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LabExamSolutions

# LabExamSolutions - Lab Test Fall 2007 I Complex numbers(25...

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Lab Test Fall 2007 I. Complex numbers(25 Points) 1. Let /9 2.75 j z e p - = and 1.23 3.62 w j = - . Use Matlab to compute 9002.5 2 4.01 j z w e z - + in both Cartesian and exponential formats. l MATLAB program instructions: (4 points) z=2.75*exp(-j*pi/9); w=1.23-j*3.62; y=abs(exp(-j*9002.5))*(4.01*z'+w)/z^2 abs(y) angle(y) l Cartesian format: (2 points) y = 1.1614 + 1.0007i l Exponential format:(2 points) y = 1.5330*exp(0.7112*j) 2. Solve 4 4 6 z j = - (5 Points) l Solutions for z: roots([1 0 0 0 -(4-6j)]) ans = -1.5895 + 0.3986i -0.3986 - 1.5895i 0.3986 + 1.5895i 1.5895 - 0.3986i 3. Plot the magnitude and phase of the function 2 /50 1 ( ) cos( /1000) 1 0.9 jw H w w e = + for w in the range [0,200]. Sketch the plots. (6 Points) l Matlab instructions: w=[0:0.1:200]; H=abs(cos(w.^2/1000))./(1+0.9*exp(j*w/50)); subplot(2,1,1) plot(w,abs(H));grid on xlabel('Frequency'); ylabel('Magniture'); subplot(2,1,2) plot(w,angle(H));grid on xlabel('Frequency');

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ylabel('Phase'); l Figure: 4. Use the compass command to plot the roots of the equation 6 241 z = (6 Points) l Matlab instructions: z=roots([1 0 0 0 0 0 -241]) compass(z) l Roots: z = -2.4946 -1.2473 + 2.1604i -1.2473 - 2.1604i 1.2473 + 2.1604i 1.2473 - 2.1604i 2.4946
II. Matrix Operation (25 points) Consider the following matrices: 1 2 3 2 5 4 3 6 1 A - ° ± ² ³ = - ² ³

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LabExamSolutions - Lab Test Fall 2007 I Complex numbers(25...

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