# ps3 - ECE 351 Systems I OSU Winter 2009 Feb 2 2009 Due Feb...

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Feb. 2, 2009 OSU, Winter 2009 Due: Feb. 11, 2009 Problem Set 3 Problem 1 Problem 2 Let x ( t ) be given by x ( t ) = 1 0 t < 1 - 1 1 < t 6 2 0 else . Find the zero state response, y ( t ), for an impulse response h ( t ) = x (2 - t ). x(t) t 1 1 -1 0 2 (In practice, this example is the matched ±lter for the communications pulse known as split- phase or “Manchester code” signaling. The pulse x ( t ) represents the symbol 1 in the 0/1 binary signaling.) Problem 3 (a) A signal x ( t ) has the two-sided line spectrum shown. Write the equation for x ( t ) as a sum of cosines. Is the signal periodic? If so, what is the period? Why do “negative” frequencies appear in the spectrum? 5 5 5 5 f (Hz) -950 -1050 0 950 1050 45 45 -45 -45 (b) Consider the 500 Hz emergency broadcast test tone played on the AM radio station 580 kHz: x ( t ) = { 1 + 5 cos(2 π 500 t + π/ 4) } cos(2 π 580000 t ) . 1

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ps3 - ECE 351 Systems I OSU Winter 2009 Feb 2 2009 Due Feb...

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