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

By Cornelius T. Leondes

Covers advances within the box of computing device concepts and algorithms in electronic sign processing.

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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)

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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 [9]. , 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.

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