1549312215-Complex_Analysis_for_Mathematics_and_Engineering_5th_edition__Mathews

384 CHAPTER 9 • z-TRANSFORMS AND APPLICATIONS EXAMPLE 9.23 (a) The filter y(n] = x [n] + x[n - 2] is designed to zero out cosG ...

9 .3 • DIGITAL SIGNAL FILTERS 385 Imz 1t 1t 4 2 Figure 9.9 Ampli tude response A(8) and zero-pole plot for y[n) = l L; • x[n - k ...

386 CHAPTER 9 • Z..TRANSFORMS AND APPLICATIONS . fil -•3w 4ff -•" in- in h ~ are z = e"', e • , e-·-, e•, e,-, e•, e•. There are ...

9.3 • DIGITAL SIGNAL FILTERS 387 lmz 7 Figure 9.10 Amplitude response A(9) and zero-pole plot for y(n] = ~ E x(n - k]. k=O Solut ...

388 CHAPTER 9 • z- TRANSFORMS AND APPLICATIONS lmz A(8') 2.5 1.5 0.5 Figure 9.11 Amplit ude response A(11) and zero-pole plot fo ...

9.3 • D IGITAL S IGNAL FILTERS 389 Imz '--~~g~~g~~ 3 ~X~~gO 4 2 4 Figure 9.12 Amplitude response A(ll) and zero-pole plot for t ...

390 CHAPTER, 9 • Z-TR.ANSFOR.MS AND APPLICATIONS Imz '-~~n~~~no..._~,___;:::,~n 9 4 2 Figure 9.13 Amplitude response A(8) a.nd z ...

9.3 • DIGITAL SIGNAL FILTERS 391 (b} y[n] = x[n]- x[n-l]+x[n- 2) will "zero-out" x[n] = cos( in} and x[n] = sin( in). (c) y[n] = ...

392 CHAPTE R 9 • z -TRANSFORMS AND APPLICATIONS (a) Start with Yo = ~xo, Y1 = !x 1 + Hxo, and show by induction that Yn = E~=O ~ ...

9.3 • DIGITAL SIGNAL F ILTERS 393 (a) Constr uct a filter using the zeros e ±~•· and e-^1 • = -1 for "zeroing out" cos(2; n), s ...

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r 10 mapping Overview The terminology "conformal mapping" should have a familiar sound. In 1569 the Flemish cartographer Gerardu ...

396 CHAPTER 10 • CONFORMAL MAPPING Let C: z (t) = x (t) + iy (t), - 1 :St :S 1 d enote a smooth curve that passes through the po ...

10. l • BASIC PROPE RTIES OF CONFORMAL MAPPI NGS 397 y v T, Figure 10.2 The analytic mapping w = f ( z) is conformal at the poin ...

398 CHAPTER 10 • CONFORMAL MAPPINC Therefore, the angle of rotation is given by -7f a1 = Argf' (i) = 2 , az = Argj' (1) = 7f, an ...

10.1 • BASIC PROPERTIES OF CONFORMAL MAPPINGS 399 y IV :f(z) v T* l Figure 10.3 The analytic mapping w 0,... , J (k - I ) (z ...

400 CHAPTER 10 • CONFORMAL MAPPING v y w=~ Z3 = i Z2 = I + i x u Zo = 0 z, = I Figure 10.4 The mapping w = z^2. From Equation (1 ...

10.l • BASIC PROPERTIES OF CONFORMAL MAPPINGS 401 the familiar expression g '( wo ) = Li m g(w)-g(wo) w-+wo W -wo Li z-zo 1 1 = ...

402 CHAPTER 10 • CONFORMAL MAPPING 11. If f is analytic at Zo and/' (zo) # 0, show that the function g (z) = f (z) preserves the ...

10.2 • BILINEAR TRANSFORMATIONS 403 (10-13) and c = 0, then S reduces to a linear transformation, which carries lines onto lines ...