Digital Control and Signal Processing Systems and Techniques - download pdf or read online

By Cornelius T. Leondes

ISBN-10: 0080529941

ISBN-13: 9780080529943

ISBN-10: 0120127784

ISBN-13: 9780120127788

Compliment for the sequence: ''This e-book may be an invaluable connection with regulate engineers and researchers. The papers contained hide good the hot advances within the box of recent keep an eye on theory.'' --IEEE team Correspondence ''This e-book can help all these researchers who valiantly try and continue abreast of what's new within the concept and perform of optimum control.'' --Control

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For consistency of notations used in higher-order spectra, it is important to introduce a parameter, which is alternative to the order, q. The parameter used here is defined as: q/2 (103) k - 2. ~ b i i=1 and corresponds to the order of multi-linearity of the P W V D kernel, or in the case of random signals, the order of polyspectra. Note that this represents a slight change of notation. The following properties, are valid Vk E N, and V(t, f ) E R 2 (see Appendix C for proofs): P - 1 . The P W V D is real for any signal x(t): rw< ) (,,f) L"{~(t)} ]" - "{~(t)) (t , f) w(k) (104) P - 2 .

H ( f ) then p (t, f) = p,(t, y) 9 Ph (t, y) t Equivalently, if Y(f) = S(f) 9H(f), that is if y(t) = s(t) . h(t) then py (t, f) - Ps (t, f ) 9 Ph (t, f) f Finite support. e. if s(t) 0 for ta < t < tb, and S ( f ) - 0 for fa < f < fb, then, ps(t, f ) -- 0 20 BOUALEM BOASHASH for ta < t < tb or fa < f < lb. ~'-1 {g(//, T)} = 0 for Itl for Ifl > 1~1/2 (38) v ---, t and in frequency holds when {g(v, 7-)} = 0 > I-I12 (39) r-+f I n s t a n t a n e o u s f r e q u e n c y a n d g r o u p delay. For FM signals, the nonstationary or time-varying aspect is directly quantified by the variation of the IF, fi(t), or the group delay (GD), vg(f), expressed as follows: 1 d f i ( t ) - ~--~-~arg(z(t)} rg(f) -- (40) 1 d 27r df arg{Z(f)}.

TIME FREQUENCYSIGNALANALYSIS 23 The WVD does not require step 2 because its smoothing function G(n, m) equals 6(n). Further details of the implementation are contained in [1, chapter 7]. 445-451]. In summary the characteristics of G(n, m) determine the properties of a bilinear TFD, such as maximising energy concentration or reducing artifacts. The source code for the implementation of TFDs is listed in [1, chapter 7]. 4 Polynomial T F D s . 1 that the investigation of the notion of the IF led us to realise that the bilinearity of the WVD makes it suitable for the analysis of linear FM signals only.

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Digital Control and Signal Processing Systems and Techniques by Cornelius T. Leondes

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