By Cornelius T. Leondes
Covers advances within the box of computing device recommendations and algorithms in electronic sign processing.
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Additional info for Computer Techniques and Algorithms in Digital Signal Processing, Volume 75: Advances in Theory and Applications (Control and Dynamic Systems)
N III. Simulated Performance Based Algorithms of the QD- In this section, we present the results of some simulations of the ToddCruz algorithm mentioned in Section II, and of the modified Todd-Cruz algorithm. A. 1. Results of Original Algorithm Applied to Single Sinusoids Here we present results of tests of the algorithm in the single sinusoid case. The test data sets were sets of 32 data points of the form di - cos(w/) i - 0 , . . , 31 (112) The frequency w was varied between 0 and the Nyquist frequency; for each frequency, 1000 test runs were performed at each of 5 different signal-tonoise ratios (SNR) with Gaussian white noise added to the test data.
1. D. Stiefel derived relationships between orthogonal polynomials, kernel polynomials, and the QD algorithm that are basically the same ones as are presented here, but in a much more restricted setting. Stiefel only discussed inner products over R[x] of the form < f,g >- I(x)g(x)p(x)dx (101) where f , g C R[x] and a,b E N and p is some function that is real and non-negative in the interval [a, b]. Actually, Stiefel does not actually use the inner product formalism; throughout his paper, he only discusses integrals of this form and does not discuss inner products over vector spaces.
J - .... " ....... 01 0 . 001 E ~. " ', ' Iy ~ . i ' yI J- ~ ~. :, . " ,, i t ' ,, ,' - -:-" ' ' 5dS ~ o ~ .. -- .... 25dB " cRB - .... '. ', :'! 01 ,,, ~'. 0001 ; / le--05 , i . . . . le--06 I [\ "k... /', '~: i [ 0 . i :: ~/".. > i ',~'I <7 :! :/ ,'~ ~i ~. i & . . . . . . . . . 45 0 Figure 48" Normalized variance of frequency 2 estimates vs CRB, p = 3 case, c~ -- 6 52 IV. RICHARD M. TODD AND J. R. , one-half the Nyquist frequency) in the p = 2 and p = 3 cases.
Computer Techniques and Algorithms in Digital Signal Processing, Volume 75: Advances in Theory and Applications (Control and Dynamic Systems) by Cornelius T. Leondes