Biomedical Signal Processing by Metin Akay (Auth.)

By Metin Akay (Auth.)

Refined suggestions for sign processing are actually to be had to the biomedical professional! Written in an easy-to-read, uncomplicated kind, Biomedical sign Processing offers suggestions to cast off history noise, increase sign detection, and research desktop facts, making effects effortless to realize and follow. as well as analyzing thoughts for electric sign research, filtering, and transforms, the writer offers an in depth appendix with numerous desktop courses that display recommendations awarded within the textual content

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Find the inverse z-transform of H(z): H(z) 3 - 4z"' (1 - 0 . 5)" + 2(3)"]«(n). E X A M P L E . Find t h e inverse z-transform of H{z): H{z) A, = = 7 - 18z"' + 6 z " 7 - 18z~' + 6 z " 7 - 1 - 3z"' 2 z= 18z"' + 6 z " 3 = 2 2 6z" (1 - 0 . 5 z - ' ( l - 3 z - ' ) . 5z - I A(«) A] (1 - 0 . 5)(-3)z" A2 1 - 3z" 2 = 4 + Z - ' [ A 3] + A, 2. 6 Properties of + 4δ(/ι). z-Transforms 1. Linearity. T h e z-transform and inverse z-transform are linear oper­ ations. 24) and for the inverse z-transform as Z~\aX\{z) 2.

3 . 9 44 3. Digital Filter D e s i g n limitation can be o v e r c o m e by multiplying E q . 21) by the sampling interval T. As a result, E q s . 22) H(z) = Ha(jj). 4 Bilinear Transformation An alternative to the impulse-invariant transformation is the bilinear transformation, widely a c c e p t e d in the design of digital filters from an analog filter function [2,6,8,10]. This type of transformation is based on numerical integration. <0. (/I7) + χΆ(η - 1)7]. 26), which is in the analog d o m a i n , can be given in the dis­ crete domain as y(n) - y(n - 1) = | [*(«) + x(n - 1)].

3 . 1 0 . s-plane into the z-plane using the bilinear transform. 10 illustrates the mapping of the analog frequency axis o n t o the unit circle using the bilinear transformation. 11 s h o w s the transformation of a typical lowpass analog fre­ q u e n c y r e s p o n s e by using the bilinear transformation. In Fig. 11, the analog frequencies, are calculated as a function of the digital frequen­ cies, ω,, w h e r e Ω, = γ tan y , i = 1, 2, 3, . . Although the bilinear transformation p r o d u c e s high-frequency oscillation in the frequency d o m a i n , it is preferable to the time-invariant transforma­ tion since it is free of aliasing p r o b l e m s .

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Biomedical Signal Processing by Metin Akay (Auth.)
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