Cornelius T. Leondes's Computer Techniques and Algorithms in Digital Signal PDF

By Cornelius T. Leondes

Covers advances within the box of laptop thoughts and algorithms in electronic sign processing.

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

Example text

CRUZ hence < y2, 1 >:/:< y, y > (64) Thus the Stiefel theorems do not apply, and one must use the theorems presented next for general inner products. D. E x t e n s i o n of the Stiefel T h e o r e m s Here we present the appropriate extension and re-development of the Stiefel theorems for the case of general inner products over C[x]. Consider an inner product defined on C[x]" Cx3 < f,g > - C~ ~-~~_~fiMijg; (65) i = 0 j =0 C<) where f, g C C[x], f - ~ i = 0 fi zi and similarly for g. M is some Hermitian matrix with elements in C.

M-- -~ ~ ---~ ""x .... ~'" . ~ . . .. " x . riB ,,! /" . . ....... --~--- / /. -- - " ~ " "~- . 4 0 45 Figure 11" Variance of frequency estimates, p=3 case, c t - 2 FREQUENCY ESTIMATION AND THE QD METHOD o0~ . . . 05 - ~ - . 2 . 25 Normalized - - . 45 0 Figure 12" Normalized variance of frequency estimates vs CRB, p - 3 case, a--2 0 . 0001 o o le--05 > le--06 2 \, le--07 le--08 .... 2 Normalized ~ .... x .... 25 ~ .... 3 *<'" ~ .... 45 0 Figure 13: Variance of frequency estimates, p - 1 case, a - 4 0 .

J.. 4 0 45 Figure 38" Variance of frequency 2 estimates, p = 3 case. 48 RICHARD M. TODD A N D J. R. CRUZ O - O1 9 . r ~. , ........ ~" ...... " " '. " ~! ~ , .. ~ , ", ", "~. ). i : .... 3odR CRB ....... ---- .... /, .. 05 , 15dB 20dB 25dB "--;:. Z_--m /". ~i: le--05 le--06 i,; ,' .... 45 0 Figure 39" Normalized variance of frequency 1 e s t i m a t e s vs CRB, p - 3 case. 01 ,,, ... /-k. ,. '" 0 . 001 . ~" "k -" ~ . ~ "" ', . " : ~ ", / '," , ". ;i ,~. ' \ . // ~. % i ": \ ,' ,, ! i ,~ / "L'x', ~ ': ....

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