20091ee114_1_PS4%20_Sol

20091ee114_1_PS4%20_Sol - UCLA Dept of Electrical...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Dept. of Electrical Engineering EE 114, Winter 2009 Problem Set 4 Solutions 1. Consider the signal: x ( n ) = β n for n 0 (1) (a) Using the autocorrelation method of linear prediction analysis, find the 1 st order predic- tion coefficient, i.e. a 1 . Find the corresponding minimum error, E min . (b) Using the covariance method of linear prediction analysis, find the 1 st order predic- tion coefficient, i.e. a 1 . Find the corresponding minimum error, E min . (c) What can you say about the accuracy of each of these linear prediction methods. Which method worked best for this example signal? Hint: N n =0 ρ n = 1 - ρ N +1 1 - ρ Answer : (a) For the 1 st -order autocorrelation case: a 1 = R (1) R (0) R (0) = N - 1 X n =0 x 2 ( n ) = N - 1 X n =0 β 2 n R (0) = 1 - β 2 N 1 - β 2 R (1) = N - 1 X n =1 x ( n ) x ( n - 1) = N - 1 X n =1 β n β n - 1 = 1 β N - 1 X n =1 β 2 n = 1 β " β 2 - β 2 N 1 - β 2 # R (1) = β " 1 - β 2 N - 2 1 - β 2 # a 1 = β " 1 - β 2 N - 2 1 - β 2 # × " 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 3

20091ee114_1_PS4%20_Sol - UCLA Dept of Electrical...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online