Unformatted text preview: EEL 3105 Fall 2011 Homework 3 For grading and credit: 1. Suppose G ( s) 2s 3 s 2s 4s 2 2s 1
4 3 Use MATLAB to find the roots of the denominator. Then compute the partial fraction expansion for G(s). 2. Suppose G ( s) as b ( s 1)( s 2)( s 3) Roots of the denominator are called poles of G(s) while the roots of the numerator are called zeros of G(s). [A pole of G(s) corresponds to a value of s where G(s) becomes infinity; a zero corresponds to a value of s for which G(s) equals 0.] Suppose the residue corresponding to the pole at ‐1 is 1 and to the pole at ‐2 is 3. Find values of a and b. What is the residue corresponding to the pole at ‐3? What is the zero of G(s)? 3. Consider two phasors x(t ) 2e j (120 t /4)
y (t ) 3e j (120 t /3) Suppose we add the two signals x(t) and y(t), let z(t)=x(t)+y(t). Find a phasor representation of z(t). What is its frequency? What are its magnitude and phase? Provide a graphical depiction of this addition operation in the complex plane. [For your own understanding, connect this to vector addition in the 2 dimensional plane.] 4. Let z1 and z2 be two unknown complex numbers. Suppose we are told that z1 e j
z2 z1 z2 r 2 Assume r > 0. Determine z1 and z2 in terms of r and . ...
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