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Unformatted text preview: v .\, The Cooper lJnion Department of Electrical & Computer Engineering ECE111 Signal Processing & Systems Analysis Exam I February 24, 2005 Time: 90 min. Closed book, closed notes. No calculators, N o t e : c o s A c o s B : , l c o s ( , 4 + A ) +  c o s ( A  A ) . 1. f10 pts.] The impedance of a circuit at 1Mffz is Z = 4 j3O. In this problem, given the appropdate units with all answers. (a) Determino th" r"sistance, reactance, admittance, conductance, susceptance. Also provide the standard letter (e.g., Z for irnpedance) used for all of these quantities. (b) Is the impedance equivalent to a resistor in seies with an inductor or capacitor? (c) Find the value of the inductance or capacitance leave the answer as an explicit numerical expression (i.e., ready to be plugged into a calculator, no symbols). 2. 16 pts.] Express the following in the form Acos (1011 d) bywingphasorc, specillcally complex 0, thmetic not trigonomet c identities, and not phasor diagrams: 3 cos (10?rl + ?r/4) + \cos(t,rtr12) 'JZ 3. f9 pts.l A chi.rp signal is given by: t(t): Acos (2r J.t + dt+ Bt') (a) Find the instantaneou,s frequency j"", (l). (b) The input voltage to a VCO rl,hich generates this chirp signal must be: 1. a step function; 2. a ramp function (grows linearly with time); 3. a quadratic function (grows  i2). (c) Assume o, B and the tine span we axe examining are small enough that the banci widthof r(t) is srnall compared with l" (o<< l",P<<f.,and j""1(t) l"l << /. for the timespan of interest). Suppose e (l) is mixed (multiplied) with another chirp given by: b (t) : B cos (2r f.t  ci  A*) and the result is iowpass flltered to reject terms near /" and above. That is: y (t) : [z (t) .u (t)]*:"". ."". .,  ,_*, i. Show that y(l) has the lorllr 1lcos(P(l)), i.e., its em,elope is constant. Find K and the instantaneous frequency of g (t). s I 4. [10 pts.] A signal c (t) is transmitted tbtou'gh a multipath Jad'r'ng channel, testittng in a received signal g (t) given byr Y (t) = aP lt  rr) + a2r lt 't2) where or, (1,2 axe constant attenuatiorN (positive real values) and 7r, r, axe f.xed delays' For example, the first term may be a lineofsight (LOS) path' which is a direct path from transmitter to receivet, and the second term may repreient a reflected path lf the input signal has a baseband equivalent rse (l) and ca.rrier frequency f., find the baseba.nd representation of g (i), yes (t). Specifically, show that: ltee ft) : AxsB (t  11) + A2t BB (t  12) where .4t are complex valued but do not depend on t (they may depend on 7i, oi, f", but not i). Thus, the baseband model is similar to the bandpass model, except that the attenuation factors become complex valued....
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This note was uploaded on 02/27/2012 for the course CHEMISTRY/ CH/ECE/PH/ taught by Professor Faculty during the Spring '08 term at Cooper Union.
 Spring '08
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