630_hw_4-1 - Advanced DSP HW#4 Problem Set ENEE 630...

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Unformatted text preview: Advanced DSP HW#4 Problem Set ENEE 630 Homework #4 Problem 1 Consider a wide-sense stationary process { u(n) } whose autocorrelation function has the following values for different lags: r (0) = 1 r (1) = 0 . 8 r (2) = 0 . 6 r (3) = 0 . 4 (a) Use the Levinson-Durbin recursion to evaluate the reflection coefficients Γ 1 , Γ 2 and Γ 3 . (b) Set up a three-stage lattice predictor for this process, using the values for the reflection coefficients found in part (a). (c) Evaluate the average power of the prediction error produced at the output of each of the three stages in this lattice predictor. Hence, make a plot of prediction error power vs. prediction order. Comment on your results. Problem 2 (a) A time series { u 1 ( n ) } consists of a single sinusoidal process of complex ampli- tude α and angular frequency w in additive white noise of zero mean and variance σ 2 v as shown by u 1 ( n ) = αe jwn + v ( n ) where E [ | α | 2 ] = σ 2 α E [ | v ( n ) | 2 ] = σ 2 v Define s M ( w ) 4 =         1 e- jw . . . e- jw ( M- 1)         The time series { u 1 ( n ) } is applied to a linear predictor of order M, optimized in the Wiener sense. Do the following (Use the Matrix Inversion Lemma if applicable): 1 Advanced DSP HW#4 Problem Set...
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This note was uploaded on 10/31/2010 for the course EE 630 taught by Professor Wu during the Spring '10 term at Aarhus Universitet, Aarhus.

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630_hw_4-1 - Advanced DSP HW#4 Problem Set ENEE 630...

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