JOO KIM 5.2.4 The Step-Up and Step-Down Recursions -20067166.

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Presentation transcript:

SUNG JOO KIM The Step-Up and Step-Down Recursions

SUNG JU KIM 2 The Levinson-Durbin recursion 2. produces an all-pole model for a signal from the autocorrelation sequence 1. autocorrelation normal equations a set of reflection coefficientsthe final modeling error the model parameters the autocorrelation sequence => the step-up and step-down recursions

SUNG JU KIM 3 -. the step-up recursion (1) Initialize the recursion : (2) For j = 0,1,...., p-1 (a) For i = 1,2,...,j (b) (3) b(0) =

SUNG JU KIM 4 Example The Step-Up Recursion reflection coefficient sequence : a 1.

SUNG JU KIM 5 The general form for the second-order all-pole model. lower-order filter

SUNG JU KIM 6 -. the step-down or backwardLRvinson recursion. -> beginning with a p, we set T p = a p (p) j j+1, a j+1 (i) The Levinson order-update equation, a j+1 (i) a j (i) a j+1 (j-i+1).