By Cornelius T. Leondes
Covers advances within the box of computing device concepts and algorithms in electronic sign processing.
Read Online or Download Computer Techniques and Algorithms in Digital Signal Processing, Volume 75: Advances in Theory and Applications (Control and Dynamic Systems) PDF
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Extra info for Computer Techniques and Algorithms in Digital Signal Processing, Volume 75: Advances in Theory and Applications (Control and Dynamic Systems)
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"~. T'-"~, O. , - 10dB 15 dE 2OdB , - .... . . 45 0 Figure 8" Normalized variance of frequency estimates vs CRB, p - 1 case, c~-2 36 R I C H A R D M. T O D D A N D J. R. C R U Z 0 . 0 0 1 . I . . . 1 ~ d B \ ( 2; ~--~ . t 0 . k ". ~ "~ ,,, "",. le--07 ""~ _ ~c~ ""w . ~__~- .. x---" ~. \! ,,. >( .... ~ /l ~ .... . .
4--- --- -- - 0 . 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.
The Second Cruz-Banjanin Algorithm The second Cruz-Banjanin algorithm was first presented in . , the frequencies are not constrained to be on the unit circle, but can be anywhere on the complex plane. Again, let di be the input data sequence, and let Z be the shift operator. The appropriate minimization criterion here is still to minimize - E trd + k + . . + b d _ ll: (50) 18 R I C H A R D M. T O D D A N D J. R. C R U Z but the polynomial b(z- 1) _ 1 + bl z - 1 + . . + bvz-V is no longer required to have roots in complex conjugate pairs.