Computer Techniques and Algorithms in Digital Signal by Cornelius T. Leondes

By Cornelius T. Leondes

Covers advances within the box of desktop options and algorithms in electronic sign processing.

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Additional resources for Computer Techniques and Algorithms in Digital Signal Processing, Volume 75: Advances in Theory and Applications (Control and Dynamic Systems)

Sample text

9i' . i! le--07 le--08 . 4 0 45 Figure 41" Variance of frequency 1 estimates, p = 3 case, ct - 2 FREQUENCY ESTIMATION AND THE QD METHOD 0 . 0001 '".. ';" . ,. ,9" ~ " / \9 ,. ,,. ~ ' /, ", . ,. , . ~, ~ ,,9" (D O , , ~' "". ~" , ..... -:: t] . ~_=<. "M" ~ / ~ q ~ , , + ~ _ . . ~ " : " ~ / ',',J.. J ~.. -. " .. 4 :. i \ '.. ,--g , B :. ~: ~Ct ::> ~9. ',. x~ . 001 ,--4 --*--- -m-- --- .... 4 / ! / / ! ~. 05 _,, _ , i. 01 %,/ ~ 0 . 001 c~ ~ . s . I dB ' x '). -- .... ~,. . . i '~ "~ , 0 i ~0 i , le-05 /" ~ t i .

D. p=3 ESTIMATION AND THE QD METHOD 47 case Figs. 37-48 show the results of the algorithms with the double sinusoid input in the case where p = 2. We show both the variance and normalized variance for each of the two frequency estimates, and we show results for both the unmodified algorithm and the modified algorithm with both c~ = 2 and o~ = 6. 0 . 001 . . '-~---~--"k . ',' le--05 ", , '~-.. I ---~ -- - ".. - ':,,. , 0 ....... ~i , l | "~, " ~.. i ] .... ~. -'" \',? 4 0 45 Figure 37" Variance of frequency 1 estimates, p - 3 case.

7-24 present graphs of the variance and normalized variance versus Cramer-Rao bound (CRB). We can see that increased values of c~ tend to alleviate the problem around f - 1/4, moving it further and further to the left of the frequency axis as c~ increases. 0 . 0001 ; --~-- ~ ..... le--05 > le-06 9,, " ~ ",'""k . . x . m . -~. "x .... /" t/" ~.. le--07 9. ~ . - ~,-- . ~. 05 1 0 . 2 i z i. e d ~ , " ~ . _ . ~ . 45 0 Figure 7: Variance of frequency estimates, p = l case, ct - 2 0 . ~\. , . ~ ,- , , 1"~.

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