Elementary mathematical and computational tools for electrical and computer engineers using Matlab - Chapter 5 potx

... wedesire that: (5. 25) (5. 26) (5. 27)Now, replacing the values of a(2) and b(2) from Eqs. (5. 26) and (5. 27) into Eq. (5. 25) , we are led to a second-degree equation in r:r2 – 3r + 1 = 0 (5. 28)The ... com-mand is poly.poly(r)In-Class ExercisePb. 5. 14 Find the roots of the polynomial p = [132103], and com-pute their sum and product.Pb. 5. 15 Consider the two polynomials:p1 = [132103]andp2 ... for com-puting the zeros using the graphical commands, the numerical techniquesknown as the Direct Iterative and the Newton-Raphson methods, and thebuilt-in fsolve and fzero functions of MATLAB. 5. 1.1...

... Top panel: b= 1, bottom panel: b = 0.9998. -2 0 -1 5 -1 0 -5 0 5 10 15 -1 5 -1 0 -5 0 5 10 15 a=0.7 b=1 -2 0 -1 5 -1 0 -5 0 5 10 15 20 -1 5 -1 0 -5 0 5 10 15 a=0.7 b=0.9998xk axk byk xkyk bxk ayk xk() ... Press LLCx1(1)=0 .56 96;y1(1)=0.1622;x2(1)=0 .56 50;y2(1)=0.1 650 ; for n=1:120x1(n+1)=a*x1(n)-b*(y1(n )-( x1(n))^2);y1(n+1)=b*x1(n)+a*(y1(n )-( x1(n))^2);x2(n+1)=a*x2(n)-b*(y2(n )-( x2(n))^2);y2(n+1)=b*x2(n)+a*(y2(n )-( x2(n))^2);endplot(x1,y1,'ro',x2,y2,'bx')2.8.2.1 ... LLC for n=1: 150 0 for m=1:40x(1,m) =-0 .99+2*rx(m);y(1,m) =-0 .99+2*ry(m);x(n+1,m)=a*x(n,m)-b*(y(n,m )-( x(n,m))^2);y(n+1,m)=b*x(n,m)+a*(y(n,m )-( x(n,m))^2);endendplot(x,y,'r.')axis( [-1 ...

... circuitparameters.b. Holding the graph for the case R = 100Ω, sketch L1 and L2 again for R = 50 Ω and R = 50 0Ω. How do the values of the voltage and the current change as R increases; and decreases?c. Determine ... while that of oil, polystyrene, glass, quartz, bakelite, and mica are,respectively, 2.1, 2.6, 4 .5 10, 3.8 5, 5, and 5. 4-6 larger.)In-Class ExercisePb. 3.18 Find the ratio of the capacitance ... 1 1 5 0 for forelsewhere© 2001 by CRC Press LLCIn-Class ExercisePb. 3.19 In a measurement of two power values, P1 and P2, it was deter-mined that:G1 = 9 dB and G2 = –11 dBUsing...

... equations for D(k) and D2(k), as given respec-tively by Eqs. (4.16) and (4.30), and with the initial conditions for the function and its derivative. The first elements for the y, D, and D2 arrays ... Phase')uc=exp(j*(2*pi*fc*t+2*pi*kf*intm));u=real(uc);phase=unwrap(angle(uc) )-2 *pi*fc*t;subplot(2,2,3)plot(t,u)axis( [-0 . 15 0. 15 -1 1])title('Modulated Signal')Dphase(1)=0; for k=1:p-1Dphase(k+1)=(2/dt)*(phase(k+1)-phase(k)) Dphase(k);endmd=Dphase/(2*pi*kf);subplot(2,2,4)plot(t,md)title('Reconstructed ... to fix a= 1/2, giving for the other quantities:(4 .52 )finally leading to the following expressions for the second-order iterator and its parameters:(4 .53 a)(4 .53 b)(4 .53 c)Next, we give, without...

... maximum directivity?Pb. 6 .50 The following program simulates a 2 5- element array-swept radarbeam.th=0:0.01:pi;t =-0 .5* sqrt(3):0. 05* sqrt(3):0 .5* sqrt(3);N= 25; M=moviein(21); for m=1:21;I=(1/N^2)*(sin(N*((pi/4)*cos(th)+(pi/4)*t(m))) ... following script M-file.N=720;z=exp(j*2*pi*[1:N]./N);plot(z)axis squareIn-Class ExercisesPb. 6.20 Using the exponential form of the n-roots of unity, and the expres-sion for the sum of a ... the first-order differential equation:(6 .54 )Solution: We guess that the particular solution of this ODE is a sinusoidal ofthe form:(6 .55 )Our task now is to find Bc and Bsthat would force...