find the bilinear trasnformation that maps the point 1+i,-i,2-i of the z plane into the points 0,1,i of the w plane
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(a) Find the bilinear transformation that maps the point (0), (1), (i) into the point (1+i), (-i), (2-1). (b) Show that the function sinhz is an analytic function. 42-3 Where C is the circle such that Evaluate the integral Sc(2-2) (1) C:Z1 = 1 (2) C:[Z= 1 (3) C:Z) = 3 200
(Complex Analysis) The linear mapping wFUz+p, where α, β e C maps the point ZFI+1 to the point wi-i, and the poin to the point w2-1i a) Determine α and β. b) Find the region in the w-plane corresponding to the upper half-plane Im(z) 20 in 9. the z-plane. Sketch the region in the w-plane. c) Find the region in the w-plane corresponding to the disk Iz 2 in the z-plane d) Find the fixed points of the mapping The...
12. Read Section 88 from the Brown and Churchill Book, 7th edition, to understand the derivation of the most general bilinear transformation that maps the upper halfplane Im (z) >0 in the z-plane onto the unit open disk w< 1 in the w-plane. By imitating the arguments, derive the most general bilinear transformation that maps the right halfplane Re (z) > 0 in the z-plane onto the unit open disk w <1 in the w-plane.
(Bilinear transformation and all pass systems in the Laplace domain). The bilinear transformation F:C→C is a mapping from the z-domain to the Laplace domain, defined as s唔倫-1) without loss of generality, let us 7 17-) Without loss of generality, let us Td 1+z-1 assume that the scaling factor Ta is not important here, so we can choose 1-z-1 Ta = 2 to simplify our discussions; hence, s(z) =-. 1+z-1 (a) Show that the transformation maps the unit circle in the...
Example 3: Find the bilinear transformation that maps the points (o, i, 0) into the points JNTU 2003 (Set No. I)I 0, i, 0o)
Problem # 1 . Topics: Bilinear Transform Assuming parameter k-1.2 and using the Bilinear Transform, map the following poles in the s-plane to the z-plane. Give z-plane. magnitude and angle for the corresponding poles in the S=-0.5 +0.5j → z=
10 Find the image of the rectangular region in the 2 – plane formed by joining the points (0,0),(2,0), (2,1),(0,1) in the w – plane under the transformation, = (1 + i)z – 2i Interpret both the regions graphically. =
Problem #2: Transform the following characteristic equations into the bilinear plane and use the Routh Array to determine stability. 2. A(Z)-4-0.97.3-0.23% + 0.222+0.05
-lot halt)= lo e uct) 1- Let T= sec and let He(s) = Stlo be an analog filter a- Find hcn),. design invariance' discrete time filter using impulse b. Find Hce) using bilinear trans tormation, it shouldbe one of the following (circle one) - |- 2-1 z-0-11 C- Using bilnear transtormation, where does the continuous time frequency sz=lo maps to tim'e freguencg w: w = 10,', /s, I, T discrete circle on e: %3D
2. Investigate the stability of the following characteristic equation using bilinear transformation $$ G(z)=\frac{(z+0.4)}{z^{3}-1.5 z^{2}+1.2 z-0.6} $$